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>< Q z Mathematical Operations ~ ~ ~ < A.l EXPONENTIAL NOTATION The numbers used in chemistry are often either extremely large or extremely small. Such numbers are conveniently expressed in the form N 10n X where N is a number between 1 and 10, and n is the exponent. Some examples of this exponential notation, which is also called scientific notation, follow. . 1,200,000 is 1.2 X 106 (read "one point two times ten to the sixth power") 0.000604 is 6.04 X 10- 4 (read "six point zero four times ten to the negative fourth power") A positive exponent, as in the first example, tells us how many times a number must be multiplied by 10 to give the long form of the number: 1.2 X 106 = 1.2 X 10 X 10 X 10 10 X X 10 X 10 (six tens) = 1,200,000 It is also convenient to think of the positive exponent as the number of places the decimal point must be moved to the left to obtain a number greater than 1 and less than 10: If we begin with 3450 and move the decimal point three places to the left, we end up with 3.45 X 103 . In a related fashion, a negative exponent tells us how many times we must divide a num~er by 10 to give the long form of the number. 6.04 X -4 - 10 - 10 X 6.04 X 10 10 X 10 - 0.000604 It is convenient to think of the negative exponent as the number of places the decimal point must be moved to the right to obtain a number greater than 1 but less than 10: If we begin with 0.0048 and move the decimal point three places to the right, we end up with 4.8 X 10- 3 . In the system of exponential notation, with each shift of the decimal point one place to the right, the exponent decreases by 1: 4.8 X 10:::-3 = 48 X 10- 4 Similarly, with each shift of the decimal point one place to the left, the exponent increases by 1: 4.8 X 10- 3 = 0.48 X 10- 2 Many scientific calculators have a key labeled EXP or EE, which is used to enter numbers in exponential notation. To enter the number 5.8 X 103 on such a calculator, the key sequence is ~ D [Ill EXP I(or [ill) [II On some calculators the display will show 5.8, then a space, followed by 03, the exponent. On other calculators, a small10 is shown with an exponent 3. 1104 A.1 To enter a negative exponent, use the key labeled +/-. For example, to enter the number 8.6 X 10- 5, the key sequence is [II D 01 EXP II +/-I~ When entering a number in exponential notation, do not key in the 10 the EXP or EE button. if you use In working with exponents, it is important to recall that 10° = 1. The following rules are useful for carrying exponents through calculations. 1. Addition and Subtraction In order to add or subtract numbers expressed in exponential notation, the powers of 10 must be the same. (5.22 X 104) + (3.21 102) = (522 X X 102) + (3.21 X 102) = 525 X 102 (3 significant figures) = 5.25 (6.25 X 10- 2) - (5.77 X 104 X 10-3) = (6.25 X 10- 2) - (0.577 X 10- 2) = 5.67 X 10- 2 (3 significant figures) When you use a calculator to add or subtract, you need not be concerned with having numbers with the same exponents, because the calculator automatically takes care of this matter. 2. Multiplication and Division When numbers expressed in exponential notation are multiplied, the exponents are added; when numbers expressed in exponential notation are divided, the exponent of the denominator is subtracted from the e~ponent of the numerator. (5.4 X 102)(2.1 X 103) = (5.4)(2.1) = 11 X 105 = 1.1 (1.2 X 105)(3.22 X X 106 10- 3) = (1.2)(3.22) 3.2 X 105 3.2 --- = 6.5 X 102 6.5 X 5 2 X 10 - X 10 - - 7 5.7 5.7 X 10 ---- = 8.5 8.5 X 10- 2 3. 102 + 3 X 105 +( - 3) = 3.9 = 0.49 7 ( 2) X = 0.67 3 X 102 10 = 4.9 X 9 X 10 = 6.7 10 X 2 8 10 Powers and Roots When numbers expressed in exponential notation are raised to a power, the exponents are multiplied by the power. When the roots of numbers expressed in exponential notation are taken, the exponents are divided by the root. (1.2 X 105 ) 3 = (1.2) 3 = 1.7 X X 105 X 3 1015 V'2.5 X 106 = \o/2.5 X 106/ 3 = 1.3 X 102 Scientific calculators usually have keys labeled x2 and Vx for sq{J.aring and taking the square root of a number, respectively. To take higher powers or roots, many calculators have yx and ~ (or INV yx) keys. For example, to perform the operation \o/'7.5 X 10- 4 on such a calculator, you would key in 7.5 X 10-4, press the ~key (or the INV and then the~ keys), enter the root, 3, and finally press =.The result is 9.1 X 10-2 . Exponential Notation 1105 1106 APPENDIX A Mathematical Operations SAMPLE EXERCISE 1 I Using Exponential Notation Perform each of the following operations, using your calculator where possible: (a) Write the number 0.0054 in standard exponential notation (b) (5.0 X 10- 2) + (4.7 X 10- 3) (c) (5.98 X 1012)(2.77 X 10- 5) (d) 'V'L75 X 10- 12 SOLUTION (a) Because we move the decimal point three places to the right to convert 0.0054 to 5.4, the exponent is -3: 5.4 X 10- 3 Scientific calculators are generally able to convert numbers to exponential notation using one or two keystrokes. Consult your instruction manual to see how this operation is accomplished on your calculator. (b) To add these numbers longhand, we must convert them to the same exponent. (5.0 X 10- 2) + (0.47 X 10- 2) = (5.0 + 0.47) X 10- 2 = 5.5 X 10- 2 (Note that the result has only two significant figures.) To perform this operation on a calculator, we enter the first number, strike the + key, then enter the second number and strike the = key. (c) Performing this operation longhand, we have (5.98 X 2.77) X 1012 - 5 = 16.6 X 10 7 = 1.66 X 108 On a scientific calculator, we enter 5.98 X 1012, press the X key, enter 2.77 X 10- 5, and press the = key. (d) To perform this operation on a calculator, we enter the number, press the Vy key (or the INV and y"r keys), enter 4, and press the = key. The result is 1.15 X 10- 3 . PRACTICE EXERCISE Perform the following operations: (a) Write 67,000 in exponential notation, showing two significant figures (b) (3.378 X 10- 3) - (4.97 X 10- 5 ) (c) (1.84 X 1015 )(7.45 X 10- 2) (d) (6.67 X 10- 8) 3 Answers: (a) 6.7 X 104, (b) 3.328 X 10- 3, (c) 2.47 X 1016, (d) 2.97 X 10- 22 A.2 LOGARITHMS Common Logarithms The common, or base-10, logarithm (abbreviated log) of any number is the power to which 10 must be raised to equal the number. For example, the common logarithm of 1000 (written log 1000) is 3 because raising 10 to the third power gives 1000. 103 = 1000, therefore, log 1000 = 3 Further examples are log 105 = 5 log 1 = 0 log 10- 2 = (Remember that 10° = 1) -2 In these examples the common logarithm can be obtained by inspection. However, it is not possible to obtain the logarithm of a number such as 31.25 by inspection. The logarithm of 31.25 is the number x that satisfies the following relationship: lOx = 31.25 A.2 Most electronic calculators have a key labeled LOG that can be used to obtain logarithms. For example, on many calculators we obtain the value of log 31.25 by entering 31.25 and pressing the LOG key. We obtain the following result: log 31.25 = 1.4949 Notice that 31.25 is greater than 10 (10 1) and less than 100 (10 2). The value for log 31.25 is accordingly between log 10 and log 100, that is, between 1 and 2. Significant Figures and Common Logarithms For the common logarithm of a measured quantity, the number of digits after the decimal point equals the number of significant figures in the original number. For example, if 23.5 is a measured quantity (three significant figures), then log 23.5 = 1.371 (three significant figures after the decimal point). Antilogarithms The process of determining the number that corresponds to a certain logarithm is known as obtaining an antilogarithm. It is the reverse of taking a logarithm. For example, we saw above that log 23.5 = 1.371. This means that the antilogarithm of 1.371 equals 23.5. log 23.5 = 1.371 antilog 1.371 = 23.5 The process of taking the antilog of a number is the same as raising 10 to a power equal to that number. antilog 1.371 = 101.371 = 23.5 Many calculators have a key labeled lOx that allows you to obtain antilogs directly. On others, it will be necessary to press a key labeled INV (for inverse), followed by the LOG key. Natural Logarithms Logarithms based on the number e are called natural, or base e,logarithms (abbreviated ln). The natural log of a number is the power to which e (which has the value 2.71828 ... ) must be raised to equal the number. For example, the naturallog of 10 equals 2.303. e2·303 = 10, therefore ln 10 = 2.303 Your calculator probably has a key labeled LN that allows you to obtain natural logarithms. For example, to obtain the natural log of 46.8, you enter 46.8 and press the LN key. ln 46.8 = 3.846 The natural antilog of a number is e raised to a power equal to that number. If your calculator can calculate natural logs, it will also be able to calculate natural antilogs. On some calculators there is a key labeled ~ that allows you to calculate natural antilogs directly; on others, it will be necessary to first press the INV key followed by the LN key. For example, the natural antilog of 1.679 is given by Natural antilog 1.679 = el. 679 = 5.36 The relation between common and natural logarithms is as follows: ln a = 2.303 log a ~ Notice that the factor relating the two, 2.303, is the natural log of 10, which we calculated above. Logarithms 1107 1108 APPENDIX A Mathematical Operations Mathematical Operations Using Logarithms Because logarithms are exponents, mathematical operations involving logarithms follow the rules for the use of exponents. For example, the product of za and zb (where z is any number) is given by 2 a. 2 b = 2 (a+b) Similarly, the logarithm (either common or natural) of a product equals the sum of the logs of the individual numbers. log ab = log a + log b ln ab = ln a + ln b For the log of a quotient, log(a/ b) = ln(a/ b) = ln a - ln b log a - log b Using the properties of exponents, we can also derive the rules for the logarithm of a number raised to a certain power. lnan = n lna log an = n log a 1 log a 1n = (1/n) log a ln alin = (1/ n) ln a pH Problems One of the most frequent uses for common logarithms in general chemistry is in working pH problems. The pH is defined as -log[H+], where [H+] is the hydrogen ion concentration of a solution (Section 16.4). The following sample exercise illustrates this application. - SAMPLE EXERCISE 2 I Using Logarithms (a) What is the pH of a solution whose hydrogen ion concentration is 0.015 M? (b) If the pH of a solution is 3.80, what is its hydrogen ion concentration? SOLUTION 1. We are given the value of [H+]. We use the LOG key of our calculator to calculate the value of log[H+]. The pH is obtained by changing the sign of the value obtained. (Be sure to change the sign after taking the logarithm.) [H+] = 0.015 = - 1.82 (2 significant figures) pH = - (- 1.82) = 1.82 log[H+] 2. To obtain the hydrogen ion concentration when given the pH, we must take the antilog of -pH. pH = - log[H+] = 3.80 log[H+] = -3.80 [H+] = antilog( - 3.80) = 10- 3·80 = 1.6 - X 10- 4 M PRACTICE EXERCISE Perform the following operations: (a) log(2.5 X 10- 5), (b) ln 32.7, (c) antilog - 3.47, (d) e- 1.89. Answers: (a) -4.60, (b) 3.487, (c) 3.4 X 10- 4, (d) 1.5 X 10- 1 A.3 QUADRATIC EQUATIONS An algebraic equation of the form ax 2 + bx + c = 0 is called a quadratic equation. The two solutions to such an equation are given by the quadratic formula: x= -b ± Vb 2 2a 4ac A.4 Graphs 1109 SAMPLE EXERCISE 3 I Using the Quadratic Formula Find the values of x that satisfy the equation 2x 2 + 4x = 1. - SOLUTION To solve the given equation for x, we must first put it in the form ax 2 + bx + c = 0 and then use the quadratic formula. If 2x 2 + 4x = 1 then 2x 2 + 4x - 1 = 0 Using the quadratic formula, where a = 2, b = 4, and c = -1, we have X -4 ± v(4)(4) - 4(2)( -1) 2(2) = -4 :±: V16+8 ----- = 4 - 4 :±: V24 -4 :±: 4.899 = ---4 4 The two solutions are x = 0 ·~ 9 = 0.225 and x = - 8~899 = -2.225 Often in chemical problems the negative solution has no physical meaning, and only the positive answer is used. A.4 GRAPHS TABLE A-1 • Interrelation between Often the clearest way to represent the interrelationship between two variables Pressure and Temperature is to graph them. Usually, the variable that is being experimentally varied, Temperature Pressure called the independent variable, is shown along the horizontal axis (x-axis). (oC) (atm) The variable that responds to the change in the independent variable, called the dependent variable, is then shown along the vertical axis (y-axis). For example, 20.0 0.120 consider an experiment in which we vary the temperature of an enclosed gas 30.0 0.124 and measure its pressure. The independent variable is temperature, and the 40.0 0.128 0.132 dependent variable is pressure. The data shown in Table A-1 .,.. can be obtained 50.0 by means of this experiment. These data are shown graphically in Figure A.1 ... . The relationship between temperature 0.140 r - - - - - - : - - - - . , . . - - - - - - - , - - - - - - - , and pressure is linear. The equation for any straight-line graph has the form y = mx + b where m is the slope of the line and b is the intercept with they-axis. In the case of Figure 1, we could say that therelationship between temperature and pressure takes the form P = mT + b 0.130 i ~ Q) gs~ 0.120 Q) &:: / / where P is pressure in atm and T is temperature in °C. As shown in Figure 1, the slope is 4.10 x 10- 4 atm;oc, and the intercept-the point where the line crosses they-axis-is 0.112 atm. Therefore, the equation for the line is P = 4 atm) ( 4.10 X 10- oc T + 0.112 atm / / / 0.110 0 20.0 40.0 60.0 Temperature (°C) .A Figure A.l 80.0 1110 APPENDIX A Mathematical Operations A.5 STANDARD DEVIATION The standard deviation from the mean, s, is a common method from describing precision. We define the standard deviation as follows: N L(Xi- :X )2 s i= l = N -1 where N is the number of measurements, :X is the average (also called the mean), and Xi represents the individual measurements. Electronic calculators with built-in statistical functions can calculate s directly by inputting the individual measurements. A smaller value of s indicates a higher precision, meaning that the data is more closely clustered around the average. The standard deviation has a statistical significance. Thus, if a large number of measurements is made, 68% of the measured values is expected to be within one standard deviation of the average, assuming only random errors are associated with the measurements. • SAMPLE EXERCISE 4 I Calculating an Average and Standard Deviation The percent carbon in a sugar is measured four times: 42.01 %, 42.28%, 41.79%, and 42.25%. Calculate (a) the average and (b) the standard deviation for these measurements. SOLUTION (a) The average is found by adding the quantities and dividing by the number of measurements: x= 42.01 + 42.28 + 41.79 + 42.25 4 168.33 4 = - = 42.08 (b) The standard deviation is found using the equation above: N ~(xi- x )2 i= l s= N - 1 N Let's tabulate the data so the calculation of ~(xi - x? can be seen clearly. i= l Percent C Difference between Measurement and Average, (xi - :X) 42.01 42.28 41.79 42.25 42.01 42.28 41.79 42.25 - Square of Difference, (xi - :X) 2 (-0.07) 2 = 0.005 (0.20) 2 = 0.040 ( - 0.29) 2 = 0.084 (0.17) 2 = 0.029 42.08 = - 0.07 42.08 = 0.20 42.08 = -0.29 42.08 = 0.17 The sum of the quantities in the last column is N ~(xi - x )2 = 0.005 + 0.040 + 0.084 + 0.029 = 0.16 i= l Thus, the standard deviation is s= N 2 ~(xi:X) = ~.16 = z= l N- 1 4- 1 N 0.16 3 = VQ.053 = 0.23 Based on these measurements, it would be appropriate to represent the measured percent carbon as 42.08 ± 0.23. >< a z Properties ofWater ~ P-. P-. ~ 0.99987 g/ mL at 0 oc Density: 1.00000 g/mL at 4 oc 0.99707 g/ mL at 25 oc 0.95838 g/ mL at 100 °C Heat of fusion: 6.008 kJ/mol at 0 oc Heat of vaporization: 44.94 kJ/mol at 0 oc 44.02 kJ/ mol at 25 oc 40.67 kJ/mol at 100 oc Ion-product constant, Kw: Specific heat: 1.14 X 10- 15 at 0 oc 1.01 X 10- 14 at 25 °C 5.47 X 10- 14 at 50 °C Ice (at - 3 °C) 2.092 J/ g-K Water (at 14.5 °C) 4.184 J/ g-K Steam (at 100 °C) 1.841 J/ g-K Vapor Pressure (torr) T(°C) p T(°C) p T(°C) p T(°C) p 0 5 10 12 14 16 17 18 19 20 4.58 6.54 9.21 10.52 11.99 13.63 14.53 15.48 16.48 17.54 21 22 23 24 25 26 27 28 29 30 18.65 19.83 21.07 22.38 23.76 25.21 26.74 28.35 30.04 31.82 35 40 45 50 55 60 65 70 80 90 42.2 55.3 71.9 92.5 118.0 149.4 187.5 233.7 355.1 525.8 92 94 96 98 100 102 104 106 108 110 567.0 610.9 657.6 707.3 760.0 815.9 875.1 937.9 1004.4 1074.6 1111 Thermodynamic Quantities for Selected Substances at 298.15 K (25 °C) >< a z t:.I.l ~ ~ ~ so 11HJ (kJ/mol) 11GJ (kJ/mol) 0 -705.6 -1669.8 0 -630.0 -1576.5 28.32 109.3 51.00 BaC03(s) BaO(s) 0 -1216.3 -553.5 0 -1137.6 -525.1 63.2 112.1 70.42 Beryllium Be(s) BeO(s) Be(OHh(s) 0 -608.4 -905.8 0 -579.1 -817.9 9.44 13.77 50.21 111.8 -120.9 30.71 0 -36.23 82.38 -102.8 3.14 0 -53.22 174.9 80.71 245.3 152.3 198.49 145.5 0 -1128.76 -748.1 -1167.3 -604.17 -898.5 -1321.8 154.8 41.4 92.88 104.6 68.87 39.75 83.4 106.7 Substance Aluminum Al(s) A1Cl3(s) Al203(s) Barium Ba(s) Bromine Br(g) Br-(aq) Br2(g) Br2(Z) HBr(g) Calcium Ca(g) Ca(s) CaC03(s, calcite) CaCl2(s) CaF2(s) CaO(s) Ca(OHh(s) CaS04(s) Carbon C(g) C(s, diamond) C(s, graphite) CCl4(g) CCl4(l) CF4(g) CH4(g) C2H2(g) 1112 179.3 0 -1207.1 -795.8 -1219.6 -635.5 -986.2 -1434.0 718.4 1.88 0 -106.7 -139.3 -679.9 -74.8 226.77 672.9 2.84 0 -64.0 -68.6 -635.1 -50.8 209.2 (Jjmol-K) 158.0 2.43 5.69 309.4 214.4 262.3 186.3 200.8 Substance C2H4(g) C2H6(g) C3Hs(g) C4H10(g) C4H10(Z) C6H6(g) C6H6(1) CH30H(g) CH30H(l) C 2H 50H(g) C2H50H(Z) C6H1206(s) CO(g) C02 (g) CH3COOH(Z) Cesium Cs(g) Cs(l) Cs(s) CsCl(s) Chlorine Cl(g) Cl- (aq) Cl2(g) HCl(aq) HCl(g) Chromium Cr(g) Cr(s) 11HJ (kJ/mol) 11GJ (kJ/mol) so (J/mol-K) 52.30 -84.68 -103.85 -124.73 -147.6 82.9 49.0 -201.2 -238.6 -235.1 -277.7 -1273.02 -110.5 -393.5 -487.0 68.11 -32.89 -23.47 -15.71 -15.0 129.7 124.5 - 161.9 -166.23 -168.5 -174.76 -910.4 -137.2 -394.4 -392.4 219.4 229.5 269.9 310.0 231.0 269.2 172.8 237.6 126.8 282.7 160.7 212.1 197.9 213.6 159.8 76.50 2.09 0 -442.8 49.53 0.03 0 -414.4 175.6 92.07 85.15 101.2 121.7 -167.2 0 -167.2 -92.30 105.7 -131.2 0 -131.2 -95.27 165.2 56.5 222.96 56.5 186.69 397.5 0 -1139.7 352.6 0 -1058.1 174.2 23.6 81.2 Cobalt Co (g) Co(s) 439 0 393 0 179 28.4 Copper Cu(g) Cu(s) 338.4 0 298.6 0 166.3 33.30 Cr203(s) i APPENDIX C Thermodynamic Quantities for Selected Substances at 298.15 K (25 °C) so 1113 so !1HJ (kJ/mol) !1GJ (kJ/mol) (J/mol-K) -601.8 -924.7 -569.6 -833.7 26.8 63.24 158.7 -13.8 202.7 173.51 Manganese Mn(g) Mn(s) MnO(s) Mn02(s) Mn04- (aq) 280.7 0 -385.2 -519.6 -541.4 238.5 0 -362.9 -464.8 -447.2 173.6 32.0 59.7 53.14 191.2 203.26 0 1517.0 0 114.60 0 108.9 130.58 Mercury Hg(g) Hg(Z) HgC12(s) Hg2Cl2(s) 60.83 0 -230.1 -264.9 31.76 0 -184.0 -210.5 174.89 77.40 144.5 192.5 106.60 -55.19 62.25 0 25.94 70.16 -51.57 19.37 0 1.30 180.66 111.3 260.57 116.73 206.3 Nickel Ni(g) Ni(s) NiC12(s) NiO(s) 429.7 0 -305.3 -239.7 384.5 0 -259.0 -211.7 182.1 29.9 97.65 37.99 415.5 0 -87.86 -47.69 -341.8 -400 -271.9 -822.16 -1117.1 -171.5 369.8 0 -84.93 -10.54 -302.3 -334 -255.2 -740.98 -1014.2 -160.1 180.5 27.15 113.4 293.3 117.9 142.3 60.75 89.96 146.4 52.92 0 -277.4 -699.1 -421.3 -451.9 -217.3 0 -260.7 -625.5 -246.9 -187.9 68.85 161 131.0 303.3 68.70 LiCl(s) 159.3 0 -278.5 685.7 -408.3 126.6 0 -273.4 648.5 -384.0 138.8 29.09 12.2 133.0 59.30 Magnesium Mg(g) Mg(s) MgC12(s) 147.1 0 -641.6 112.5 0 -592.1 148.6 32.51 89.6 Substance 11HJ (kJ/mol) !1GJ (kJ/mol) CuCl2(s) CuO(s) Cu20(s) -205.9 -156.1 -170.7 -161.7 -128.3 -147.9 108.1 42.59 92.36 80.0 -332.6 0 -268.61 61.9 -278.8 0 -270.70 217.94 0 1536.2 0 Fluorine F(g) F-(aq) F2(g) HF(g) Hydrogen H(g) H+(aq) H+(g) H2(g) Iodine I (g) 1- (aq) 12(g) l2(s) HI(g) Iron Fe(g) Fe(s) Fe 2+(aq) Fe 3+(aq) FeC12(s) FeCl3(s) FeO(s) Fe203(s) Fe304(s) FeS2(s) Lead Pb(s) PbBr2(s) PbC03(s) Pb(N03h(aq) Pb(N03h(s) PbO(s) Lithium Li(g) Li(s) u+(aq) Li+(g) (J/mol-K) Substance MgO(s) Mg(OHh(s) Nitrogen N(g) N2(g) NH3(aq) NH3(g) NH 4+(aq) N2H4(g) NH4CN(s) NH4Cl(s) NH4N03(s) NO(g) N02(g) N20(g) N204(g) NOCl(g) HN03(aq) HN03(g) Oxygen O(g) 02(g) 03(g) OH-(aq) H20(g) H20(l) H202(g) H202(g) Phosphorus P(g) P2(g) 472.7 0 -80.29 -46.19 -132.5 95.40 0.0 -314.4 -365.6 90.37 33.84 81.6 9.66 52.6 -206.6 -134.3 455.5 0 -26.50 -16.66 -79.31 159.4 153.3 191.50 111.3 192.5 113.4 238.5 -203.0 -184.0 86.71 51.84 103.59 98.28 66.3 -110.5 -73.94 94.6 151 210.62 240.45 220.0 304.3 264 146 266.4 247.5 0 142.3 -230.0 -241.82 -285.83 -136.10 -187.8 230.1 0 163.4 -157.3 -228.57 -237.13 -105.48 -120.4 161.0 205.0 237.6 -10.7 188.83 69.91 232.9 109.6 316.4 144.3 280.0 103.7 163.2 218.1 1114 Thermodynamic Quantities for Selected Substances at 298.15 K (25 oc) APPENDIX C Substance 1:1HJ (kJ/mol) Phosphorus (cont.) P4(g) P4(s, red) P 4(s, white) PCl3(g) PCl3(l) PF5 (g) PH3(g) P406(s) P 4010(s) POCl3(g) POCl3(l) H3P04(aq) 58.9 -17.46 0 -288.07 -319.6 -1594.4 ,5.4 -1640.1 -2940.1 -542.2 -597.0 -1288.3 Potassium K(g) K(s) KCl(s) KC103(s) KCl03(aq) KzC03(s) KN0 3(s) K20(s) K0 2 (s) KzOz(s) KOH(s) KOH(aq) Rubidium Rb(g) Rb(s) RbCl(s) RbCl03(s) 1:1GJ (kJ/mol) so (Jfmol-K) 24.4 -12.03 0 -269.6 - 272.4 -1520.7 13.4 -2675.2 - 502.5 -520.9 -1142.6 280 22.85 41.08 311.7 217 300.8 210.2 228.9 325 222 158.2 89.99 0 -435.9 -391.2 -349.5 -1150.18 -492.70 -363.2 -284.5 -495.8 -424.7 -482.4 61.17 0 -408.3 -289.9 -284.9 - 1064.58 -393.13 -322.1 -240.6 - 429.8 - 378.9 -440.5 160.2 64.67 82.7 143.0 265.7 155.44 132.9 94.14 122.5 113.0 78.91 91.6 85.8 0 -430.5 -392.4 55.8 0 -412.0 -292.0 170.0 76.78 92 152 Scandium Sc(g) Sc(s) 377.8 0 336.1 0 174.7 34.6 Selenium HzSe(g) 29.7 15.9 219.0 Silicon Si(g) Si(s) SiC(s) SiCl4(l) Si02 (s, quartz) Silver Ag(s) Ag+(aq) 368.2 0 -73.22 -640.1 -910.9 ~ 323.9 0 -70.85 -572.8 -856.5 167.8 18.7 16.61 239.3 41.84 ' 0 105.90 0 77.11 42.55 73.93 Substance AgCl(s) Ag 20(s) AgN03(s) Sodium Na(g) Na(s) Na+(aq) Na+(g) NaBr(aq) NaBr(s) NazC03(s) · NaCl(aq) NaCl(g) NaCl(s) NaHC03(s) NaN0 3 (aq) NaN03(s) NaOH(aq) NaOH(s) Strontium SrO(s) Sr(g) Sulfur S(s, rhombic) 1:1HJ (kJ/mol) 1:1GJ (kJ/mol) -127.0 -31.05 -124.4 -109.70 -11.20 -33.41 107.7 0 -240.1 609.3 -360.6 -361.4 -1130.9 -407.1 -181.4 -410.9 -947.7 -446.2 -467.9 -469.6 -425.6 77.3 0 -261.9 574.3 -364.7 -349.3 -1047.7 -393.0 -201.3 -384.0 -851.8 -372.4 -367.0 -419.2 -379.5 -592.0 164.4 561.9 110.0 so (J/mol-K) 96.11 121.3 140.9 153.7 51.45 59.0 148.0 141.00 86.82 136.0 115.5 229.8 72.33 102.1 207 116.5 49.8 64.46 54.9 164.6 0 102.3 -296.9 -395.2 -909.3 - 245.6 -20.17 -909.3 -814.0 0 49.7 -300.4 -370.4 -744.5 31.88 430.9 248.5 256.2 20.1 -33.01 -744.5 - 689.9 205.6 20.1 156.1 Titanium Ti(g) Ti(s) TiCl4(g) TiCl4(l) Ti02 (s) 468 0 -763.2 -804.2 -944.7 422 0 -726.8 -728.1 -889.4 180.3 30.76 354.9 221.9 50.29 Vanadium V(g) V(s) 514.2 0 453.1 0 Zinc Zn(g) Zn(s) ZnC12 (s) ZnO(s) 130.7 0 - 415.1 -348.0 95.2 0 -369.4 -318.2 Ss(g) SOz(g) S03(g) S04 2- (aq) SOC12 (l) HzS(g) HzS04(aq) HzS04(l) 182.2 28.9 160.9 41.63 111.5 43.9 >< a z Aqueous Equilibrium Constants ~ ~ ~ ~ TABLE D-1 • Dissociation Constants for Acids at 25 oc Name Formula Ka1 Acetic CH3COOH (or HC 2H302) H 3As04 H 3As03 1.8 X 5.6 X 5.1 X H2C6H606 C6H 5COOH (or HC7H50 2) 8.0 X 6.3 X H3B03 C3H7COOH (or HC4H702) 5.8 X 1.5 X 4.3 X Chloroacetic H2C03 CH2ClCOOH (or HC 2H 20 2Cl) Chlorous HC102 Citric HOOCC(OH)(CH2COOH)z (or H3C6H507) HCNO 7.4 X 3.5 X HCOOH (or HCH02) 1.8 X HN3 HCN 1.9 X 4.9 X 6.8 X 3.0 X 2.4 X Hydrogen selenate ion H202 HSe0 4- 10- 7 10- 12 2.2 X 10- 2 Hydrosulfuric H 2S 9.5 X Hypobromous HBrO 2.5 X 10- 8 10- 9 Hypochlorous HClO 3.0 X 10- 8 Hypoiodous Iodic HIO 2.3 X HI03 CH3CH(OH)COOH (or HC 3H 50 3) 1.7 X 10- 11 10- 1 1.4 X 10- 4 CH2(COOH)z (or H2C3H204) HN02 1.5 X Arsenic Arsenous Ascorbic Benzoic Boric Butanoic Carbonic Cyanic Formic Hydroazoic Hydrocyanic Hydrofluoric Hydrogen chromate ion Hydrogen peroxide Lactic Malonic Nitrous Oxalic Par aperiodic HF HCr04- (COOH)z (or H2C204) H 5I06 Ka2 Ka3 10- 5 10- 3 1.0 X 10-7 10- 10 10- 5 1.6 X 10-12 5.6 X 10- 11 1.7 X 10- 5 10- 5 10- 7 4.5 X 5.9 X 2.8 X 10- 4 10- 4 4.0 X 10- 7 10- 4 10- 5 10- 10 10- 4 1 X 10- 19 10- 6 10- 3 10- 4 2.0 X 10- 2 10- 2 6.4 X 5.3 X 10-5 10- 9 10- 3 10- 5 6.2 X 10- 8 4.2 X 10- 13 2.1 X 10- 7 C6H50H (or HC6H50) 1.3 Phosphoric H3P04 C2H5COOH (or HC3H502) 7.5 X 1.3 X H4P207 H 2Se03 3.0 X 4.4 X 2.3 X 10- 2 10- 3 5.3 X 10- 3 10- 9 Sulfuric H2S04 1.2 X 10- 2 Sulfurous H2S03 HOOC(CJ-lOH)zCOOH (or H2C 4H 40 6) Strong acid 1.7 X 10- 2 1.0 X 10- 3 6.4 X 4.6 X Tartaric 10- 12 1.4 X 10- 3 1.1 X 10- 2 Phenol Pyrophosphoric Selenous X 10- 5 10- 10 X 10- 10 Propionic 3.0 10- 8 10- 5 1115 1116 APPENDIX D Aqueous Equilibrium Constants TABlE D-2 • Dissociation Constants for Bases at 25 Name Formula Kb Ammonia NH3 C6H 5NH2 1.8 X 4.3 X (CH3hNH C 2H 5NH2 5.4 X 6.4 X H2NNH2 HONH2 1.3 X 1.1 X 10-6 10- 8 4.4 X 10-4 Pyridine CH3NH2 C5H 5N 1.7 X Trimethylamine (CH3)3N 6.4 X Aniline Dimethylamine Ethylamine Hydrazine Hydroxylamine Methylamine oc 10-5 10-10 10-4 10- 4 10-9 10-5 .......,. TABlE D-3 • Solubility-Product Constants for Compounds at 25 Name Formula Ksp 5.0 Barium chromate BaC03 BaCr04 X 10- 9 2.1 X Barium fluoride BaF2 1.7 X 10- 10 10- 6 Barium oxalate BaC204 1.6 X 10- 6 BaS04 1.1 X 10- 10 Cadmium carbonate CdC03 Cadmium hydroxide Cd(OHh Cadmium sulfide* CdS 1.8 x 10- 14 2.s x 10- 14 8 X 10- 28 Barium carbonate Barium sulfate Calcium carbonate (calcite) Calcium chromate Calcium fluoride CaC03 CaCr04 CaF2 4.5 X 10- 9 · 10- 4 oc Name Formula Ksp Lead(II) fluoride PbF2 3.6 X Lead(II) sulfate PbS04 PbS 6.3 X Lead(II) sulfide* Magnesium hydroxide Mg(OHh 1.8 X Magnesium carbonate MgC03 3.5 X Magnesium oxalate MgC204 8.6 X Manganese(II) carbonate MnC03 5.0 X Manganese(II) hydroxide 1.6 X Manganese(II) sulfide* Mn(OHh MnS Mercury(!) chloride Hg2Cl2 Mercury(!) iodide 1.3 X Nickel(II) hydroxide Ni(OHh NiS 6.0 X 3 10- 29 10- 5 2.0 X Calcium sulfate CaS04 2.4 X Chromium(III) hydroxide Cr(OHh 1.6 x 1o- 30 Cobalt(II) carbonate CoC03 1.0 X 10- 10 Cobalt(II) hydroxide Co(OHh 1.3 X Cobalt(II) sulfide* CoS 5 Copper(!) bromide CuBr 5.3 X X Nickel(II) sulfide* Silver bromate X AgBr03 AgBr 5.5 X 5.0 X 8.1 X 1.8 X Silver bromide 10- 9 Silver chloride Ag2C03 AgCl Silver chromate Ag 2Cr04 1.2 X Silver iodide Agl 8.3 X Silver sulfate Ag2S04 1.5 X Silver sulfide* 6 Strontium carbonate Ag2S SrC03 Tin(II) sulfide* SnS 1 Zinc carbonate ZnC03 1.0 X Copper(II) carbonate CuC03 2.3 Copper(II) hydroxide Cu(OHh 4.8 X Copper(II) sulfide* CuS 6 Iron(II) carbonate FeC03 Iron(II) hydroxide . Fe(OHh 2.1 7.9 Lanthanum fluoride Lanthanum iodate LaF3 La(I03h 10- 11 X 10- 16 . 2 X 10- 19 6.1 X 10- 12 Lead(II) carbonate PbC03 7.4 X Lead(II) chloride PbCl2 1.7 Lead(II) chromate PbCr04 2.8 10- 20 10- 37 X Silver carbonate X 9.3 X 10- 12 10- 17 10- 10 10-26 Zinc hydroxide Zn(OHh 3.0 X Zinc oxalate 2.7 X X 10- 13 Zinc sulfide* ZnC204 ZnS *For a solubility equilibrium of the type MS(s) + H 20(/) ~ M 2+(aq) + HS- (aq) + OH- (aq) 10- 12 10- 10 X X X 10- 5 10- 13 10- 5 10-51 10- 14 10- 5 2 10- 7 10- 16 10- 20 10- 15 10-22 X 10- 10 X 10- 13 10-53 NiC03 Mercury(II) sulfide* Ca3(P04h 10- 5 10- 10 Nickel(II) carbonate 10- 6 Calcium phosphate 10- 11 10- 8 Hg2I2 HgS 3.9 X X 10-28 10- 18 1.1 x 1o- 28 2 X 10- 53 X 10- 11 6.5 2 X X X Ca(OHh 3 1.2 7.1 Calcium hydroxide ' 10- 8 10- 7 10- 10 10-16 10- 8 10-25 Standard Reduction Potentials at 25 °C ><: a z ~ A.. A.. ~ Half-Reaction E 0 (V) Half-Reaction E 0 (V) A g+(aq) + e- ~ Ag(s) +0.799 +0.095 +0.222 -0.31 +0.446 -0.151 +0.01 -1.66 2 H 20(Z) + 2 e- ~ H 2_(g) + 2 OH- (aq) H02- (aq) + H 20(l) + 2 e- ~ 3 OH- (aq) H 20 2(aq) + 2 H +(aq) + 2 e- ~ 2 H 20(l) Hg22+(aq) + 2 e- ~ 2 Hg(l) 2 Hg 2+(aq) + 2 e- ~ Hgl+(aq) Hg 2+(aq) + 2 e- ~ Hg(l) 12(-s) + 2 e- ~ 2 1- (aq) 210 3- (aq) + 12 H +(aq) + 10 e- ~ l2(s) + 6 H 20(Z) K +(aq) + e- ~ K(s) Li+(aq) + e- ~ Li(s) Mg 2+(aq) + 2 e- ~ Mg(s) Mn2+(aq) + 2 e- ~ Mn(s) Mn0 2(s) + 4 H +(aq) + 2 e- ~ Mn2+(aq) + 2 H 20(l) Mn04- (aq) + 8 H +(aq) + 5 e- ~ Mn2+(aq) + 4 H20(l) Mn04- (aq) + 2 H20(Z) + 3 e- ~ Mn0 2(s) + 4 OH- (aq) HN02(aq) + H +(aq) + e- ~ NO(g) + H 20(l) N2(g) + 4 H20(l) + 4 e- ~ 4 OH- (aq) + N 2H 4(aq) N2(g) + 5 H +(aq) + 4 e- ~ N2Hs+(aq) N03- (aq) + 4 H +(aq) + 3 e- ~ NO(g) + 2 H20(l) N-a+(aq) + e- ~ Na(s) Ni2+(aq) + 2 e- ~ Ni(s) 0 2(g) + 4 H +(aq) + 4 e- ~ 2 H2 0(~) 02(g) + 2 H20(Z) + -4 e- ~ 4 OH- (aq) 02(g) + 2 H +(aq) + 2 e- ~ H 20 2(aq) 0 3(g) + 2 H +(aq) + 2 e- ~ 0 2(g) + H 20(Z) Pb 2+(aq) + 2 e- ~ Pb(s) Pb0 2(s) + HS0 4- (aq) + 3 H +(aq) + 2 e- ~ PbS0 4(s) + 2 H20(l) PbS0 4(s) + H +(aq) + 2 e- ~ Pb(s) + HS0 4- (aq) PtC142- (aq) + 2 e- ~ Pt(s) + 4 Cl- (aq) S(s) + 2 H +(aq) + 2 e- ~ H2S(g) · H 2S03(aq) + 4 H +(aq) + 4 e- ~ S(s) + 3 H 20(l) HS0 4- (aq) + 3 H +(aq) + 2 e- ~ H2S03(aq) + H 20(Z) Sn2+(aq) + 2 e- ~ Sn(s) Sn4+(aq) + 2 e- ~ Sn2+(aq) V02+(aq) + 2 H +(aq) + e- ~ V0 2+(aq) + H 20(Z) Zn2+(aq) + 2 e- ~ Zn(s) -0.83 +0.88 + 1.776 +0.789 +0.920 +0.854 +0.536 AgBr(s) + e- ~ Ag(s) + Br- (aq) AgCl(s) + e- ~ Ag(s) + Cl- (aq) Ag(CNh - (aq) + e- ~ Ag(s) + 2 CN- (aq) Ag2Cr04(s) + 2 e- ~ 2 Ag(s) + Cr042- (aq) Agl(s) + e- ~ Ag(s) + 1- (aq) Ag(S203h 3- (aq) + e- ~ Ag(s) + 2 S2032- (aq) Al3+(aq) + 3 e- ~ Al(s) H 3As0 4(aq) + 2 H +(aq) + 2 e- ~ H 3As03(aq) + H20(Z) Ba 2+(aq) + 2 e~ ~ Ba(s) BiO+(aq) + 2 H+(aq) + 3 e- ~ Bi(s) + H 20(Z) Br2 (Z) + 2 e~ ~ 2 Br- (aq) 2 Br03- (aq) + 12 H +(aq) + 10 e- ~ Br2(l) + 6 H20(l) 2 C02(g) + 2 H +(aq) + 2 e- ~ H2C204(aq) ea2+(aq) + 2 e- ~ Ca(s) ""'· Cd 2+(alJ) + 2 e- ~ Cd(s) Ce4 ~(aq) + e- ~ Ce3+(aq) Cl2(g) + 2 e- ~ 2 Cl- (aq) 2 HClO(aq) + 2 H +(aq) + 2 e- ~ Cl2(g) + 2 H20(l) ClO- (aq) + H 20(l) + 2 e- ~ Cl- (aq) + 2 OH- (aq) 2 Cl0 3- (aq) + 12 H +(aq) + 10 e- ~ Cl2(g) + 6 H20(l) Co 2+(aq) + 2 e- ~ Co(s) Co 3+(aq) + e- ~ Co 2+(aq) Cr 3+(aq) + 3 e- ~ Cr(s) Cr 3+(aq) + e- ~ Cr2+(aq) Cr0 7 2- (aq) + 1'21: H +(aq) + 6 e- ~ 2 cr-?7 (aq) + 7 B 20(l) Cr0 42- (aq) + 4 H20(l) + 3 e- ~ Cr(OH)3(s) + 5 OH- (aq) Cu2+(aq) + 2 e- ~ Cu(s) Cu 2+(aq) + e- ~ Cu+(aq) Cu+(aq) + e- ~ Cu(s) Cul(s) + e- ~ Cu(s) + 1- (aq) F2(g) + 2 e- ~ 2 F- (aq) Fe2+(aq) + 2 e- ~ Fe(s) Fe3+(aq) + e- ~ Fe 2+(aq) Fe(CN)63- (aq) + e- ~ Fe(CN) 64- (aq) 2 H +-(aq) + 2 e- ~ H 2(g) ,...;. +0.559 -2.90 +0.32 +1.065 +1.52 -0.49 ' -2.87 -0.403 +1.61 +1.359 +1.63 +0.89 +1.47 -0.277 +1.842 -0.74 -0.41 +1.33 -0.13 +0.337 +0.153 +0.521 -0.185 +2.87 -0.440 +0.771 +0.36 0.000 + 1.195 - 2.925 -3.05 -2.37 -1.18 +1.23 +1.51 +0.59 +1.00 -1.16 -0.23 +0.96 -2.7 -0.28 +1.23] +0.40 +0.68 +2.07 -0.126 +1.685 -0.356 +0.73 +0.141 +0.45 +0.17 - 0.136 +0.154 +1.00 -0.763 1117 ·. ,,. >< a z AP Exam Practice Problems ~ ~ ~ -< UNIT I. ATOMS, MOLECULES, IONS, AND STOICHIOMETRY Multiple-Choice Questions 1.1 What volume will contain 5.0 mol of aluminum? The density of aluminum is 2.7 g mL- l. (a) 10. mL (b) 20.mL (c) 40. mL (d) 50. mL (e) 100. mL 1.2 Which metal reacts most vigorously with water? (a) K (b) Na (c) Ca (d) Li (e) Zn 1.3 Which of these compounds is the least soluble in water? (a) sodium sulfate (b) potassium hydrogen carbonate (c) lead(II) nitrate (d) magnesium chloride (e) calcium phosphate 1.4 Under the conditions of excess oxygen, the reaction of one mole of glucose, C6H1206, with atmospheric oxygen can theoretically produce: (a) 6 mol of C02 and 6 mol of H 20 (b) 6 mol of C02 and 3 mol of H 20 (c) 3 mol of C02 and 6 mol of H 20 (d) 3 mol of C02 and 6 mol of H 20 (e) 6 mol of CO and 6 mol of H 20 1.5 Carbon monoxide reduces iron(III) oxide to metallic iron: Fe203 +CO~ Fe+ C0 2 (unbalanced) How many moles of CO are required to form one mole of Fe from Fe203? (a) 0.5 (b) 1 (c) 1.5 (d) 2 (e) 3 1.6 Which of the following species will not react with acid to produce a gas? (a) NazS (b) NaHC03 (c) NazS03 (d) Zn (e) (NH4)zS04 1.7 Which of the following 0.1 M solutions will form a precipitate with 0.1 M copper(II) sulfate? (a) NazS04 (b) KCl (c) LiCzH302 (d ) NH4N03 (e) Pb(N03)z 1.8 When added to water, which substance produces a basic solution? (a) HN3 (b) NaCl (c) Ca (d) H2S (e) NH4Cl 1.9 Of the metals that do react with water, which reacts least readily? (a) Zn (b) Mg (c) K (d) Li (e) Cu 1.10 Strong heating of 7.534 g of a hydrate yields 5.957 g of anhydrous calcium sulfate. What is the ratio of water molecules to calcium sulfate units in the hydrate? (a) [(7.534 - 5.957)/ 18] -:-- (5.957/ 136) (b) (5.957/ 136) -;- [(7.534 - 1.577)/ 18] (c) (7.534/ 18) -:-- (5.957/ 136) (d ) [(7.534 - 5.957)/ 18] -;- (7.534/ 136) (e) (5.957/ 136) -:-- (7.534/ 18) 1.11 If 56 g of lithium reacts with 56 grams of nitrogen and the reaction proceeds with a 50% yield of product, how many grams of lithium nitride are obtained? (a) 21 g (b) 28 g (c) 47 g (d) 56 g (e) 84 g 1.12 Which is a strong acid? I. HBr II. HC103 (a) I only . (b) I and II only (c) I and III only (d) II and III only (e) I, II, and III III. HN02 1119 1120 APPENDIX F AP Exam Practice Problems 1.13 Which set of reactants produces a gaseous product? I. 6 M HCl(aq) + Zn(s) II. 6 M HN0 3 (aq) + MgC0 3(s) Ill. CH4(g) + 0 2(g) (a) I only (b) I and II only (c) I and III only (d) II and III only (e) I, II, and III 1.14 What products result when aqueous solutions of Co(N03h and K2C03 are mixed? (a) CoC03(aq) and KN03(s) (b) CoC03(s) and KN03(aq) (c) CoC03(aq) and KN03(aq) (d) CoC03(s) and KN03(s) (e) CoC03(s) and K2N03(aq) 1.15 Which aqueous solution contains the largest number of ions dissolved in solution? (a) 0.5 M NaOH (b) 0.2 M FeCl3 (c) 0.3 M Ca(N03h (d) 0.4 M K2S04 (e) 0.2 M Al2(S04)3 Free-Response Questions 1.1 Decomposition of 36.54 g of a pure solid compound produces 4.06 g of nitrogen gas, 10.44 g of water, and a solid metal oxide. The metal oxide is found to contain 68.42% chromium. (a) What is the simplest formula for the metal oxide? (b) What is the oxidation number of chromium in the oxide? (c) How many moles of each element are present in the unknown compound? (d) What is the simplest formula for the unknown compound? (e) Express the formula of the compound in terms of a common cation-anion pair and name the compound. (f) Write and balance a chemical equation for the decomposition reaction. 1.2 Muriatic acid is a solution of hydrochloric acid used by masons to clean brick work and etch concrete. An experiment was carried out to determine the percent of hydrochloric acid in a bottle of muriatic acid by titration. (a) First, the concentration of a standard sodium hydroxide solution was determined by titration of potassium acid phthalate, KHC 8H 80 4, a solid monoprotic acid. It was found that 1.789 g of KHP required 24.25 mL of NaOH solution to reach a suitable end point. Calculate the concentration of NaOH. (b) A 50.00 mL sample of muriatic acid was diluted to a total volume of 1000.0 mL. Then 20.00 mL of the diluted acid required 27.40 mL of standard NaOH solution to reach the end point. Calculate the concentration of the diluted muriatic acid solution. (c) Calculate the concentration of the original muriatic acid solution. (d) The density of the original muriatic acid solution was found to be 1.15 g/ mL. What is the percent by mass of HCl in the original muriatic acid solution? Laboratory grade hydrochloric acid is 37.0% HCl and has a density of 1.185 g/ mL. Calculate the molarity of laboratory hydrochloric acid. (f) Tell why it would not be practical to use laboratory hydrochloric acid to prepare a solution of the same concentration as the original muriatic acid in this experiment. (e) 1.3 Two experiments are carried out to determine the molecular formula of a monoprotic organic acid containing only carbon, hydrogen, and oxygen. First, combustion of 3.332 grams of the acid produces 8.624 grams of carbon dioxide and 1'.764 g of water. In a second experiment, titration of 0.4326 g of acid requires 18.15 mL of 0.1752 M NaOH solution to reach a suitable end point. (a) How many moles of oxygen gas are needed for the combustion reaction? (b) What is the simplest formula of the acid? (c) Calculate the molar mass of the acid. (d) What is the molecular formula of the acid? (e) Write and balance an equation for the complete combustion of the acid. 1.4 Write balanced net ionic equations for each of the following laboratory situations. Then answer the questions. Assume a reaction occurs in each case. (a) Aqueous nickel(II) sulfate is added to a solution of sodium hydroxide. i. Would you expect any of the reactants and/ or products to be colored? If so, which? Explain. ii. What would you observe if excess hydrochloric acid is added to the resulting reaction mixture? Write a net ionic equation to explain your predicted observation. iii. Which (if any) of these reactions can be classified as redox? Explain. (b) Nitric acid solution is added to solid sodium sulfide. i. Classify this reaction as acid-base, redox, combustion, or complex ion. ii. Would you expect this procedure to be dangerous? Why or why not? (c) Silver nitrate solution is added to a piece of aluminum foil. i. How many electrons transfer in the balanced equation? ii. Would a potassium nitrate solution cause a similar reaction with aluminum? Explain. (d) Zinc metal is placed in a solution of acetic acid. i. What would you observe happening? ii. Is this an acid-base reaction or a redox reaction? Explain. (e) Stomach acid (hydrochloric acid) reacts with a solid antacid tablet (active ingredient: calcium carbonate). i. What other substances contain calcium carbonate? ii. Solid calcium sulfite undergoes a similar reaction with hydrochloric acid. Write a net ionic equation. 1.5 A mixture contains NaCl, NaC103, NaHC03, and Na2C03. The mixture is heated and the following reactions occur: + 2 C02(g) + H 20(g) Na20(s) + C02(g) 2 NaCl(s) + 3 0 2(g) 2 NaHC03 ~ Na20(s) Na2C03 ~ 2 NaC10 3 ~ NaCl ~no reaction APPENDIX F When 200.0 g of the mixture is heated, 5.50 g of water, 38.70 g of carbon dioxide, and 16.57 g of oxygen are produced. Assume complete decomposition of the mixture. (a) How many grams of NaHC03 are in the mixture? (b) How many grams of C02(g) are formed from the decomposition of sodium carbonate? (c) How many mvles of NaC103 are in the mixture? (d) Calculate the % composition of the original mixture. (e) Upon heating another 200.0 g sample of the mixture, it was found that all the sodium hydrogen carbonate decomposed but some of the sodium carbonate remained. If 9.20 g of sodium carbonate remained, how many grams of C02 would have formed in this experiment? AP Exam Practice Problems 1121 2.7 When placed in the highest to lowest order for ionization energy, what is the correct order for the species, Cl- , Ar, K+? (a) Cl- > Ar > K+ (b) Ar > K+ > Cl(c) K+ > Cl- > Ar (d) K+ > Ar > Cl(e) Cl- = Ar = K+ 2.8 Which set contains all trigonal pyramidal species? (a) NH3, S03, N03<b> NF3, C032- , so/<c> BF3, H 30 +, NH3 (d) so3, N03- , co3 2<e> NF3, S032-, H 30 + 2.9 What is the correct order of increasing bond energy? UNIT II. ATOMIC STRUCTURE, PERIODICITY, AND BONDING Multiple-Choice Questions 2.1 Which of these molecules contains two pi bonds? C2H6 C2H4 CH20 co CH3COOH 2.2 Which electronic transition in the hydrogen atom results in the emission of visible light? (a) (b) (c) (d) (e) (a) n = 3 ton = = = = = (b) n = 3 to n (c) n = 4 ton (d) n = 2 to n (e) n = 2 to n 2 1 3 4 6 2.3 The maximum number of electrons in an atom that can have quantum numbers n = 5, l = 3 is (a) 2 (b) 6 (c) 8 (d) 10 (e) 14 (a) (b) (c) (d) (e) Br- Br < Br - Cl < Br- F Br - F < Br-Cl < Br- Br Br-Cl < Br - Br < Br- F Br - F < Br- Br < Br-Cl Br- Br < Br- F < Br - Cl 2.10 What geometrical arrangement is associated with orbitals that are sp 2 hybridized? (a) linear (b) octahedral (c) trigonal bipyramidal (d) trigonal planar (e) tetrahedral 2.11 Which compounds contain both ionic and covalent bonds? I. NH4N03 II. KAl(S04h Ill. CH3COOH (a) II only (b) II and III only (c) I and II only (d) I and III only (e) I, II, and III 2.12 When the following species are arranged according to in- creasing 0-S - 0 bond angle, what is the correct order? (a) S02 < S03 < S0 42- < so/(b) so3 < S04 2- < so3- < S032(c) so/-< S04 2- < so2 < so3 (d) so3 < so2 < S04 2- < S032(e) S0 42- < so/- < so2 < S03 2.4 Which compound is expected to have the highest melting point? (a) NaF (b) KF (c) RbF (d) KCl (e) NaCl 2.5 What is the electron configuration of the Ti 3+ ion? (a) 1s 22s 22p 63s 23p63d24s 2 (b) 1s 22s 22p 63s23p63d2 (c) 1s22s 22p63s 23p63d 1 (d) 1s 22s 22p63s 23p64s 1 (e) 1s 22s 22p63s 23p6 2.13 Which compound is expected to have the largest lattice energy? (a) KF (b) CaO (c) CaCl2 (d) NaF (e) KCl 2.6 What is the total number of completely or partially filled " p" orbitals in a gaseous arsenic atom in the ground state? (a) 3 2.15 Which energy transition in the hydrogen atom will be the greatest? (a) n = 2 ton = 1 (b) n = 3 to n = 2 (c) n = 4 to n = 3 (d) n = 5 to n = 4 (e) n = 6 to n = 5 (b) 6 (c) 8 (d) 9 (e) 10 2.14 Which element has the largest first ionization energy? (a) Be (b) B (c) C (d) N (e) 0 1122 APPENDIX F AP Exam Practice Problems Unit II. Free-Response Questions 2.1 Fluorine combines with sulfur to form SF2, SF4, and SF 6. (a) Draw a Lewis structure for SF2. (b) Identify the hybridization of the sulfur in SF4. (c) State the geometry of SF6. (d) Predict the F-S- F bond angles for each of the three compounds: SF2, SF4, and SF 6. State your reasons. (e) Predict which, if any, of the three sulfur compounds is (are) polar. Explain your reasoning. (f) Explain why chlorine combines with sulfur to form SC14 but not SC16· (g) Oxygen forms OF2, but not OF4 or OF6. Explain. colors of the lines are red, blue-green, blue-violet, and violet, not necessarily in order. (a) Calculate the frequency associated with the 410 nm line. (b) Calculate the energy of a single photon associated with the 434 nm line. (c) Calculate the energy of a mole of photons associated with the 486 nm line. (d) How may photons associated with the 656 nm line will provide 1.00 kJ of energy? (e) Match each colored line with its wavelength. Order the lines by increasing energy and increasing frequency. (f) Explain the origin of the four colored lines of the hydrogen spectrum. Explain why hydrogen does not display a continuous spectrum. (g) Is it possible that the atomic emission spectrum of hydrogen has more than four lines? Explain. 2.2 Consider an atom of titanium. (a) Write the complete electron configuration of titanium. (b) Write the complete electron configuration of Ti 2+. (c) Write the set of four quantum numbers for each valence electron in Ti 2+. (d) Write the chemical formula for titanium(IV) oxide. Would you expect titanium(IV) oxide to be colored? Explain your answer. (e) Predict the relative values of the first ionization energies of calcium and titanium. Explain the basis of your prediction. UNIT III. GASES, INTERMOLECULAR FORCES, AND SOLUTIONS 2.3 The values of the first ionization energies of the period 3 elements are given in units of kJ/ mol. Multiple-Choice Questions (a) (b) (c) (d) (e) Na = 495; Mg = 738; Al = 578; Si = 786; P = 1012; S = 1000; Cl = 1251; Ar = 1521. State the general trend and explain the trend using the terms screening effect and effective nuclear charge. Explain why the first ionization energy of aluminum is lower than that of magnesium. Explain why the first ionization energy of sulfur is lower than that of phosphorus. Predict the relative values of the second ionization energies of sodium and magnesium. Explain your reasoning. Why is the first ionization energy of potassium lower than that of sodium? 2.4 Write balanced net ionic equations for each of the following laboratory situations. Then answer the questions. Assume a reaction occurs in each case. (a) Chlorine gas is bubbled into liquid water. i. Identify the oxidizing agent and the reducing agent in this reaction. ii. Name a common use of gaseous chlorine. (b) Fluorine gas is bubbled into liquid water. i. Would you expect this reaction to be exothermic or endothermic? Explain. ii. Would the aqueous solution resulting from this reaction conduct electricity strongly, weakly, or not at all. Explain. (c) Hydrogen peroxide is allowed to stand at room temperature. i. When storing hydrogen peroxide what precautions should be taken? Why? ii. Assign oxidation numbers to each oxygen in the equation and tell whether oxygen is oxidized or reduced. 2.5 Four visible lines of the atomic emission spectrum of hydrogen have wavelengths of 410, 434, 486, and 656 nm. The 3.1 A given gas will show the greatest deviation from ideal behavior at which set of conditions of temperature and pressure? (a) 0 oc and 1 atm (b) 100 oc and 1 atm (c) 100 °C and 0.5 atm (d) 0 oc and 0.5 atm (e) - 100 oc and 1 atm 3.2 Equal numbers of moles of three gases are mixed in a 20.0 L container at 25 oc. If the container has a pinhole leak, what is the proper order of the partial pressures of the gases after two hours? (a) C02 > H2 > CH4 (b) H2 > C02 > CH4 (c) C02 > CH4 > H2 (d) H2 > CH4 > C02 (e) CH 4 > C02 > H 2 3.3 Which substance in the solid phase has the strongest intermolecular forces? (a) Cl2 (b) Na (c) C02 (d) c (e) CsH 12 3.4 Which gas is most soluble in water? (a) carbon dioxide (b) ammonia (c) methane (d) oxygen (e) nitrogen 3.5 The kinetic-molecular theory predicts that two gases at the same temperature will have the same (a) average speed. (b) average kinetic energy. (c) pressure. APPENDIX F (d) rate of effusion. (e) number of particles. 3.6 The density of a typical gas at normal atmospheric temper- atures and pressures is (a) 1gmL- 1 (b) 1 g L - 1 (c) 100 g L - 1 (d) 0.1 g mL- 1 (e) 0.01 g L- 1 3.7 Real gases tend to exhibit non-ideal behavior because their particles possess which properties? I. Attractive forces between molecules II. Attractive forces between molecules and their containers III. Finite volumes (a) I only (b) II only (c) III only (d) I, II, and III (e) I and II only 3.8 A solute dissolved in benzene lowers the freezing point of the solution to a temperature that is lower than the freezing point of pure benzene. The amount of change in freezing point depends on (a) the number of particles formed by the solute when dissolved. (b) the molar mass of the solvent. (c) the freezing point of the solute. (d) the atmospheric pressure. (e) the temperature of the solvent. 3.9 Consider two solutions: a 0.25 molal solution of Fe(N03)3 and a 0.50 molal solution of NaCl. Which statement about the solutions is correct? (a) The sodium chloride solution has a lower freezing point because the salt concentration is greater. (b) The iron(III) nitrate solution has a higher boiling point because the total ion concentration is greater. (c) Both solutions freeze at approximately the same negative Celsius temperature because they have equal ion concentrations. (d) The iron(III) nitrate solution has a higher vapor pressure because the total ion concentration is greater. (e) The iron(III) nitrate solution freezes at a higher temperature because it is more acidic. 3.10 When comparing carbon dioxide with oxygen under the same conditions of temperature and pressure, what can be said about carbon dioxide? (a) C02 moves faster and effuses more slowly. (b) C02 moves more slowly and effuses more slowly. (c) C02 moves faster and effuses faster. (d) C02 moves more slowly and effuses faster. (e) C02 moves at the same average speed but effuses more slowly. 3.11 Three balloons are filled with the same number of mole- cules of 0 2, H 2, and C02, respectively, under the same conditions of temperature and pressure. Which is not the same for each gas? I. average kinetic energy II. volume III. average velocity of molecules IV. density (a) (b) (c) (d) (e) AP Exam Practice Problems 1123 I and III only III and IV only III only II and IV only I, II, and III only 3.12 Which compound would be expected to be most soluble in water? (a) C6H6 (b) C2H4 (c) (C2HshO (d) CHCl3 (e) (CH3hNH 3.13 Which aqueous solution will boil at the highest temperature? (a) 0.5 m C6H1206 (b) 1.0 m C 2H 50H (c) 1.25 m NaCl (d) 1.0 m CaCl2 (e) 0.5 m A1Cl3 3.14 How does the average velocity of molecules change when the absolute temperature is halved? (a) The average velocity stays the same. (b) The average velocity decreases by 1/ 2. (c) The average velocity decreases by 1/ 4. (d) The average velocity doubles. (e) The average velocity decreases by an amount depending on the masses of the molecules. 3.15 A given liquid would have which combination of properties? Vapor Pressure (a) high (b) low (c) high (d) low (e) high Heat of Vaporization Attractive Forces high low low low high high low low high low Free-Response Questions 3.1 A mixture of 0.300 mol each of hydrogen gas, oxygen gas, and liquid water are present in a 20.00 liter container at 25 °C. The equilibrium vapor pressure of water at 25 °C is 23.76 torr. (a) Calculate the total pressure inside the flask. (b) Using principles of kinetic molecular theory, explain which gas has the i. highest average kinetic energy ii. highest average velocity of molecules iii. highest density (c) The mixture is sparked, a reaction ensues consuming one of the reactants entirely, and the resulting mixture is allowed to come to equilibrium at 80 oc. i. Write and balance a chemical equation to describe the reaction. ii. Which is the limiting reactant? Explain. iii. Calculate the total pressure in the flask after thereaction is complete. The water vapor pressure at 80 oc is 355 torr. iv. Calculate the number of moles of water present as vapor when the reaction is complete. 1124 APPENDIX F AP Exam Practice Problems 3.2 Consider the following 0.10 M solutions: I. iron(III) chloride II. copper(II) nitrate III. hydrogen sulfide (a) Describe the color of each solution. (b) Predict whether each solution's conductivity would measure high, low, or nonconducting and explain your predictions. (c) Which pair(s) of solutions, when mixed, would not produce a detectable reaction? Why? (d) Write a net ionic equation for each reaction produced when the solutions are mixed in pairs. (e) Which solution would have the: i. highest boiling point? Explain. ii. highest freezing point? Explain. iii. lowest vapor pressure? Explain. 3.3 The empirical and molecular formulas of an unknown compound are determined by combustion analysis and a freezing point depression experiment. (a) When a 0.8425 g sample of an unknown molecular compound containing only carbon, hydrogen, and oxygen is combusted in excess oxygen, 1.8850 g of carbon dioxide are produced and 0.8996 g of water is formed. i. Calculate the mass in grams of oxygen required for the combustion. ii. Calculate the mass in grams of oxygen contained in the sample of unknown compound. iii. Determine the empirical formula for the unknown compound. (b) The unknown compound dissolves readily in chloroform, CHC13 . The freezing point of a solution prepared by ~ixing 150.0 grams of CHC13 and 3.100 grams of the unknown compound is -64.32 oc. The molal freezing. point depression constant of CHC13 is 4.68 oC/ molal and its normal freezing point is -63.50 oc. i. Calculate the molality of the unknown compound in the chloroform solution. ii. Calculate the molar mass of the unknown compound. iii. Determine the molecular formula of the unknown compound. iv. Write and balance an equation for the combustion of the unknown compound. 3.4 Ethylene glycol, HOCH2CH20H, is a nonvolatile liquid used as an antifreeze for automotive cooling systems. A solution is made by dissolving 250. grams of ethylene glycol in 650. grams of water. (a) Calculate the mass % of ethylene glycol in water. (b) Calculate the molality of ethylene glycol in the solution. (c) Calculate the mole fraction of water in the solution. (d) Calculate the theoretical freezing point of the solution. The freezing point constant for water is 1.86 oc j m. (e) Calculate the vapor pressure of the solution at 90 °C. The vapor pressure of water at 90 oc is 525.8 torr. (f) What quantity is needed to calculate the molarity of ethylene glycol in the solution? Show how you would do the calculation if you had this missing quantity. (g) Explain how you would measure this missing quantity in the laboratory. 3.5 Consider the following laboratory observations and answer the questions about them. When solid ammonium chloride is added to liquid water, the solid dissolves completely. i. Distinguish between intramolecular forces of attraction and intermolecular forces of attraction. Specify which give rise to chemical properties and which are largely responsible for physical properties. ii. What are the forces of attraction in pure solid ammonium chloride? iii. What are the forces of attraction in pure liquid water? iv. What intermolecular forces of attraction exist in an aqueous solution of ammonium chloride that do not exist in either pure ammonium chloride or pure water? (b) When an aqueous solution of silver nitrate is added to an aqueous solution of ammonium chloride a white precipitate forms. i. Write and balance a net ionic equation to describe the reaction. ii. What forces of attraction exist within the white precipitate? (c) When aqueous sodium hydroxide is added to the mixture in Part b, the white precipitate dissolves and the heretofore odorless mixture now imparts a distinctive odor. i. Write and balance a net ionic equation to describe the formation of the odiferous substance. ii. Write and balance a net ionic equation to explain the dissolution of the precipitate. iii. Predict whether the odiferous substance is soluble in water. Explain your prediction based on intermolecular forces of attraction. (d) An aqueous solution of ammonium bromide is mixed with a 3% aqueous solution of hydrogen peroxide. The solution turns brown. The brown solution is then shaken with hexane and allowed to stand. Two distinct layers separate. The top layer is pink and the bottom layer is colorless. i. Predict the chemical formula of the brown substance. ii. Identify the composition of the top layer and the bottom layer. Explain why they do not dissolve in each other. iii. Discuss the intermolecular forces of attraction present in the top layer. (a) UNIT IV. KINETICS AND EQUILIBRIUM Multiple-Choice Questions 4.1 The half-life of mercury-203 is about 1.5 months. What mass of a 64 gram sample of this isotope will remain after nine months? (a) 1 g (b) 2 g (c) 4 g (d) 8 g (e) 16 g 4.2 The rate constants for a forward reaction and its corresponding reverse reaction are generally expected to APPENDIX F be independent of temperature. decrease with increasing temperature. increase with increasing temperature. increase with increasing temperature, only for the endothermic reaction. (e) increase with increasing temperature, only for the exothermic reaction. (a) (b) (c) (d) 4.3 The rate expression for a second-order reaction could be (a) rate = k[A] (b) rate = k[Af[B] (c) rate = k[A][B] (d) rate = k[Af[Bf (e) rate = k[B] 4.4 The rate law of the reaction 2X + 2Y ~ 2XY is rate = k[Xf[Y]. If [X] is doubled and [Y] is halved, the rate of the reaction will (a) increase by a factor of 4. (b) remain the same. (c) decrease by a factor of 4. (d) increase by a factor of 2. (e) decrease by a factor of 2. 4.5 What can be correctly said about the energy diagram for a reversible endothermic reaction? (a) The energy of activation is greater for the reverse reaction than for the forward reaction. (b) The energy of activation is greater for the forward reaction than for the reverse reaction. (c) The energy of activation is the same for the reaction in both directions. (d) The enthalpy of products is less than the enthalpy of reactants. (e) The forward reaction is faster than the reverse reaction. 4.6 An aqueous solution of sodium hydrogen carbonate has a pH greater than 7 because: (a) Sodium hydrogen carbonate donates a proton to water. (b) Sodium hydrogen carbonate accepts a proton from water. (c) Hydrogen carbonate ion is acidic. (d) Sodium ion is basic. (e) Sodium ion accepts a proton from water. 4.7 Which species ionizes the least in water? (a) HN03 (b) H2S04 (c) HC104 (d) HN02 (e) HBr 4.8 When one mole of sulfuric acid ionizes in water, the number of moles of ions present in solution is closest to which value? (a) 1 (b) 2 (c) 3 (d) 4 (e) 7 4.9 Which of these solutions can be used to prepare a buffer? (a) HN03 and KOH (b) HN03 and CH3COOH (c) HN03 and NaCH3COO (d) KOH and NH3 (e) KCl and NaCl AP Exam Practice Problems 1125 4.10 The solubility of lead(II) carbonate is (a) the same in water as it is in nitric acid. (b) greater in water than it is in nitric acid. (c) greater in water than it is in aqueous lead(II) nitrate. (d) less in water than it is in aqueous sodium carbonate. (e) the same in water as it is in aqueous sodium carbonate. 4.11 For the reaction, 2X(g) + Y(s) ~ X2Y(s), which factors affect the value of the rate constant? I. concentration II. pressure III. temperature (a) I, II, and III {b) I and II only (c) II and III only (d) I only (e) III only 4.12 A certain reaction is believed to occur in the following steps: 1. A2 ~ 2A 2. A+ B ~ AB 3. A + AB ~ A2B slow What is the most likely rate law? (a) rate = k[A2][B] (b) rate = k[Af[B] (c) rate = k[A] 2 (d) rate = k[A] 112[B] (e) rate = k[A2f[B] 4.13 Which is the strongest base in aqueous solution? (a) HP042(b) H2P04(c) HC03(d) co32- <e> P0 43 4.14 A 0.1 M aqueous solution of which salt has the lowest pH? (a) NH4Cl (b) KCl (c) CaCl2 (d) CuCl2 (e) AlCl3 4.15 If for the reaction 2A(g) ~ B(g), Kc = 4 at 25 °C, what is KP at 25 oc for the following reaction? 1/2 B(g) ~ A (g ) (a) KP = 2(RT) 112 (b) KP = 4(RT) 112 (c) · KP = 2(RT) 2 (d) KP = 4(RT) 2 (e) Kp = 1/ 2(RT) 112 Free-Response Questions 4.1 Consider 3.00 liters of a saturated solution of calcium hydroxide. (a) The pH of the saturated solution is 12.370. i. Write the chemical equation for the dissolution of solid calcium hydroxide in water. Assume calcium hydroxide dissociates completely. ii. Calculate the concentration of hydroxide ion in a saturated solution of calcium hydroxide. iii. Calculate the solubility of calcium hydroxide in water. iv. Calculate the K sp of calcium hydroxide. 1126 (b) APPENDIX F AP Exam Practice Problems The saturated solution is filtered to remove any solid calcium hydroxide and separated into three 1.00 liter parts. i. The pH of one part is adjusted to 13.000. Calculate the mass of the calcium hydroxide that will precipitate from this solution under these conditions. ii. To a second 1.00 liter solution, 500 mL of 0.100 M magnesium chloride is added. Write the balanced equation for the dissolution of magnesium hydroxide, calculate the reaction quotient for the reaction and predict whether a precipitate of magnesium hydroxide will form. Explain your reasoning. The Ksp of magnesium hydroxide is 1.8 X 10- 11 . iii. To a third 1.00 liter saturated solution of calcium hydroxide, 10.00 mL of 0.5000 M hydroazoic acid, HN3, is added. Calculate the pH of the resulting solution. The Ka of hydroazoic acid is 1.9 X 10- 5 . 4.2 21.60 g of sodium benzoate, NaC 6H 5COO, is dissolved in enough water to make 0.750 liters of solution. The Ka for benzoic acid, C6H5COOH, is 6.3 X 10- 5 . (a) Write a chemical equation for the reaction of benzoate ion, C6H 5Coo- , and water. (b) Calculate the percent ionization of benzoate ion. (c) Calculate the pH of the sodium benzoate solution. (d) Calculate the pH of a solution made by adding 6.100 g of benzoic acid to 250.0 mL of the sodium benzoate solution. Assume no volume change. (e) Calculate the pH of a solution made by adding 100.0 mL of a 0.400 M solution of hydrochloric acid to 250.0 mL of the original sodium benzoate solution. Assume volumes are additive. (f) If an additional 25.0 mL of the hydrochloric acid solution is added to the solution produced in Parte, calculate the pH of the final solution. 4.3 Gaseous ammonia is produced in an exothermic reaction when hydrogen gas and nitrogen gas are combined under the right conditions. 3 H 2(g) + N2(g) ~ 2 NH3(g) ~ 3/ 2 H2(g) + 1/ 2 N2(g) At another temperature, 1.700 g of ammonia is placed in a 2.00 L flask and allowed to come to equilibrium. At equilibrium, there are 0.120 grams of hydrogen gas present in the mixture. i. Calculate number of grams of nitrogen at equilibrium. ii. Calculate the equilibrium constant, K 0 for the reaction: 2 NH3(g) ~ 3 H2(g) 4.4 Write balanced net ionic equations for each of the following laboratory situations. Then answer the questions. Assume a reaction occurs in each case. (a) Two moles of a sodium hydroxide solution are added to a solution containing one mole of phosphoric acid. i. Can the mixture of products act as a buffer solution? Explain. ii. Write three separate equations showing the successive ionization of phosphoric acid. In each equation, identify the conjugate acid-base pairs. (b) Sodium fluoride is added to water. i. Predict the pH of this solution relative to water. ii. Suggest a substance that when added to the resulting mixture will produce a buffer solution. (c) An aqueous solution of sodium hydroxide solution is added to solid ammonium chloride. OH- (aq) + NH4Cl(s) ~ H 20(l) + NH3(aq) + Cl- (aq) i. Can the resulting solution act as buffer? Explain. ii. One product of the reaction is exposed to hydrogen chloride gas. Write and balance an equation for the resulting reaction. 4.5 Use chemical principles to explain the following: (a) The rates of chemical reactions generally increase with an increase in temperature. (b) Increasing concentrations of reactants increase reaction rate. (c) The orders of reactants in a rate equation cannot be obtained from the coefficients in the balanced overall equation for a reaction. (d) Upon mixing reactants, often no observable reaction is observed until something is done to initiate the reaction. Cite a common example. (e) Addition of a catalyst speeds up a chemical reaction. NH3(g) At 500 oc, KP for the reaction is 1.45 X 10- 5 . (a) Calculate Kc for the reaction at 500 °C. (b) If the temperature is decreased for the reaction, predict whether the value of Kp will increase, decrease, or stay the same. Explain your answer. (c) Calculate KP for the following reaction at 500 °C: (d) hydrogen gas increase, decrease, or stay the same? Explain your answer. + N2(g) iii. Is the temperature of this equilibrium mixture greater or less than 500 °C? Explain your answer. iv. If the temperature of this equilibrium mixture were returned to 500 oc, would the number of moles of UNIT V. THERMODYNAMICS, ELECTROCHEMISTRY, NUCLEAR AND ORGANIC CHEMISTRY Multiple-Choice Questions 5.1 What is a product formed at the anode of the electrolysis of an aqueous sodium sulfate solution? (a) H2(g) (b) 02(g) (c) Na(s) (d) S(s) (e) S02(g) 5.2 What is a product formed at the cathode of the electrolysis of an aqueous copper nitrate solution? (a) H2(g) (b) 0 2(g) (c) Cu(s) (d) N2(g) (e) NO(g) APPENDIX F 5.3 Carbon monoxide reacts with oxygen according to the following thermodynamic equation at 25 oc and 1 atmosphere pressure: 2 CO(g) + 0 2 (g) ~ 2C0 2 (g) L'lH = - 566 kJ Which statement(s) is (are) true? I. The reaction is endothermic II. The heat of combustion of gaseous carbon monoxide is -283 kJ/ mol. III. The heat of standard formation of C02(g) is - 283 kJ/ mol. (a) 1 only (b) 2 only (c) 3 only (d) 2 and 3 only (e) 1 and 2 only 5.4 Assume one mole of each of the following chemical species. Which has the greatest absolute entropy under the same conditions of temperature and pressure? (a) I(g) (b) 12 (g) (c) lz(s) (d) 1- (aq) (e) Fz(g) 5.5 The specific heats of three unknown substances vary in the following order: X > Y > Z. A 1.0 gram sample of substance X at 100 oc is added to 100 g of water at 20 oc and the temperature change is recorded. The procedure is repeated with substance Y and then with substance Z. How will the final temperatures of the water compare? (a) X= Y = Z (b) X > Y > Z (c) Z > Y > X (d) Y > Z > X (e) Y > X > Z 5.6 Which change will increase the voltage of an electrochemical cell based on this reaction: (a) (b) (c) (d) (e) Fe(s) + Cl2(g) ~ Fe 2+(aq) + 2 Cl- (aq) Increase the mass of Fe. Increase the Rartial pressure of Cl2(g). Increase [Fe +]. Increase [Cl- ]. All of the above changes will decrease the voltage. 5.7 Which two half reactions, when suitably coupled, will make a voltaic cell that will produce the largest initial voltage? I. Fe 2+(aq) + 2 e- ~ Fe(s) Eo = - 0.440 volts II. Cu2+(aq) + 2 e- ~ Cu(s) Eo = +0.337 volts III. Fe 3+(aq) + 3 e- ~ Fe(s) Eo = - 1.660 volts IV. Ag+(aq) + 1 e- ~ Ag(s) Eo = +0.799 volts (a) I and II (b) II and III (c) I and III (d) II and IV (e) III and IV 5.8 At 25 oc, which change occurs with the largest increase in entropy? (a) H 20(Z) ~ H20(g) (b) H20(s) ~ H 20(g) (c) H20(Z) ~ HCl(g) ~ H 30 +(aq) + Cl- (aq) (d) H 20(l) + 1/ 2 0 2(g) ~ H20 2(l) (e) H 20(l) + NH3(g) ~ NH 4+(aq) + OH- (aq) AP Exam Practice Problems 1127 5.9 What is the correct order when the following substances are placed in increasing order of oxidation number for sulfur? (a) H2S < S < Na2S203 < KHS03 < Al2(S04h (b) Al2(S04h < KHS03 < NazS203 < S < H zS (c) S < H2S < KHS03 < NazS203 < Al2(S04h (d) Al2(S04h < KHS03 < NazS203 < H2S < S (e) H 2S < S < KHS03 < Na2S203 < Al2(S04h 5.10 The bond dissociation energy for N=N is 940 kJ/ mol. What is the standard heat formation of the gaseous nitrogen molecule in kJ/ mol? (a) +940 (b) - 940 (c) - 1880 (d) - 470 (e) 0 5.11 Which of these compounds have cis and trans isomers? I. 1-pentene II. 2-pentene Ill. 2-methyl-2-pentene (a) II only (b) II and III only (c) I and II only (d) I and III only (e) I, II, and III 5.12 Which set of reactants produces a gaseous product? I. Cu + H 2S04 II. Cu + HN03 Ill. Cu + HCl (a) I only (b) II only (c) I and II only (d) I and III only (e) I, II, and III 5.13 How many isomers exist for C6H14? (a) 2 (b) 3 (c) 4 (d) 5 (e) 6 5.14 Which change will generally produce an increase in the en- tropy of a system? (a) decreasing the temperature (b) formation of a precipitate from solution (c) decreasing the volume (d) sublimation (e) condensation 5.15 What are the signs of tlH, tlG, and L'lS for the freezing of liquid water at - 5 °C? (a) tlH tlG tlS + + + (b) (c) (d) (e) + + - + 1128 AP Exam Practice Problems APPENDIX F FREE-RESPONSE QUESTIONS 5.1 The half-cell reactions for rechargeable nickel-cadmium (nicad) batteries are: Cd(OHh(s) + 2 e- ~ Cd(s) + 2 OH- (aq) E0 = -0.809 NiOOH(s) + H 20(l) + e- ~ Ni(OHh(s) + OH- (aq) E0 (a) (b) (c) (d) (e) (f) = +0.490 Write a balanced equation for the overall process. Identify the half-reaction that occurs at the cathode. Calculate the cell potential. If a nicad battery produces a current of 40.0 milliamps for 5.00 hours, how many electrons are transferred? How many grams of cadmium will be oxidized or reduced (specify which) under the conditions of Part d? As the cell discharges, will the pH of each compartment increase, decrease, or stay the same? Explain. 5.2 Consider the reaction: C0 2(g) + 2 HCl(g) ~ Cl 2CO(g) + H 20(g) Draw the Lewis structure for each reactant and each product. (b) Using the table of bond enthalpies below, calculate .clH for the reaction. Be sure to include units. (a) C-0 Bond Bond enthalpy (kJ/ mol) 351 C=O C==O C-Cl H-Cl H-0 715 1073 331 Calculate the equilibrium constant, Keq, for the reaction at 25 oc. (f) At what temperature will the reaction come to equilibrium? (g) If the tetrachloroethane produced in this reaction formed as a liquid rather than as a gas, would .clHrxn change and if so, how would it change? Explain your answer. (e) 431 5.4 Write balanced net ionic equations for each of the following laboratory situations. Then answer the questions. Assume a reaction occurs in each case. (a) Electricity is applied to an aqueous solution of sodium sulfate. H20(l) ~ H 2(g) + 1/ 2 02(g) i. Write the half reactions that occur at the cathode and anode. Specify at which electrode each half reaction occurs. ii. In the presence of an acid-base indicator, specify two observations you would make at each electrode. (b) An acidic solution of potassium dichromate is added to a solution of hydrogen peroxide. i. Identify the oxidizing agent and the reducing agent in this reaction. ii. Describe any color change you would observe. (c) A copper half cell is suitably connected to a silver half cell. 2 Ag +(aq) + Cu(s) ~ 2 Ag(s) + Cu2+(aq) i. Which electrode acts as the cathode and which acts as the anode? In which direction do the electrons flow? ii. If a gold half cell replaced the copper half cell, would the electrons flow in the same direction? Explain? 464 (c) Is the reaction exothermic or endothermic? Explain. Predict the sign of ilS for the reaction. Explain your reasoning. (e) Will the reaction be more spontaneous at high temperatures or at low temperatures? Explain. (f) Given the standard heats of formation of the following molecules, calculate the heat of formation of Cl2CO(g). ilH'J of C0 2(g) = -393.5 kJ/ mol (d) ilH'J of HCl(g) = -92.30 kJ/ mol ilH'J of H 20(g) = -241.8 kJ/ mol 5.3 Consider the reaction of gaseous ethyne, C2H 2(g), with chlorine to produce tetrachloroethane, C 2H 2Cl4(g). Thermodynamic data at 25 oc for the reaction are: tlH 0 = -405 KJ tl5° = - 349 JK - 1 5.5 In separate experiments, five grams each of three salts are dissolved in water and the temperature change of the water is recorded. The results are summarized in the table. Salt sodium chloride calcium chloride ammonium chloride (a) Some thermodynamic data for selected reactants and products are: (b) Substance AHJ(kJ mol- 1) so (J mol- 1 K- 1) C2H2(g) Cl2(g) C2H2Cl4(g) 227 201 (c) +298 (d) 0 Write a balanced equation for the reaction assuming all the reactants and products are gaseous. (b) Calculate ilH'J for C2H2Cl4(g). (c) Calculate sofor Cl2(g). (d) Calculate .clGo for the reaction at 25 oc. (a) (e) (f) Initial H2 0 temp Final H2 0 temp 22 oc 21 oc 45 oc 22 oc 10 oc 23 oc Give the sign of ilH for the dissolving of calcium chloride and for the dissolving of ammonium chloride and state whether each dissolves exothermically or endothermic ally. Give the sign of .clS for the dissolving of calcium chloride and ammonium chloride and state whether each dissolves with an increase or decrease in entropy. Give the sign of .clG for the dissolving of each of the three salts. Explain your answers. State what effect an increase in temperature will have on the solubility of ammonium chloride. Explain using thermodynamic principles. For which salt is the relative magnitude of the lattice energy significantly greater than the relative energy of the hydration energy? Explain your reasoning. What are the principle driving influences for the dissolution of each of the three salts? lications and Essavs I Strate ies in Chemistr Estimating Answers 26 The Importance of Practice 28 Pattern Recognition 58 Problem Solving 89 How to Take a Test 106 Analyzing Chemical Reactions 143 Using Enthalpy as a Guide 180 Calculations Involving Many Variables 404 What Now? 1094 I Chemistr and Li e The Battle for Iron in Living Systems 1024 Polycyclic Aromatic Hydrocarbons 1070 The Origins of Chirality in Living Systems 1085 ~ Chemistr Put to W'llrk Chemistry and the Chemical Industry 4 Chemistry in the News 18 Antacids 135 The Hybrid Car 196 Explosives and Alfred Nobel 328 Orbitals and Energy 380 Gas Pipelines 409 Gas Separations 420 Supercritical Fluid Extraction 453 Cell Phone Tower Range 498 Recycling Plastics 501 Toward the Plastic Car 506 Liquid Crystal Displays 513 Methyl Bromide in the Atmosphere 590 Catalytic Converters 608 The Haber Process 631 Controlling Nitric Oxide Emissions 656 Amines and Amine Hydrochlorides 694 Direct Methanol Fuel Cells 874 Environmental Applications of Radioisotopes 921 Carbon Fibers and Composites 962 Gasoline 1061 Portrait of an Organic Chemical 1076 Elements Required by Living Organisms 57 Glucose Monitoring 102 Drinking Too Much Water Can Kill You 147 The Regulation of Human Body Temperature 185 Nuclear Spin and Magnetic Resonance Imaging 236 Ionic Size Makes a Big Difference 265 The Improbable Development of Lithium Drugs 280 The Chemistry ofVision 36 7 Blood Pressure 398 Fat- and Water-Soluble Vitamins 538 Blood Gases and Deep-Sea Diving 540 Sickle-Cell Anemia 559 Nitrogen Fixation and Nitrogenase 610 The Amphiprotic Behavior of Amino Acids 703 Blood as a Buffered Solution 729 Sinkholes 744 Tooth Decay and Fluoridation 74 7 Entropy and Life 815 Driving Nonspontaneous Reactions 830 Heartbeats and Electrocardiography 868 Medical Applications of Radiotracers 910 Radiation Therapy 922 How Much Perchlorate Is Too Much? 944 Nitroglycerin and Heart Disease 956 The Mass Spectrometer 48 Glenn Seaborg and Seaborgium 51 The Aura of Gold 143 Arsenic in Drinking Water 960 Energy, Enthalpy, and P- V Work 176 The Scientific Method 13 Basic Forces 45 1129 1130 CHEMICAL APPLICATIONS AND ESSAYS The Speed of Light 214 Measurement and the Uncertainty Principle 225 Probability Density and Radial Probability Functions 230 Experimental Evidence for Electron Spin 234 Effective Nuclear Charge 260 Calculation of Lattice Energies: The Born-Haber Cycle 304 Oxidation Numbers, Formal Charges, and Actual Partial Charges 318 Phases in Atomic and Molecular Orbitals 3 73 The Ideal-Gas Equation 416 The Clausius-Clapeyron Equation 456 X-Ray Diffraction by Crystals 465 The Third Form of Carbon 468 The Transistor 490 Hydrates 533 Ideal Solutions with Two or More Volatile Components 548 Colligative Properties of Electrolyte Solutions 554 Using Spectroscopic Methods to Measure Reaction Rates 580 Limitations of Solubility Products 741 Other Greenhouse Gases 782 Water Softening 788 The Entropy Change when a Gas Expands Isothermally 808 Entropy and Probability 812 What's "Free" About Free Energy? 822 The Dawning of the Nuclear Age 915 The Hydrogen Economy 937 Charles M. Hall 990 Shape-Memory Alloys 998 Entropy and the Chelate Effect 1021 Charge-Transfer Color 1040