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CHM 1045 - General Chemistry 1 (U05) Fall 2013 Dr. Jeff Joens Classroom: CP 145 Time: M, W, F 2:00pm to 3:15pm Office: CP 331 phone 348-3121 email: [email protected] web page: www.joenschem.com Homework Problems Chapter 1 Homework Problems: 6, 10, 12, 13, 18, 24, 26, 30, 36, 43, 44, 48, 50, 54, 58, 64, 74, 78, 86, 110 Note: Homework is not to be turned in. My solutions to the homework problems are available at my website (www.joenschem.com). Answers (but not detailed solutions) to the odd numbered end of chapter problems are given at the end of the book. Math Review Appendix 1 of the textbook reviews several math concepts that you need to be familiar with, including the following: Scientific notation - Writing numbers in scientific notation, converting to and from scientific notation, mathematical operations in scientific notation. Trigonometry - Basic relationships. Logarithms and exponents - Use of base 10 and natural logarithms, conversions involving logarithms. Quadratic formula - Use in calculations. CHAPTER 1 The Study of Chemistry Basic Definitions Chemistry - The study of the properties and transformation of matter. Matter - Possesses mass and occupies space. Mass - A measure of the quantity of matter possessed by an object. Measured in comparison to the standard kilogram. Basic Definitions Energy - The capacity to do work or provide heat. Kinetic energy - Energy due to the motion of an object EK = 1/2 (mv2) Potential energy - Energy due to the position or composition of an object (gravitational, electrical, chemical, nuclear…) Conservation laws Conservation of mass Conservation of energy States of Matter There are three common states (phases) of matter. Solid - State where the particles making up a substance occupy a fixed volume and have fixed locations (do not move about). There are two general types of solids: Crystalline solid - Particles making up the solid have a regular repeating arrangement (crystal structure) Amorphous solid - Particles making up the solid do not have a regular arrangement. Liquid - State where the particles making up a substance occupy a fixed volume but can freely move about within that volume. Gas - State where the particles making up a substance occupy the entire volume of their container and can freely move about within that volume. The volume occupied by a gas strongly depends on the applied pressure. Solids and liquids are called condensed phases, and have little unoccupied space. Gases, in contrast, consist of particles that are generally far apart from one another. Liquids and gases, because they can change their shape, are classified as fluids. State of matter Volume Shape solid fixed volume fixed shape liquid fixed volume fluid shape gas volume depends on pressure fluid shape ice liquid water water vapor Types of Substances Pure substance - A substance with fixed composition and properties (both physical and chemical properties). For example, methane is a pure substance that is 75% carbon and 25% hydrogen by mass, that is a gas at room temperature, and which can react with oxygen to form carbon dioxide and water. Mixture - A combination of two or more pure substances that have not chemically reacted. The composition of a mixture can be continuously varied over a range of values. Heterogeneous - Composition differs from place to place within the mixture. Homogeneous (solution) - Composition is the same throughout the mixture. Examples of Mixtures A mixture of iron and sulfur (heterogeneous). Mix A solution of sugar dissolved in water. (homogeneous) A mixture of solid salt and sugar crystals (heterogeneous) Air, a mixture of nitrogen (78%), oxygen (21%), argon (0.9%) and a large number of additional trace gases (homogeneous). Elements and Compounds Element - A pure substance that cannot be decomposed into more simple substances by chemical means. Compound - A pure substance that can be decomposed into two or more simple substances. Copper (II) sulfate pentahydrate copper (II) sulfate copper, sulfur, oxygen water hydrogen, oxygen Atoms and Molecules An atom is the smallest particle making up an element. When two or more atoms combine they form a molecule. Molecules are the smallest particles making up most pure chemical substances (exceptions include ionic compounds such as sodium chloride). Scientific Notation Scientific notation is a convenient method for expressing very large or very small numbers. (see Appendix I for a review of scientific notation and other basic mathematical concepts) Form: (mantissa) x 10power mantissa - a number between 1 and 10 10power - a power of 10, related to the number of places the decimal point must be shifted to the left (positive exponent) or right (negative exponent) Examples: 4135. = 4.135 x 103 0.00048 = 4.8 x 10-4 0.000000000074 m = 7.4 x 10-11 m (bond length in H2) SI (Systeme Internationale) Units SI units are the standard system of units used in science. Units are divided into two type Base (Fundamental) units (7 total) length meter m mass kilogram kg time second s electrical current ampere A temperature Kelvin K amount of substance mole mol light intensity cd candala These units are sometimes called MKS (meter/kilogram/seconds) units Derived units - Formed from combinations of one or more fundamental units. Examples: Area = (length) . (width) = m2 Volume = (length) . (width) . (height) = m3 Density = mass/volume = kg/m3 Velocity = distance/time = m/s Energy = Joule = kgm2/s2 In principle all physical quantities can be expressed in SI base (fundamental) or derived units. In practice, other units (metric and nonmetric) are often used. Metric System In science, the units used to express values for physical properties are usually metric units. In a metric system different units for the same property are related in a regular manner. Metric unit = (prefix) + (base unit) prefix factor giga 1,000,000,000 or 109 mega 1,000,000 or 106 kilo 1,000 or 103 deci 0.1 or 10-1 centi 0.01 or 10-2 milli 0.001 or 10-3 micro 0.000001 or 10-6 nano 0.000000001 or 10-9 pico 0.000000000001 or 10-12 symbol G M k d c m n p Metric System (Example) The base unit for length is the meter (m). So: 1 gigameter (Gm) = 1000000000 m = 109 m 1 megameter (Mm) = 1000000 m = 106 m 1 kilometer (km) = 1000 m = 103 m 1 decimeter (dm) = 0.1 m = 10-1 m 1 centimeter (cm) = 0.01 m = 10-2 m 1 millimeter (mm) 0.001 m = 10-3 m 1 micrometer (m) = 0.000001 m = 10-6 m 1 nanometer (nm) = 0.000000001 m = 10-9 m 1 picometer (pm) = 0.000000000001 m = 10-12 m One can interconvert between any two metric units for the same property simply by an appropriate change in the power of 10. Volume m3 (cubic meters; derived SI unit) L (liters) volume occupied by a cube with 10 cm sides cm3 (cubic centimeters) volume occupied by a cube with 1 cm sides) Conversions 1. m3 = 1000. L (exact) 1. L = 1000. mL (exact) 1. L = 1000. cm3 (exact) 1. mL = 1. cm3 (exact) 1. m3 = 106 cm3 (exact) Temperature Scales Centigrade (Celsius) 0 C (normal freezing point of water) 100 °C (normal boiling point of water) Fahrenheit 32 F (normal freezing point of water) 212 F (normal boiling point of water) Kelvin (SI unit) 0 K (absolute zero - lowest possible temperature) 273.15 K (normal freezing point of water) 373.15 K (normal boiling point of water) Relationships Among Temperature Scales Conversions T(K) = T(C) + 273.15 T(°C) = T(K) - 273.15 T(°F) = 9/5 T(°C) + 32 T(°C) = 5/9 [ T(°F) - 32 ] Example The highest and lowest official recorded temperatures (1895 present) for Miami are: high temperature low temperature 100. °F (July 21, 1942) 27. °F (February 3, 1917) Express these temperatures in °C. Example The highest and lowest official recorded temperatures (1895 present) for Miami are: high temperature low temperature 100. °F (July 21, 1942) 27. °F (February 3, 1917) Express these temperatures in °C. T(°C) = 5/9 [ T(°F) - 32 ] So high T(°C) = 5/9 [ 100 - 32 ] = 37.8 °C (38. °C) low T(°C) = 5/9 [ 27 - 32 ] = - 2.8 °C (- 3. °C) Chemical and Physical Property Chemical property - A property involving the chemical transformation of a substance. Physical property - A property that does not involve the chemical transformation of a substance Examples: The normal boiling point of benzene is 80.1 C (physical) Carbon can react with oxygen to form carbon dioxide (chemical) The density of liquid water is 1.00 g/mL (physical) Iron metal rusts in the presence of oxygen and water (chemical) Intensive and Extensive Property Properties can often be divided into two categories Extensive property - Value depends on the size of the system Intensive property - Value does not depend on the size of the system Extensive - mass volume Intensive - temperature density (mass/volume) Precision and Accuracy Precision is a measure of how close successive independent measurements of the same quantity are to one another. Accuracy is a measure of how close a particular measurement (or the average of several measurements) is to the true value of the measured quantity. Good precision; poor accuracy Good precision, good accuracy Significant Figures The total number of digits in a number that provide information about the value of a quantity is called the number of significant figures. It is assumed that all but the rightmost digit are exact, and that there is an uncertainty of ± a few in the last digit. Example: The mass of a metal cylinder is measured and found to be 42.816 g. This is interpreted as follows 42.816 error is ± 1 or 2 considered as certain 42.81623 Number of significant figures is 5 Result known to a higher degree of precision Examples Level of liquid = 4.58 mL Temperature = 103.4 oC Rules For Counting Significant Figures 1) All nonzero digits are significant (28.548 = 5 sig figs; 189. = 3 sig figs)) 2) All zeros located between nonzero digits are significant (302.8 = 4 sig figs; 21.033 = 5 sig figs) 3) Zeros to the left of the first nonzero digit are not significant (0.004108 = 4 sig figs; 0.075 = 2 sig figs) 4) Zeros to the right of the last nonzero digit are significant if the number contains a decimal point (3.80 = 3 sig figs; 18000. = 5 sig figs) 5) Zeros to the right of the last nonzero digit in a number without a decimal point may or may not be significant (6700 = 2, 3, or 4 sig figs, as zeros might be placeholders) Note that exact numbers have an infinite number of significant figures. Example: 1 dozen = 12 (exact) Counting Significant Figures (Examples) 3.108 0.00175 7214.0 4000. 34000 Counting Significant Figures (Examples) 3.108 4 significant figures 0.00175 3 significant figures (zeros are placeholders) 7214.0 5 significant figures 4000. 4 significant figures 34000 2, 3, 4, or 5 significant figures (some or all zeros may be placeholders) We can always make clear how many significant figures are present in a number by writing the number in scientific notation. 3.4 x 104 2 significant figure 3.40 x 104 3 significant figures Significant Figures in Calculations There are two general cases. Multiplication and/or division - The number of significant figures in the result is equal to the smallest number of significant figures present in the numbers used in the calculation. Example. For a particular sample of a solid, the mass of the solid is 34.1764 g and the volume of the solid is 8.7 cm3. What is the value for D, the density of the solid? D = mass = 34.1764 g = 3.9283218 g/cm3 = 3.9 g/cm3 volume 8.7 cm3 Addition and/or subtraction. The result carries the same number of decimal places as the quantity in the calculation with the fewest decimal places. Example. The masses for three rocks are 24.18 g, 2.7684 g, and 91.8 g. What is the combined mass of the rocks? 24.18 g 2.7684 g 91.8 g 118.7484 g = 118.7 g Additional Cases 1) For calculations involving both addition/subtraction and multiplication/division the rules for significant figures are applied one at a time, rounding off to the correct number of significant figures at the end of the calculation. Example. (46.38 - 39.981) = 13.821 6.399 = 0.4629911 = 0.463 13.821 If we had stopped the above calculation after subtracting the two numbers in parentheses we would have rounded the result to 6.40. While you should keep track of significant figures as you do calculations it is a good idea not to round off until you get to the final answer, to avoid roundoff error. 2) Significant figures for other kinds of mathematical operations (logarithm, exponential, etc.) will be discussed when appropriate. Rounding Numbers In the above calculations we had to round off the results to the correct number of significant figures. The general procedure for doing so is as follows: 1) If the first digit dropped is 4 or less, round down. 2) If the first digit dropped is 5 or more, round up. Examples: Correctly round each of the following numbers as indicated. 3.4682 to 3 sig figs 18.4513 to 4 sig figs 1.4500 to 2 sig figs 6.3499 to 2 sig figs Examples: Correctly round each of the following numbers as indicated. 3.4682 to 3 sig figs 3.47 18.4513 to 4 sig figs 18.45 1.4500 to 2 sig figs 1.5 6.3499 to 2 sig figs 6.3 Conversion Factors and Dimensional Analysis A conversion factor converts a number from one set of units to another set of units. Dimensional analysis is the process used to check that the correct final units are obtained in a calculation. Example: Based on our metric relationships we know 1000. mL = 1. L We can find two conversion factors from this relationship 1000. mL = 1. L Divide by 1. L 1000. mL = 1. L = 1 1. L 1. L Divide by 1000. mL 1. L = 1000. mL = 1 1000. mL 1000. mL Since multiplying a number by 1 does not change the value of that number, multiplying by 1000. mL/1. L or 1. L/1000. mL also does not change the value of the number, only the units in which the value is expressed. For example, to convert 46.8 mL to L # L = 46.8 mL 1L = 0.0468 L = 4.68 x 10-2 L 1000. mL We can also use relationships to convert between units that apply to different types of quantities (mass and volume, for example). Example. The density of silver iodide is 5.69 g/cm3. the mass of a pure sample of silver iodide is 48.316 g. What is the volume occupied by this sample? V = 48.316 g 1. cm3 = 8.49 cm3 5.69 g Notice in this case we used our conversion factor to go from one type of quantity (mass) to a different type of quantity (volume). Dimensional Analysis Dimensional analysis is the process used to make sure the dimensions that appear in the result of a calculation are correct. Example: How many inches are there in 75.8 cm? Since 1 in = 2.54 cm, there are two conversion factors we can construct. 1. in 2.54 cm = 1 2.54 cm 1. in So # in = 75.8 cm 1. in = 29.8425… = 29.8 in 2.54 cm # in = 75.8 cm 2.54 cm = 192.532 = 193. cm2/in ?!? 1. in Conversion Factors (Example) The Washington Monument is 555.4 feet high. What is the height of the monument in meters? height(m) = 555.4 ft 12 in 2.54 cm 1 m = 169.28592 m = 169.3 m 1 ft 1 in 100 cm (note all conversion factors are exact) height(m) = 555.4 ft 12 in 2.54 cm 1 m m 1 ft 1 in 100 cm Practice Problems 1) The normal boiling point for nitrogen (N2) is - 195.8 °C. Express this temperature in °F and K. 2) The density of liquid mercury (Hg) is 13.594 g/cm3. Give the density in the appropriate SI units. 3) What is the conversion factor between in3 (cubic inches) and cm3 (cubic centimeters)? 1) The normal boiling point for nitrogen (N2) is - 195.8 °C. Express this temperature in °F and K. We use the equations for converting between temperature scales. T(K) = T(C) + 273.15 = (- 195.8) + 273.15 = 77.35 = 77.4 K T(°F) = 9/5 T(°C) + 32 = 9/5 (- 195.8) + 32 = - 320.44 = - 320.4 °F 2) The density of liquid mercury (Hg) is 13. 594 g/cm3. Give the density in the appropriate SI units. The SI unit for density (a derived unit) is kg/m3. Therefore D = 13.594 g cm3 1 kg 100 cm 100 cm 100 cm = 13594. kg/m3 1000 g 1 m 1m 1m = 1.3594 x 104 kg/m3 3) What is the conversion factor between in3 (cubic inches) and cm3 (cubic centimeters)? # cm3 = 1 in3 2.54 cm 2.54 cm 2.54 cm = 16.387064 cm3 1 in 1 in 1 in Note that the above is an exact conversion factor, since the relationship 1 in = 2.54 cm is exact. End of Chapter 1 Chemistry. From the word alchemy, from Old French alkemie, from Middle Latin alkimia, from Arabic al-kimiya, from Greek khemeioa (found about 300 AD in a decree of Diocletian against "the old writings of the Egyptians"), all meaning "alchemy." Perhaps from an old name for Egypt (Khemia, literally "land of black earth," found in Plutarch), or from Greek khymatos "that which is poured out," from khein "to pour," related to khymos "juice, sap." The word seems to have elements of both origins. - from The Online Etymology Dictionary “A tidy laboratory means a lazy chemist.” - Jöns Jacob Berzelius “Research is what I'm doing when I don't know what I'm doing.” - Wernher Von Braun