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CP Chemistry 2016-2017 Unit 6 Notes Name: Accuracy Density Precision Newtons milli micro Important Vocabulary Signif figures Dimensional Analysis kilo Pascals Mega Celsius Fahrenheit SI Base unit Joules centi nano Section 6-1 Systems of measurement: Name Where it is used 1. English/Imperial USA Percent error weight Derived unit Giga Kelvin Advantages Human appendages makes estimating simple Disadvantages Difficult conversions Example units: miles, feet, inches 2. Metric Rest of the world Easy conversions Need to know prefixes Easy conversions Need to know prefixes Example units: meter, seconds, kilograms 3. System International (SI) Science Example units: meters, seconds, kilograms (note that Kelvin is used and not Celsius) The 7 SI base units Name 1 Meter 2 Second 3 Kilogram (not grams) 4 Kelvin 5 Luminous intensity 6 Ampere 7 mole Symbol Quantity it measures distance Time Mass Temperature candela Electric current Amount of substance M s kg K cd A mol Examples of standards for the SI base units: The meter is defined at the distance travelled by light in a vacuum in 1/299,792,458 seconds. One second is the time that elapses during 9,192,631,770 (9.192631770 x 10 9 ) cycles of the radiation produced by the transition between two levels of the cesium 133 atom. 1 SI derived units A Derived unit is: a combination of more than 1 base unit Examples of derived units Newton = Kgm/s2 Joule = Nm = kgm2/s2 Pascal = N/m2 unit of force unit of energy unit of pressure Density = g/cm3 Volume = m3 (note that ALL volume units are derived and that the Liter is NOT a base unit!) SI Prefixes to know Prefix Name Symbol Meaning Exponential factor Example 1 Giga G 1,000,000,000 1 x109 1 x106 m = 1 Gm 6 2 Mega M 1,000,000 1 x10 1 x106 m = 1 Mm 3 kilo K 1000 1 x103 1000m = 1km 4 centi C 0.01 1 x10-2 1 m = 100 cm 5 milli m 0.001 1 x10-3 1 m = 1x103 mm -6 6 micro µ 0.000001 1 x10 1 m = 1x106 µm 7 nano N 0.000000001 1x10-9 1 m = 1x109 nm -12 8 pico P 0.000000000001 1 x10 1 m = 1x1012 pm Converting between metric and English units(these equalities given on exam) 1 mile = 1.61 km 2.54 cm = 1 inch 2.2 lbs = 1 kg Converting between temperature scales What are the 3 temperature scales?: Celsius, Fahrenheit, Kelvin What are the equations to convert between them (given on exams)? K = °C + 273 °C = K -273 °C= (5/9)( °F – 32) °F = (9/5)( °C) + 32 Examples: a. b. T = 70 °F T = 300 K °C = (5/9)(70-32) = 21°C °C = 300 – 273 = 27°C d. T = -20 °F °C = (5/9)(-20-32) = -29°C K = -29 + 273 = 244 e. 2 c. T= 100 °C 8K = 100 + 273 = 373 K f. Examples of dimensional analysis problems a. convert 5.0 km into m 5 km * 1000 m 1 km = 5000 m b. Convert 200. lbs into kg 200 lbs * 1 kg 2.2 lbs = 91 kg c. Convert 2.5 hrs into seconds 2.5 hrs * 60 min 1 hr * 60 sec 1 min = 9000 s d. Convert 4.5 mm into m 4.5 mm * 1m = 0.0045 m 1000 mm e. Convert 0.500 kg into mg 0.500 kg * 1000g 1 kg * f. Convert 5.0 miles into inches 5.0 miles * 5280 ft 1 mi g. Convert 1 yr into seconds 1 yr * 365.25 days 1 yr * * h. Convert 2.45 nJ into MJ 2.45 nJ * 1J * 9 1 x10 nJ i. Convert 75 MW into cW 75 MW * 1 x106 W 1 MW j. Convert 0.0050 µs into ks 0.0050 µs * 1 s * 1 x106 µs 1000 mg 1g 12 in 1 ft = 5.0 x105 mg = 316,800 in 24 hrs 1 day * 1 MJ 1 x 106 J = 2.45 x10-15 MJ * 100 cW 1W 1 ks = 5.0 x10-12 ks 1000 s 3 3600 s 1 hr = 75 x108 cW = 3.16 x107s Section 6-2 Density equation: density = mass/volume How to rearrange the equation: One can switch the variables V and D and cross multiply to get M = DV V = M/D Why is density important? (examples): How do metal ships float in water? Isn’t the metal more dense than the water? Why do regular sodas sink to the bottom of a cooler when diet sodas float? Density example problems (copy from board): 1. Mass of sample of zinc = 20.0 grams If the density of zinc is 7.14 g/mL, how much Volume does the zinc sample occupy? 2. A sample of gold has a volume of 40 cm3. If the density of gold is 19.3 g/mL, what is the mass of the gold sample? V = M/D = 20 g/(7.14 g/mL) = 2.80 mL M = DV = 19.3 g/mL (40 cm3) = 772 g 3.A sample of metal displaces 30.0 mL of water. If the mass of the sample is 210. grams, is the sample zinc? 4. A cube of aluminum has a length of one side of 4.0 cm. What is the mass of the cube? The density of aluminum is 2.7 g/cm3. D = m/v = 210/30 = 7.0 g/cm3; yes V cube = (4.0 cm)3 = 64 cm3 M = DV = (2.7 g/cm3)(64 cm3) = 173 g 5. A gold bar is a rectangular shape and has the dimensions of 12 inches long by 4 inches high by 5 inches wide. What is the mass of this bar? V = 240 in3 240 in3 * 2.54 cm 1 in * 2.54 cm 1 in * 2.54 cm 1 in = 3933 cm3 M = DV = (19.3 g/cm3) (3933 cm3) = 75, 905 g = 75.9 kg = 167 lbs Scientific Notation Review Why we use scientific notation: to show the proper amount of significant figures. Yes, it also helps with writing large and small numbers in manageable form. Writing large numbers in scientific notation: The decimal point is moved to the LEFT until there is one non zero integer. The number of places moved is equal to the exponent. 4 Examples: 5000. = 5.0 x103 12,000,000. = 1.2 x107 Writing small numbers in scientific notation: The decimal point is moved to the RIGHT until there is one non zero integer. The number of places moved is equal to the negative exponent. Examples: 0.002 = 2.0 x10-3 0.000 000 005 = 5.0 x10-9 Adding and subtracting in scientific notation examples: The exponents must be the same to add or subtract 2.0 x105 + 1.0 x103 = 200 x103 + 1.0 x103 = 201 x103 OR 2.01 x105 Multiplying and dividing in scientific notation examples: Multiplying = add exponents; division = subtract (5.0 x102)(2.0 x103) = 5.0 x108 2.0 x10-2 Significant Figures Definition: all certain(known) digits and 1 estimated digit Reasons why we use them: 1. To relay the proper number of measured digits from a measurement 2. To convey the type of measuring instrument used What do significant figures tell us?: Examples a. Ruler 5 b. Balances 0.01 g precision = about $10.0 0.001 g precision = about $200.0 0.0001 g precision = about $2500.0 Rules for Significant Figures (SF) 1. All non zero integers are significant Examples 123 = 3 SF 512.5 = 4 SF 2. “trapped” zeros are significant 505 = 3 SF 2002.1 = 5 SF 3. “trailing” zeroes are significant UNLESS they are before a non-existent decimal point 500.000 = 6 SF 0.5050 = 4 SF 1000 = 1 SF 20 = 1 SF 5000. = 4 SF 4. “leading” zeroes are NOT significant 0.00005 = 1 SF 0.00009090 = 4 SF * note that writing these in scientific notation tells exactly how many SF there are 5. Some numbers have an infinite number of SF Pi = 3.1415…….. 2/3 = 0.66666666666…… 1 m = 100 cm is infinitely true 5 people = 5.000000000…… Determine the number of SF in the following (copy from board) a. 5.000 b. 50.00090 d. 0.005 e. 20.0 grams g. 10.0 h. 32.0050 j. 100 k. 100.00050 m. 5 people n. 90.0 cars p. 0.000006 q. 6/7 6 c. 1000 mm = 1 m f. 25.00000 i. 0.909090 l. 50000 o. 2 cars r. 20.0 L Practice determining the number of SF in the following 0.50 2 0.070 2 2.000 4 90 1 1.010 4 20 apples inf 0.90901 5 0.0000910 3 100 cm = 1m inf 50 nickels inf 18.00 4 0.100000 5 0.0010010 5 800 1 1.0 0.00009 1000 50. 12 5.0100 55.0010 2 1 1 2 2 5 6 Guidelines for rounding numbers If the last number removed is a 5 or above, then round the last number kept up one digit. If the last number removed is a 4 or below, leave the last number kept alone. Rule for adding and subtracting SF: round to the least number of decimal places in the original numbers Examples: a. 5.000 + 4.0 - 1.00 = 8.0 b. 5.0 + 9.0000 + 1. 10. c. d. 16.0 + 6. - 10.000 12. 10.00 - 6.0 + 15.00 = 19.0 Rule for multiplying and dividing SF: round to the least number of SF in the original numbers Examples: a. 10.0(5.0)(1.) c. = 5 x101 50.0(5.0)(1.00) = 2.5 x102 b. (15.00)(1.) = 3 (5.00) d. (1.000)(5.) = 5 (1.0) What happens when you have different operations in the same problem? One must separate the rules from each other and perform them separately Examples: 1. 1.000 + 2.0(5) = 1.000 + 1 x101 = 1 x101 2. 10.00 - 2.0 = 8 1.0 7 3. 50.0 – 2.0 + (40.0)(2) = 50.0 – 2.0 + 8 x101 = 128 = 1.3 x102 4. 100.0 (2.00) + 5.0 2 2 = 1 x10 + 5.0 = 1 x102 Section 6-3 Accuracy: the agreement between the observed value and the accepted/true value Precision: the agreement between different experimental values Examples of the difference between accuracy and precision: 1.Dartboards 2. A ruler: the actual length of an object is 10.0 cm a. 12.0 cm is recorded b. 12.0 cm is recorded These observations are not very accurate, but they are precise. Perhaps the person systematically read the ruler incorrectly? 8 Percent Error (know this equation – not given on exams) Why we use percent error: the determine accuracy The equation is: % error = (observed value – true/accepted value) X 100 True value Examples: 1.In an experiment, the density of water was determined to be 1.2 g/mL % error = (1.0 – 1.2) 1.0 x 100 = 20% 2. The mass of a sample of gold was recorded as 20.0 grams. When placed into a graduated cylinder with 50.0 mL of water, the volume changed to 51.5 mL. What is the percent error for the density determination? V = 51.5 – 50.0 = 1.5 mL D = m/V = 20.0g/1.5 mL = 13.3 g/mL Should be 2 SF = 13 g/mL TV = 19.3 g/mL (from earlier in the notes) % error = (13 – 19.3) x100 = - 6 x 100 = 31.09 % = 30% 19.3 19.3 9