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Chem 121 Problem Set 1 - 1 Chem 121 - Problem Set I: Significant Figures, Error Analysis and Dimensional Analysis 1) How many significant figures? (i) 0.0276 (ii) 1.670 x 106 (iii) 0.05670 (iv) 6.0001 (v) 1.000 (vi) 100.0 (vii) 100 2) If A = 18.6 ± 0.1 and B = 126.0 ± 0.5, calculate the following, including calculation of the error. (i) A+B= (ii) B/A = (iii) A2 = (iv) 100 x A = 3) Solve the equation and give your answer to the correct number of significant figures. The 1 in (1-x) is exact. 1.429x + 1.063(1-x) = 1.21 4) Do the following calculations and express your answers in scientific notation to the correct number of significant figures. 2045 kg − 0.21kg 492.7(0.4971− 0.00064) a) b) 10.421cm − 4.9 cm 3 3 7.634 x 103 + 6 5) Do the following calculations and express your answers to the correct number of significant figures and include the absolute error. a) The density of a liquid can be determined by weighing a volume of liquid dispensed from a burette. Initial burette reading 0.01 ± 0.02 ml Final burette reading 10.42 ± 0.02 ml Mass of beaker 143.2174 ± 0.0001 g Mass of beaker + liquid 151.8647 ± 0.0001 g b) The density of a piece of metal can be determined by measuring the volume that a known mass of metal displaces in a graduated cylinder partially filled with water. Initial balance reading 0.00 ± 0.01 g Final balance reading 34.08 ± 0.01 g Initial cylinder volume 14.2 ± 0.1 ml Final cylinder volume 17.1 ± 0.1 ml 6) In the opening scenes of the movie 'Raiders of the Lost Ark'. Indiana Jones tries to remove a gold idol from a booby-trapped pedestal. He replaces the idol with a bag of sand of approximately equal volume. (Density of gold = 19.32 g/cm3; density of sand = 3 g/cm3.) a) Did he have a reasonable chance of not activating the mass sensitive booby trap? b) In a later scene he and an unscrupulous guide play catch with the idol. Assume the volume of the idol is about 1 L. If it were solid gold, what mass would the idol have? Is playing catch with it plausible? For the following conversions use scientific notation when appropriate and record your answer to the correct number of significant figures. 7. The circumference of the earth is 2.5 x 104 miles at the equator. What is the circumference in meters? 8. The fastest recorded fastball had a velocity of 100.8 mi/h. a) Calculate the velocity in m/s. b) How long would it take for this pitch to travel the 60 ft 6 in from the mound to the home plate? 9. How many square feet (ft2) correspond to an area of 1.00 square meter (m2)? Chem 121 Problem Set 1 - 2 10. What is the volume in litres, occupied by 50.0 kg of ethanol at 20°C? The density of ethanol at 20°C is 0.789 g/cm3. h 11. The de Broglie wavelength of an electron is given by: λ= mv h is Planks Constant = 6.63 x 10-34 ± 0.01 x 10-34 kg m2 s-1 m is the electron's mass = 9.11 x 10-31 ± 0.03 x 10-31 kg v is the electron's velocity = 7.3 x 107 ± 0.8 x 107 m s-1 Calculate the electron's wavelength and associated error. 12. A solution containing 72.7 mL of liquid A and 59.4 mL of liquid B, has a density of 1.024 g/mL. On adding a further 60.0 mL of liquid B to the mixture, the density increases to 1.1301 g/mL. Assuming that volumes are additive, calculate the densities of both liquids.