Stoichiometry I: Calculations Based on Formulas
LAW OF DIFFUSION AND EFFUSION
When we put two gases together, the molecules throughout the con-tainer, so that within a short time the mixture is homogeneous, or of uniform concentration throughout. Not all gases at the same rate, however: the lighter the molecule, the more rapid the process.
If different gases are put into a container at the same temperature and pressure and then allowed to effuse (leak out) through a in the con-tainer, you can compare their rates of effusion (measured in The to do this is to determine the times (t) required for equal volumes to effuse through the pinhole. The rates are just inversely proportional to the times; the shorter the time, the faster the rate. Such a comparison of any two gases shows that these rates of effusion (and diffusion) are related to the molec-ular weights of the gases according to the equation
(11-5) which is known as law of diffusion and effusion. This same relationship can be derived theoretically from the kinetic theory of gases. This equation offers a simple way to determine the molecular weights of gases.
PROBLEM:
The molecular weight of an unknown gas is found by measuring the time required for a known volume of the gas to effuse through a small pinhole, under constant pressure. The apparatus is calibrated by measuring the time needed for the same volume of wt = 32) to through the same pinhole, under the same conditions. The time found for is 60 sec, and that for the unknown gas is sec. Compute the molecular weight of the unknown gas.
SOLUTION:
If we use Graham's law, and let gas 1 be and gas 2 be the unknown gas, then
120 sec
60 sec V 3232
Problems A
By squaring both sides we get
= 12°
mole
PROBLEMS
1. A graduated tube, sealed at the upper end, has a mercury-filled leveling bulb connected to the lower end. The gas volume is 25.0 ml when the mercury level is the same both tubes. The barometric pressure is 732 torr. What is the volume when the level on the open side is 10.0 cm above the level of the closed side?
If a barometer were filled with a liquid of density what would be the reading when the mercury barometer read 730 torr? The density of mercury is
13.56 g/ml.
3. A mercury barometer reading of 728.3 mm is obtained at with a brass scale. What is the barometer reading "corrected to is, in torr?
4. What is the atmospheric pressure in when the barometer reading is 720 torr?
5. A student collects 265 ml of a gas over Hg at and 750 torr. What is the volume at standard conditions?
6. What is the volume at room conditions (740 torr and 25°C) of 750 ml of a gas at standard conditions?
7. A sealed vessel containing methane, at 730 torr and is put into a box cooled with "dry ice" ( What pressure will the exert under these conditions?
8. Liquid nitrogen (boiling point, - is commonly used as a cooling agent. A vessel containing helium at 10 at the temperature of boiling water is sealed and then cooled with boiling liquid nitrogen. What will be its pressure expressed in torr?
9. Two liters at 1.0 5.0 liters of at 5.0 and 3.0 liters of at 2.0 atm are mixed and transferred to a 10.0 liter vessel. What is the resulting 10. A low pressure easily achieved with a diffusion pump and a mechanical vac-uum pump is x torr. Calculate the number of molecules still present in 1.00 ml of gas at this pressure and at
A sample of nitrous oxide is collected over water at and 735 torr. The volume is 235 ml. What is the volume at standard conditions?
168 Gases 12 (a) What volume 0 500 g of occupy at 750 torr 26°C over
(b) What volume occupy collected over mercury at the same condi-13 A sample of tested for purity by heating an excess of
and collecting the evolved over water The volume collected 567 3 ml at a barometric pressure of 741 torr The temperature 22°C What volume would the dry, occupy at
14 What the weight of 250 ml of measured 740 torr and
What volume be occupied by I 00 g of measured over water at 27°C and 730
What the molecular weight of a gas 250 ml measured over water at torr and 28°C weighs 1 25
17 What the density of chlorine gas at 83°F and 723
18 Calculate the density of (a) at standard conditions, (b) at 730 torr and dry
19 It found experimentally that 0 563 g of a vapor at 100°C and 725 torr has a volume of 265 ml the molecular weight
20 A compound has the formula What volume 1 00 g of material have at 735 torr and
What the apparent mole weight of a gas mixture composed of 20 0%
70 0% and 10 0% (Composition given by volume ) 22 An oxygen-containing gas mixture at 1 00 subjected to the action of
yellow phosphorus, which removes the oxygen In way found that oxygen makes up 35 0% by volume of the mixture What the partial pressure of the
23 A mixture of gases contained a vessel at 0 500 atm found to comprise 0% 50 0% and 35 0% by volume
(a) What the partial pressure of each
(b) A of solid added to remove the Calculate the resulting total pressure, and the pressures of the remaining gases
24 A vessel whose volume 235 0 ml, whose weight evacuated g + a tare vessel, filled an u n k n o w n gas at a pressure of 725 torr and a temperature of It then closed, wiped a damp and hung the balance case to come to equilibrium the tare vessel The tare vessel has about the same surface area and needed to minimize surface moisture effects second weighing 13 6109 g + the tare vessel What the mole weight of the gas
25 Two or three of a liquid that boils at about 50°C are put an Erlenmeyer flask The flask closed polystyrene stopper that has a fine glass capillary running through The gas-containing part of the flask then completely immersed a bath of boiling water, which (at the elevation of the experiment) boils at 99 2°C After a short the has been completely
Problems A 169
swept out through the capillary, and the excess liquid has boiled leav-ing the flask filled only the vapor of the liquid At point the flask removed from the boiling water cooled The vapor condenses to liquid, and rushes to fill the flask again Whereas the flask, when and dry, weighed g, after the experiment weighs g The barometric pressure during the experiment 735 torr The volume of the flask
determined by filling the flask water, inserting the stopper to
ous position, and squeezing out the excess water through the capillary The volume of water so held 263 2 ml What the mole weight of the liquid ' 26 The liquid used Problem 25 analyzed and found to be 54 5% C, 9 10% H,
36 4% O What the true molecular formula of
27 An automobile has a gauge pressure of 32 at 20°C when the prevail-ing atmospheric pressure 14 7 What the gauge pressure the temperature rises to
28 It takes 1 mm and 37 sec for a given volume of chlorine to effuse through a under given conditions of temperature and pressure How long take for the same volume of water vapor to effuse through the same hole under the same
29 Argon effuses through a hole (under prescribed conditions of temperature and pressure) at the rate of 3 0 ml/mm At what velocity xenon effuse through the same hole under the same
30 A rubber balloon weighing 5 0 g 12 inches diameter when filled hydrogen at 730 torr and 25°C How much the balloon addition to own (Assume the density of to be under these condi-tions )
(a) If the balloon of Problem 30 were filled ammonia gas under the same conditions, would
(b) If so, how much weight would
32 What must be the composition of a mixture of and inflates a balloon to a diameter of 15 inches and yet the balloon rises from a table (The balloon weighs 6 0 g, and the pressure and temperature are 740 torr and 30°C )
33 Oxygen commonly sold 6 0 steel cylinders at a pressure of 2000 (at 70°F) What weight of oxygen does such a cylinder (Assume oxygen to be an ideal gas under these conditions )
34 The average breath that an old takes when not exercising about 300 ml at 20°C and 750 torr respiratory rate about 20 breaths/mm (a) What volume of corrected to standard conditions, does an average
18-year-old breathe each
(b) What weight of does he breathe each (Assume that 21%
oxygen and 79% nitrogen by volume )
35 The percentage of normal 0 035% by volume, and that the exhaled of the average 18-year-old about 4 0%
170 Gases (a) What volume of at does the average 18-year-old
make each
(b) What weight of does he make
36 An compound containing C, H, O, and N analyzed When a sample weighing 0 01230 g burned, produces 62 of (absorbed a soda-lime tube) and 7 62 mg of a tube containing
When another sample, weighing 0 l ( ) g , burned, the
are absorbed, and the formed collected a measuring tube At 730 and 22°C, the gas displaces an equal volume of mercury, which weighed and found to weigh 000 g The density of mercury 13 56 Calculate the empirical formula of the compound
PROBLEMS B
37 A graduated gas tube, sealed at the upper end, has a mercury filled leveling bulb connected to the lower end The gas volume 17 2 ml when the leveling bulb 8 cm above the other mercury level What be the gas volume when the leveling bulb 8 cm below the other mercury The barometric pressure 738 torr
38 If a barometer were filled a fluid whose vapor pressure very low but whose density 1 15 g/ml, what would be the barometer reading when the atmospheric pressure (The density of mercury 56 g/ml )
39 A gas pressure measured as 826 4 mm a mercury manometer a lab whose temperature 24°C A brass scale used Express gas pressure torr
40 A gas pressure 690 torr What pressure
What the volume at 730 torr and 27°C of 350 ml of at standard
condi-42 A 50 0 ml quartz vessel filled at 300 torr and at 35°C It then heated to an electric furnace What be the oxygen pressure at the higher
43 A sample of collected over mercury measures 595 ml at 19°C and 755 torr What be volume at standard
44 What be the final gas pressure when 3 0 liters of CO at 2 0 atm, 6 0 liters of Ar at 4 0 atm, and 2 0 liters of at 5 0 atm are mixed and transferred to a 8 0 liter
45 A 375 ml sample of hydrogen collected over water at 18 C and 720 torr What volume at standard
46 What be the difference volume occupied by 0 g of hydrogen at 740 torr and collected over water instead of
Problems B 171
47. A mixture of copper and zinc is analyzed for the percentage of zinc by adding an excess of and collecting the evolved over water. (Copper will not react with HCl.) The volume of collected is 229.5 ml at a barometric pressure of 732 The temperature is 29°C. What volume would the occupy at standard conditions, dry?
48. In some recent work at the Bell Telephone Research a low pressure of torr of mercury was used. This is an unusually low pressure, one not easily obtained. Calculate the number of molecules still remaining in 1 ml of gas at this pressure at 27°C.
49. A 1 g sample of helium occupies 5.6 liters at standard conditions. What will be its weight when expanded to a pressure of atm?
50. What volume will 5.00 g of methyl alcohol, occupy at 720 torr and 98°C?
51. What is the weight of 420 ml of measured at 735 torr and 27°C?
52. What volume will be occupied by 2.50 g of CO measured over water at and 725 torr?
53. What is the molecular weight of a gas if 365 ml of it measured over water at 727 torr and 30°C weighs 1.42 g?
54. What is the density of gas at 78°F and torr?
55. Calculate the density of (a) at standard conditions; (b) at 725 torr and 27°C, dry.
56. What is the apparent mole weight of a gas mixture whose composition by
2?
57. If 0.670 g of a vapor at 100°C and 735 torr has a volume of 249 ml, what must its mole weight be?
58. A mixture of gases contained in a vessel at atm is found to be 60.0%
25.0% NO, and 15.0% by volume.
(a) What is the partial pressure of each gas?
(b) A bit of solid is added to remove the Calculate the resulting total pressure, and the partial pressures of the remaining gases.
59. A gas mixture containing is subjected, at atm, to the action of which removes the In this way, the is found to be 27.0% by volume of the mixture. What is the partial pressure of in the mixture?
60. A vessel, whose volume is 205.3 ml and whose weight evacuated is 5.3095 g + a tare flask, is filled with an unknown gas to a pressure of 750 torr at a temperature of It is then cleaned, wiped with a damp cloth, and hung in the balance case to come to equilibrium with the tare vessel. The tare vessel has about the same surface area and is needed to minimize effects of surface moisture. The second weighing is g + the tare flask. What is the mole weight of the gas?
172 Gases 61 Two or three of a liquid that boils about 60°C are put an Erlenmeyer flask The flask closed a polystyrene stopper that has a fine glass capillary running through The gas-containing part of the flask then completely immersed a bath of boiling water, which (at the elevation of the experiment) boils at 98 8°C After a short the has been completely swept out through the capillary, and the excess liquid has boiled away, leav-ing the flask filled only the vapor of the liquid At point the flask removed from the boiling water and cooled The vapor condenses to liquid and rushes to fill the flask again The flask, when dry and empty had weighed 39 5762 g, after the experiment weighs 40 3183 g The barometric pressure during the experiment 730 The volume of the flask deter-mined by filling the flask water, inserting the stopper to previous position, and squeezing out the excess water through the capillary The
of water so held 239 6 ml What the mole weight of the
62 The liquid used Problem 61 analyzed and found to be 24 2% 4 05% H, and 71 7% What the true molecular formula of
63 An automobile has a gauge pressure of 35 0 when the atmospheric pressure 14 7 and the temperature 40°F What be gauge pressure temperature rises to
64 Hydrogen chloride effuses through a hole (under prescribed conditions of temperature and pressure) at the rate of 2 70 ml/mm At what velocity helium effuse through the same hole under the same
65 It takes 45 sec for a given volume of CO to effuse through a under given conditions of temperature and pressure How long take for the same volume of vapor to effuse through the same hole under the same
66 Under certain prescribed conditions, effuses through a pinhole at the rate of 3 65 ml/mm A mixture of CO and effuses through the same pinhole under the same conditions at the rate of 3 21 ml/mm Calculate the percentage of CO the gas mixture
67 A rubber balloon weighing 10 g 15 inches diameter when inflated helium at 735 torr and How much weight the balloon addition to own (Assume the density of to be 1 20 under these conditions )
68 If the balloon of Problem 67 were filled methane, at 735 torr and would If so, how much additional weight would
69 A mixture of and has a density of 0 267 g/hter at 700 torr and For mixture, calculate (a) the apparent molecular weight, (b) the percentage composition by volume, and (c) the number of molecules one ml
70 Show the mathematical steps needed order to combine Boyle s and Charles' laws to Equation 11-2 on p 159
71 Use the methods of calculus to combine Boyle's and Charles' laws to Equation on p 159