Page 200 - Theory and Problems of BEGINNING CHEMISTRY

CHAP. 12] GASES 189

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12.25. Calculate the volume of 0.193 mol of a gas at 27 C and 825 torr.
nRT (0.193 mol)[0.0821 L·atm/(mol·K)](300 K)
Ans. V = = = 4.38 L
P (825 torr)(1 atm/760 torr)
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12.26. Calculate the volume of 1.00 mol of H 2 O at 1.00-atm pressure and a temperature of 25 C.
Ans. Water (H 2 O) is not a gas under these conditions, and so the equation PV = nRT does not apply. (The ideal
gas law can be used for water vapor, e.g., water over 100 C at 1 atm or water at lower temperatures mixed
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with air.) At 1-atm pressure and 25 C, water is a liquid with a density about 1.00 g/mL.
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18.0g 1mL
1.00 mol = 18.0mL
1 mol 1.00 g
12.27. Calculate the number of moles of a gas that occupies 4.00 L at 303 K and 1.12 atm.
PV (1.12 atm)(4.00 L)
Ans. n = = = 0.180 mol
RT [0.0821 L·atm/(mol·K)](303 K)
12.28. Calculate the number of moles of gas present in Problem 12.18d.
Ans. Since the number of moles of gas does not change during the process of changing from state 1 to state 2,
either set of data can be used to calculate the number of moles of gas. Since all three values are given for
state 1, it is easier to use that state:
PV (1.00 atm)(4.00 L)
n = = = 0.178 mol
RT [0.0821 L·atm/(mol·K)](273 K)
12.29. (a) Compare qualitatively the volumes at STP of 6.8 mol N 2 and 6.8 mol H 2 .(b) Compare the volumes
at STP of 6.8 g N 2 and 6.8 g H 2 .
Ans. (a) Since the pressures, temperature, and numbers of moles are the same, the volumes also must be the same.
(b) The number of moles of nitrogen is less than the number of moles of hydrogen because its molar mass
is greater. Since the number of moles of nitrogen is less, so is its volume.

12.30. Calculate the volume of 7.07 g of helium at 27 C and 1.00 atm.
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1 mol He

Ans. 7.07gHe = 1.77 mol He
4.00gHe
nRT (1.77 mol)[0.0821 L·atm/(mol·K)](300 K)
V = = = 43.6L
P 1.00 atm
12.31. Repeat the prior problem, using hydrogen gas instead of helium. Explain why the occurrence of hydrogen
gas in diatomic molecules is so important.
Ans. n = 3.51 mol V = 86.5L
The gas laws work with moles of molecules, not atoms. It is necessary to know that hydrogen gas occurs in
diatomic molecules so that the proper number of moles of gas may be calculated from the mass of the gas.

DALTON’S LAW OF PARTIAL PRESSURES
12.32. What is the total pressure of a gas mixture containing He at 0.173 atm, Ne at 0.201 atm, and Ar at
0.550 atm?
Ans. P total = P He + P Ne + P Ar = 0.173 atm + 0.201 atm + 0.550 atm = 0.924 atm

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12.33. What is the pressure of H 2 if 0.250 mol of H 2 and 0.120 mol of He are placed in a 10.0-L vessel at 27 C?
Ans. The presence of He makes no difference. The pressure of H 2 is calculated with the ideal gas law, using the
number of moles of H 2 .
nRT (0.250 mol)[0.0821 L·atm/(mol·K)](300 K)
P = = = 0.616 atm
V 10.0L