Gas Laws - Problem Set #4

Honors Chemistry I

Gas Laws - Problem Set #4

Solution Set

1. When 2.00 moles of helium gas effuses, it takes 56.0 sec. An unknown gas takes 88.0 sec. for 2.00 moles of this gas to effuse. What is the molecular weight of this unknown gas?

Time He / Time X = 56.0 sec / 88.0 sec = (4.0 g/mol)/ MWUnknown

MWX = 9.9 g/mol

2. What is the density of sulfur dioxide gas at 35.5 in. Hg and 305oC?

D = (MW)(P) / RT = [(64.1 g/mol)(35.5 / 29.92)] / [(0.0821)(578 K)]

D = 1.60 g/liter

3. What is the partial pressure of argon in a system that contains 45.0 grams of water vapor, 22.1 grams of argon, and 35.4 grams of carbon dioxide? The total pressure of the system is 223 kPa.

45.0 g H2O = 2.50 mol; 22.1 g Ar = 0.554 mol; 35.4 g CO2 = 0.805 mol

PAr = XAr Ptotal = (0.554 mol / 3.86 mol)(223 kPa) = 32.0 kPa

4. How many grams of NO2 gas are needed in a 250.0 ml container to exert a pressure of 20.0 psi at a temperature of 355 K? MW = gRT / PV

g = [(46.0 g/mol)(20.0 psi / 14.7 psi)(0.2500 liters)] / [(0.0821 liter-atm/mol-K)(355 K)]

g = 0.537 grams

5. If 4.00 liters of an ideal gas has its pressure doubled and its absolute temperature quadrupled, what will be the new volume? V1P1 / T1 = V2P2 / T2

V2 = [(4.00 liters)(P1)]/T1 x [4T1 / 2P1] = 8.00 liters

6. How many times faster will phosphorus trichloride gas effuse than xenon hexafluoride?

Rate PCl3 / Rate XeF6 = MWXeF6 / MWPCl3 = (245.3 g/mol) / (137.5 g/mol)

Rate PCl3 = 1.34 times faster than the rate of XeF6

-2-

7. How many seconds will it take for 3.00 moles of hydrogen gas to effuse if it takes 34.00 seconds for 3.00 moles of chlorine gas to effuse?

Time H2 / Time Cl2 = MWHydrogen / MWChlorine = (2.0 g/mol) / (71. g/mol)

Time H2 / 34.00 sec = 0.168 => Time H2 = 5.7 sec

8. What is the molecular weight of a gas if 0.1337 grams in a 200.0 ml container exerts a pressure of 222 torr at a temperature of 309 K? MW = gRT / PV

MW = [(0.1337 g)(0.0821 liter-atm/mol-K)(309 K)] / [(222 torr / 760 torr)(0.2000 liters)]

MW = 58.1 g/mol

9. What is the partial pressure of gas C if the total pressure of a three gas system is 24.5 cm Hg? Gas A is known to have a partial pressure of 125 mm Hg and gas B has twice the partial pressure of gas C.

PB = 2X PC = X Ptotal = 245 mm = 125 mm + X + 2X

PC = X = 40 mm

10. To what temperature (oC) must 45.00 liters of a gas originally at -200oC be raised in order to increase the volume to 100.0 liters? V1 / T1 = V2 / T2

T2 = V2 x T1 / V2 = (100.0 liters)(73 K) / (45.00 liters)

T2 = 162 K = - 111oC

11. What is the density of hydrogen chloride gas at STP conditions?

D = 36.5 g/mole x 1 mole / 22.4 liters =

D = 1.63 g/liter