Key to The Molar Mass and Density of Gases
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1. A gas sample has a mass of 3.50 grams, a volume of 300. cm , a pressure of 99.5 kPa, and a temperature of 52.0 C.
What is the gas’s density?
This one doesn’t need all the information provided.
D = 3.50 g / 0.300 L = 11.7 g/L
2. For the gas in problem 1, what would its density be at STP?
First, use the combined gas law to find the new volume at STP: (99.5 kPa)(0.300 L)
325 K
V2 = 0.248 L
Now, recalculate density: 3.50 g / 0.248 L = 14.1 g/L
=
(101.3 kPa)(V2)
273 K
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3. The density of a gas was measured at 1.50 atm and 27.0 C, and found to be 1.95 g/L. What is the molar mass of this
gas?
MM = DRT/P
(1.95 g/L)(0.08205)(300K) / (1.50 atm) = 32.0 g/mol
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4. Calculate the density of ammonia gas (NH3) at 27.0 C and 635 torr.
D = (molar mass)P/RT
(17 g/mol)(635 torr) / (62.36)(300 K) = 0.577 g/L
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5. A sample of gas takes up 30.8 dm at a temperature of 325 K and a pressure of 149 kPa. How many moles of gas are
present?
(149 kpa)(30.8 L) = (n)(8.31)(325 K)
n = 1.70 moles
6. What is the molar mass of the gas in the previous question, if 41.00 grams are present?
41.00 g / 1.70 moles = 24.1 g/mol
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7. What pressure is exerted by 0.625 moles of a gas in a 45.0 dm container at -24.0 C?
(P)(45.0 L) = (0.625 mol)(8.31)(249 K)
P = 28.7 kPa
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8. What is the density of nitrogen dioxide gas when contained at 50.0 kPa and 37.0 C?
NO2 has a molar mass of 46 g/mol.
(46 g/mol)(50.0 kPa) / (8.31)(310 K) = 0.893 g/L
9. A chemist must determine what unknown gas is present in a flask. The choices are NO 2, H2CO, and Cl2O. The data
looks like this:
Volume of flask:
524.5 mLs
Gas pressure: 681 mm Hg
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Gas temperature:
25.3 C
Mass of empty flask:
76.25 g
Mass of flask + gas:
77.13 g
What is the molar mass of this gas & what gas is it?
Mass of the gas in the flask = 77.13 g – 76.25 g = 0.88 g.
Therefore, the gas’s density = 0.88 g / 0.5245 L = 1.68 g/L (we’ll keep 2 sig figs in the final answer)
molar mass = (1.68 g/L)(62.36)(298.3 K) / (681 mm) = 46 g/mol
Compare this molar mass with the 3 unknowns: NO2 = 46 g/mol, H2CO = 30 g/mol, Cl2O = 87 g/mol.
The unknown must be NO2.
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10. 0.36 g of an unknown gas is collected at 25.5 C and 90.3 kPa. The volume of the gas is 46.5 mls. What is the molar
mass of the gas? What is the gas’s density?
D = 0.36 g / .0465 L = 7.74 g/L (a very dense gas!)
molar mass = (7.74 g/L)(8.31)(298.5 K) / (90.3 kPa) = 213 g/mol
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11. How many grams of sulfur dioxide are contained in a 200. cm flask at 12.0 C and 0.7266 atm pressure?
Find n from ideal gas law, or calculate Density: D = (64 g/mol)(0.7266 atm) / (0.08205)(285 K) = 1.99 g/L.
Find grams from D. 1.99 g/L = grams / 0.200 L
grams = 0.398 grams
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12. A sample of gas at STP has a density of 3.12 g/L. What will the gas’s density be at 21.0 C and 100.5 kPa?
First, find molar mass from the density: molar mass = (3.12 g/L)(8.31)(273K) / 101.3 kPa = 69.87 g/mol
Next, find new density from molar mass: Dnew = (69.87 g/mol)(100.5 kPa) / (8.31)(294 K) = 2.87 g/L
13. What is the density of nitrogen gas at STP (in g/L)? Hint: you don’t really need the density formula for this one!
28 g/mol / 22.4 L/mol = 1.25 g/L
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14. A gas is composed only of C and H. It has the empirical formula CH2. The gas has a density of 1.65 g/L at 27.0 C
and 734 torr.
a) What is the molar mass of this gas?
b) What is the molecular formula of this gas?
molar mass = (1.65 g/L)(62.36)(300 K) / 734 torr = 42 g/mol
molecular formula: 42 g/mol / 14 g/mol = 3
3 x CH2 = C3H6