alleryStart learning →A gas has a density of 0.0847 g/L at 17.0 degrees C and 760 torr. What is its molar mass?
A4.00 g/mol
B28.0 g/mol
C2.02 g/mol
D32.0 g/mol
Answer & Solution
Correct answer: C. 2.02 g/mol
1. Density equals PM over RT, so rearranged the molar mass M equals density times R times T divided by P.
2. Convert the temperature to kelvin: 17.0 + 273 = 290 K.
3. Convert the pressure to atmospheres: 760 torr / 760 torr per atm = 1.00 atm.
4. Multiply density by R: 0.0847 g/L x 0.0821 L atm/mol K = 0.006954 g atm per mol per K.
5. Multiply by the temperature: 0.006954 x 290 = 2.02 g per mol per atm.
6. Divide by 1.00 atm to get M = 2.02 g/mol.
7. That molar mass identifies the gas as hydrogen, and the option 4.00 g/mol is helium, the next lightest, offered as a near miss.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 9 "Gases", section 9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions_
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