Multiple Choice
An unknown gas occupies a volume of 1250 mL at 26°C and 705 torr. If the mass is 2.37 g, what is the molar mass of the gas? (R = 0.0821 L·atm/mol·K)
7. Gases
The Ideal Gas Law: Molar Mass
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What is the molar mass of a gas if a 0.212 g sample takes up a volume of 99.056 mL at 122°C and 1.02 atm pressure?
A
32.00 g/mol
B
44.01 g/mol
C
28.02 g/mol
D
16.04 g/mol
Verified step by step guidance1
Convert the temperature from Celsius to Kelvin by adding 273.15 to the given temperature: \( T(K) = 122 + 273.15 \).
Convert the volume from milliliters to liters by dividing by 1000: \( V(L) = 99.056 \text{ mL} / 1000 \).
Use the ideal gas law equation \( PV = nRT \) to solve for the number of moles \( n \). Rearrange the equation to \( n = \frac{PV}{RT} \), where \( P \) is the pressure in atm, \( V \) is the volume in liters, \( R \) is the ideal gas constant \( 0.0821 \text{ L atm/mol K} \), and \( T \) is the temperature in Kelvin.
Substitute the known values into the rearranged ideal gas law equation to calculate the number of moles \( n \).
Calculate the molar mass by dividing the mass of the gas sample by the number of moles: \( \text{Molar Mass} = \frac{\text{mass (g)}}{n} \).
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