Multiple Choice
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?
7. Gases
The Ideal Gas Law: Molar Mass
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To identify a homonuclear diatomic gas, a chemist weighted an evacuated flask with a volume of 3.9 L then filled it with the gas at a pressure of 2.00 atm and 29.0 ºC. The chemist then re-weighted the flask and recorded the difference in mass as 8.81 g. Identify the gas.
A
H2
B
N2
C
Cl2
D
F2
E
O2
Verified step by step guidance1
First, use the ideal gas law equation: \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( T = 29.0 + 273.15 \).
Rearrange the ideal gas law to solve for the number of moles \( n \): \( n = \frac{PV}{RT} \). Substitute the known values: \( P = 2.00 \) atm, \( V = 3.9 \) L, \( R = 0.0821 \) L·atm/mol·K, and \( T \) in Kelvin.
Calculate the molar mass of the gas using the formula: \( \text{Molar mass} = \frac{\text{mass}}{n} \), where the mass is 8.81 g and \( n \) is the number of moles calculated in the previous step.
Compare the calculated molar mass with the molar masses of the given diatomic gases (H2, N2, Cl2, F2, O2) to identify the gas. The gas with the closest molar mass to the calculated value is the correct answer.
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