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?
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7. Gases
The Ideal Gas Law: Molar Mass
Multiple Choice
An unknown gas has a density of 2.00 g/L at 1.00 atm and 25.0 °C. What is the molar mass of the gas?
A
2.00 g/mol
B
32.0 g/mol
C
22.4 g/mol
D
48.9 g/mol
Verified step by step guidance1
Identify the known variables: density (d) = 2.00 g/L, pressure (P) = 1.00 atm, temperature (T) = 25.0 °C. Convert temperature to Kelvin using the formula \(T(K) = T(°C) + 273.15\).
Recall the ideal gas law equation: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.
Express the number of moles \(n\) in terms of mass and molar mass: \(n = \frac{m}{M}\), where \(m\) is mass and \(M\) is molar mass.
Use the definition of density \(d = \frac{m}{V}\) to rewrite the ideal gas law in terms of density and molar mass: starting from \(P V = \frac{m}{M} R T\), rearrange to get \(M = \frac{d R T}{P}\).
Substitute the known values for \(d\), \(R\) (use \$0.0821\( L·atm/mol·K), \)T\( (in K), and \)P\( into the equation \(M = \frac{d R T}{P}\) to solve for the molar mass \)M$.
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