Calculate the molar mass for 2.50 g of an unknown gas in a 0.500-L container at a pressure of 735 mmHg and a temperature of 22℃.

• A. 12.7 g/mol
• B. 60.5 g/mol
• C. 62.6 g/mol
• D. 121 g/mol
• E. 125 g/mol

Answer: (E)

Verified step by step guidance

1. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. This is necessary because the ideal gas law requires temperature in Kelvin.
2. Use the ideal gas law equation, \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin. Rearrange the equation to solve for \( n \), the number of moles: \( n = \frac{PV}{RT} \).
3. Convert the pressure from mmHg to atm because the ideal gas constant \( R \) is typically given in terms of atm. Use the conversion factor: 1 atm = 760 mmHg.
4. Substitute the known values into the rearranged ideal gas law equation: \( P \) in atm, \( V \) in liters, \( R = 0.0821 \text{ L atm/mol K} \), and \( T \) in Kelvin, to calculate the number of moles \( n \).
5. Calculate the molar mass of the gas by dividing the mass of the gas (2.50 g) by the number of moles \( n \) calculated in the previous step. The formula for molar mass is \( \text{Molar Mass} = \frac{\text{mass}}{n} \).