Calculate the molar mass of an unknown gas if its average speed is 920 m/s at 303 K.

• A. 0.0105 kg/mol
• B. 0.0136 kg/mol
• C. 0.0238 kg/mol
• D. 0.0262 kg/mol
• E. 0.0281 kg/mol

Answer: (C)

Verified step by step guidance

1. Start by understanding the relationship between the average speed of gas molecules and their molar mass using the formula for root-mean-square speed: \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( v_{rms} \) is the root-mean-square speed, \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass.
2. Rearrange the formula to solve for molar mass \( M \): \( M = \frac{3RT}{v_{rms}^2} \). This will allow you to calculate the molar mass using the given average speed.
3. Substitute the known values into the equation: \( R = 8.314 \text{ J/(mol·K)} \), \( T = 303 \text{ K} \), and \( v_{rms} = 920 \text{ m/s} \).
4. Calculate \( v_{rms}^2 \) by squaring the average speed: \( v_{rms}^2 = (920 \text{ m/s})^2 \).
5. Plug the values into the rearranged formula \( M = \frac{3 \times 8.314 \times 303}{920^2} \) to find the molar mass of the gas.