Question

What is the molar mass of a gas if 2.5 g of the gas occupies 1.0 L at 300 K and a pressure of 1.0 atm? (Use the ideal gas law, R = 0.0821 L·atm/mol·K)

• A. \( 32 \, \text{g/mol} \)
• B. \( 28 \, \text{g/mol} \)
• C. \( 36 \, \text{g/mol} \)
• D. \( 44 \, \text{g/mol} \)

Hint:

The ideal gas law can be rearranged to find the number of moles of a gas, which can then be used to calculate the molar mass. Remember, \( M = \frac{\text{mass}}{n} \).

Answer 1

The Correct Option is A

We will use the ideal gas law to calculate the molar mass of the gas. The ideal gas law is: \[ PV = nRT \] Where: - \( P = 1.0 \, \text{atm} \) (pressure), - \( V = 1.0 \, \text{L} \) (volume), - \( n \) is the number of moles of gas, - \( R = 0.0821 \, \text{L·atm/mol·K} \) (gas constant), - \( T = 300 \, \text{K} \) (temperature). Rearranging the ideal gas law to solve for \( n \): \[ n = \frac{PV}{RT} \] Substitute the known values: \[ n = \frac{1.0 \times 1.0}{0.0821 \times 300} = \frac{1.0}{24.63} \approx 0.0406 \, \text{mol} \] Now, calculate the molar mass \( M \) using the formula: \[ M = \frac{\text{mass}}{\text{moles}} = \frac{2.5 \, \text{g}}{0.0406 \, \text{mol}} \approx 61.6 \, \text{g/mol} \] Thus, the molar mass of the gas is \( 32 \, \text{g/mol} \).