Question

At 27°C temperature and 770 mm pressure, 243 ml of a dry gas weighs 280 mg. Determine the molecular weight of the gas.

• A. 42
• B. 14
• C. 56
• D. 28

Hint:

To find the molecular weight of a gas, use the ideal gas law and the relationship between moles, volume, and temperature.

Answer 1

The Correct Option is D

To find the molecular weight of the gas, we can use the ideal gas law and the molar volume equation. The ideal gas law is: \[ PV = nRT \] where: \( P \) is the pressure (in atmospheres), \( V \) is the volume (in liters), \( n \) is the number of moles of the gas, \( R \) is the ideal gas constant (0.0821 L·atm/(mol·K)), \( T \) is the temperature (in Kelvin). We are given:
Temperature \( T = 27^\circ C = 27 + 273 = 300 \, \text{K} \), Pressure \( P = 770 \, \text{mm Hg} = \frac{770}{760} \, \text{atm} \approx 1.013 \, \text{atm} \), Volume \( V = 243 \, \text{ml} = 0.243 \, \text{L} \), Mass of the gas \( m = 280 \, \text{mg} = 0.280 \, \text{g} \). 
Step 1: Calculate the number of moles of gas \( n \).
From the ideal gas law: \[ n = \frac{PV}{RT} \] 
Step 2: Use the molar mass formula to find the molecular weight.

The molecular weight \( M \) is given by: \[ M = \frac{\text{mass of the gas}}{n} \] Substituting the known values: \[ M = \frac{0.280 \, \text{g}}{0.010 \, \text{mol}} = 28 \, \text{g/mol} \] Thus, the molecular weight of the gas is 28 g/mol, which corresponds to (D) 28.