Question

An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density 0.95 g mL^–1 and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K. The molar mass of the gas in g mol^–1 is: (Given : R = 0.082 L atm K^–1 mol^–1)

• A. 35
• B. 50
• C. 75
• D. 125

Answer 1

The Correct Option is D

To find the molar mass of the gas, we can use the Ideal Gas Law, which is:

PV = nRT

Where:

• P is the pressure of the gas,
• V is the volume of the gas,
• n is the number of moles of the gas,
• R is the gas constant, and
• T is the temperature in Kelvin.

First, we need to identify the volume of the vessel using the liquid's density information:

• Weight of the empty vessel = 40.0 \text{ g}
• Weight when filled with liquid = 135.0 \text{ g}
• Weight of the liquid = 135.0 - 40.0 = 95.0 \text{ g}
• Density of the liquid = 0.95 \text{ g mL}^{-1}

Using the formula for density \rho = \frac{m}{V}, we can find the volume (V) of the vessel:

V = \frac{95.0 \text{ g}}{0.95 \text{ g mL}^{-1}} = 100.0 \text{ mL} = 0.1 \text{ L}

Next, calculate the mass of the gas using:

• Weight of vessel with gas = 40.5 \text{ g}
• Weight of gas = 40.5 - 40.0 = 0.5 \text{ g}

Now, apply the Ideal Gas Law to find the number of moles (n):

P = 0.82 \text{ atm}

T = 250 \text{ K}

R = 0.082 \text{ L atm K}^{-1} \text{ mol}^{-1}

n = \frac{PV}{RT} = \frac{0.82 \times 0.1}{0.082 \times 250}

n = \frac{0.082}{20.5} = 0.004 \text{ mol}

Finally, calculate the molar mass (M) of the gas:

M = \frac{\text{mass (g)}}{n} = \frac{0.5}{0.004} = 125 \text{ g mol}^{-1}

Therefore, the molar mass of the gas is 125 g mol^–1.