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

Hint:

Always keep an eye on the units! Since \(R\) is given in L atm, ensure your volume is converted from mL to Liters ($100\text{ mL} = 0.1\text{ L}$) before plugging it into the equation.

Answer 1

The Correct Option is D

To find the molar mass of the gas, we'll utilize the ideal gas law and the data provided in the question.

1. First, determine the volume of the evacuated vessel using the density of the liquid and its weight. The mass of the liquid when filled in the vessel is: \(135.0\, \text{g} - 40.0\, \text{g} = 95.0\, \text{g}\).
2. Using the density formula: \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\), we can calculate the volume of the vessel. \(\text{Volume} = \frac{95.0\, \text{g}}{0.95\, \text{g/mL}} = 100.0\, \text{mL} = 0.100\, \text{L}\).
3. Next, calculate the mass of the gas using the weight of the vessel filled with gas: \(40.5\, \text{g} - 40.0\, \text{g} = 0.5\, \text{g}\).
4. Apply the ideal gas law: \(PV = nRT\), where \(P = 0.82\, \text{atm}\), \(V = 0.100\, \text{L}\), \(R = 0.082\, \text{L atm K}^{-1} \text{mol}^{-1}\), and \(T = 250\, \text{K}\).
5. Rearrange the formula to find \(n\), the number of moles: \(n = \frac{PV}{RT} = \frac{0.82 \times 0.100}{0.082 \times 250}\).
6. Calculate \(n\): \(n = \frac{0.082}{20.5} = 0.004 \, \text{mol}\).
7. Determine the molar mass of the gas: \(\text{Molar Mass} = \frac{\text{Mass of gas}}{\text{Number of moles}} = \frac{0.5\, \text{g}}{0.004\, \text{mol}} = 125\, \text{g/mol}\).

Therefore, the molar mass of the gas is 125 g/mol, which is the correct answer.