At 150 °C and 1.00 atm, 500 mL of a vapor has a mass of 0.8365 g. What is the molecular weight of the compound?

Question

Quizplus · Accepted Answer

The molecular weight can be calculated using the ideal gas law, $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is the temperature in Kelvin. First, convert the temperature to Kelvin: $150 °C + 273.15 = 423.15 K$. The volume should be in cubic meters for standard units, so $500 mL = 0.0005 m^3$. The gas constant $R = 8.314 \frac{m^3 \cdot Pa}{K \cdot mol}$, but since the pressure is given in atm, we use the value of $R = 0.0821 \frac{L \cdot atm}{K \cdot mol}$ for convenience, converting the volume to liters. Solving for $n$, we get $n = \frac{PV}{RT} = \frac{(1.00 \, \text{atm})(0.500 \, \text{L})}{(0.0821 \, \frac{\text{L} \cdot \text{atm}}{\text{K} \cdot \text{mol}})(423.15 \, \text{K})}$. The mass of the gas is given as 0.8365 g, so the molecular weight (MW) is the mass divided by the number of moles. Plugging in the numbers, we find that the molecular weight is closest to 58.1 g/mol, making option D correct.