Question

In an experiment in a general chemistry laboratory, a student collected a sample of gas over water. The volume of the gas was 265 mL at a pressure of 753 torrs and a temperature of 27 °C. The mass of the gas was 0.472g. What was the molar mass of the gas?

Short answer

The molar mass of the gas is 45.6g/mol.

Step-by-step solution

Definition of molar mass

The mass equivalent to Avogadro's number of atoms in an element is called molar mass.

Calculating the pressure of gas

According to Dalton's law, the total pressure of 753 torrs is the sum of the partial pressure of gas and the partial pressure of gaseous water:

$$P_{\mathrm{T}}=P_{\mathrm{g}\mathrm{a}\mathrm{s}}+P_{{\mathrm{H}}_2\mathrm{O}}$$

Rearranging this equation to solve for the pressure of carbon monoxide gives:

$$P_{\mathrm{g}\mathrm{a}\mathrm{s}}=P_{\mathrm{T}}-P_{{\mathrm{H}}_2\mathrm{O}}$$

From table 9.2, the pressure of water vapor above a sample of liquid water at 27 °C is 26.7 torr, so:

$$\begin{array}{r}{P}_{\mathrm{g}\mathrm{a}\mathrm{s}}=753\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}-26.7\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}\\ =726.3\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}\end{array}$$

The pressure of a gas is 726.3 torr.

Calculate the molar mass

The equation to calculate molar mass is,

$$\begin{array}{rl}\frac{m}{V}& =\rho \\ & =\frac{PcalM}{RT}calM\\ & =\frac{mRT}{PV}\\ & =\frac{(0.472\mathrm{g})\times 0.08206\mathrm{L}\cdot \mathrm{a}\mathrm{t}\mathrm{m}/\mathrm{m}\mathrm{o}\mathrm{l}\cdot \mathrm{K}\times 300\mathrm{K}}{726\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}\times \frac{1\mathrm{a}\mathrm{t}\mathrm{m}}{760\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{r}}\times 0.265\mathrm{L}}\\ & =45.9\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}\end{array}$$

Therefore, the calculated mass is 45.9g/mol.