Question

biphenyl, $\text{c}_{12}\text{h}_{10}$, is a nonvolatile, nonionizing solute that is soluble in benzene, $\text{c}_{6}\text{h}_{6}$.
at $25 ^{circ}\text{c}$, the vapor pressure of pure benzene is 100.84 torr. what is the vapor pressure of a solution made from dissolving 13.4 g of biphenyl in 29.4 g of benzene?
$p_{solution} = square$ torr

Explanation:

Step1: Calculate molar mass of biphenyl

Molar mass of $\text{C}_{12}\text{H}_{10}$: $12\times12 + 10\times1 = 154\ \text{g/mol}$

Step2: Calculate moles of biphenyl

$n_{\text{biphenyl}} = \frac{13.4\ \text{g}}{154\ \text{g/mol}} \approx 0.08701\ \text{mol}$

Step3: Calculate molar mass of benzene

Molar mass of $\text{C}_{6}\text{H}_{6}$: $6\times12 + 6\times1 = 78\ \text{g/mol}$

Step4: Calculate moles of benzene

$n_{\text{benzene}} = \frac{29.4\ \text{g}}{78\ \text{g/mol}} \approx 0.3769\ \text{mol}$

Step5: Calculate mole fraction of benzene

$X_{\text{benzene}} = \frac{n_{\text{benzene}}}{n_{\text{benzene}}+n_{\text{biphenyl}}} = \frac{0.3769}{0.3769+0.08701} \approx 0.812$

Step6: Apply Raoult's Law

$P_{\text{solution}} = X_{\text{benzene}} \times P^0_{\text{benzene}}$
$P_{\text{solution}} = 0.812 \times 100.84\ \text{Torr}$

Answer:

$81.9\ \text{Torr}$