At $\mathrm{T}(\mathrm{K})$, the vapour pressures of two liquids, heptane and octane are $106 \mathrm{kPa}$ and $47 \mathrm{kPa}$ respectively. If $25 \mathrm{~g}$ of heptane and $57 \mathrm{~g}$ of octane form an ideal solution, at $\mathrm{T}(\mathrm{K})$ the vapour pressure of solution in…

Question

At $\mathrm{T}(\mathrm{K})$, the vapour pressures of two liquids, heptane and octane are $106 \mathrm{kPa}$ and $47 \mathrm{kPa}$ respectively. If $25 \mathrm{~g}$ of heptane and $57 \mathrm{~g}$ of octane form an ideal solution, at $\mathrm{T}(\mathrm{K})$ the vapour pressure of solution in $\mathrm{kPa}$ is :

Aicharya · Accepted Answer

Calculation of Vapour Pressure of Solution The vapour pressure of an ideal solution can be calculated using Raoult's Law.

Step 1: Determine the Molar Masses

The molar mass of heptane ($\text{C}_{7}\text{H}_{16}$) is calculated as follows: $M_{\text{heptane}}=(7\times 12.01)+(16\times 1.01)=84.07+16.16=100.23\text{\ g/mol}$. The molar mass of octane ($\text{C}_{8}\text{H}_{18}$) is calculated as follows: $M_{\text{octane}}=(8\times 12.01)+(18\times 1.01)=96.08+18.18=114.26\text{\ g/mol}$.

Step 2: Calculate the Number of Moles The number of moles of heptane is calculated as follows: $n_{\text{heptane}}=\frac{25\text{\ g}}{100.23\text{\ g/mol}}\approx 0.2494\text{\ mol}$. The number of moles of octane is calculated as follows: $n_{\text{octane}}=\frac{57\text{\ g}}{114.26\text{\ g/mol}}\approx 0.4989\text{\ mol}$.

Step 3: Calculate the Mole Fractions The total number of moles is calculated as follows: $n_{\text{total}}=n_{\text{heptane}}+n_{\text{octane}}=0.2494+0.4989=0.7483\text{\ mol}$. The mole fraction of heptane is calculated as follows: $X_{\text{heptane}}=\frac{n_{\text{heptane}}}{n_{\text{total}}}=\frac{0.2494}{0.7483}\approx 0.3333$. The mole fraction of octane is calculated as follows: $X_{\text{octane}}=\frac{n_{\text{octane}}}{n_{\text{total}}}=\frac{0.4989}{0.7483}\approx 0.6667$.

Step 4: Calculate the Vapour Pressure of the Solution According to Raoult's Law, the total vapour pressure of the solution ($P_{\text{solution}}$) is given by: $P_{\text{solution}}=X_{\text{heptane}}\times P_{\text{heptane}}^{\circ }+X_{\text{octane}}\times P_{\text{octane}}^{\circ }$. Substituting the given values: $P_{\text{solution}}=(0.3333\times 106\text{\ kPa})+(0.6667\times 47\text{\ kPa})$. $P_{\text{solution}}=35.3298\text{\ kPa}+31.3349\text{\ kPa}$. $P_{\text{solution}}=66.6647\text{\ kPa}$.

Final Answer

The vapour pressure of the solution is approximately $66.66\text{\ kPa}$.

At $\mathrm{T}(\mathrm{K})$, the vapour pressures of two liquids, heptane and octane are $106 \mathrm{kPa}$…

Solution