Question

At ${55^0}C$, ethanol has a vapour pressure of 168 mm Hg, and the vapour pressure of methylcyclohexane is 280 mm Hg. A solution of the two in which the mole fraction of ethanol is 0.68, has a total vapour pressure of 225 mm Hg. This solution is formed from its components with:
A) The evolution of heat
B) The absorption of heat
C) Neither absorption nor evolution of heat
D) Nothing can be predicted on the basis of given information

Answer 1

Hint: Refer to Raoult's law. First, calculate the total vapour pressure of the solution assuming it as an ideal solution. Then, relate the calculated total vapour pressure value from Raoult’s law with the given value. Non-ideal solutions show positive and negative deviations from Raoult's law. For positive deviation from Raoult’s law, $\Delta H > 0$ and for negative deviation, $\Delta H < 0$.

Complete step by step solution:
According to Raoult's law, for any solution the partial vapour pressure of each volatile component in the solution is directly proportional to its mole fraction. Thus, we can write:
$p \propto x$
And, $p = x{\text{ }}{p^0}$
$p$ is the vapour pressure of the volatile component, $x$ is the mole fraction of the respective component and ${p^0}$ is the proportionality constant and is the vapour pressure of the component in pure state.
Now, let ethanol be the component A and methylcyclohexane be the component B in the solution.
Thus, vapour pressure of ethanol (${p_A}$) can be calculated as follows:
${p_A} = {x_A}{\text{ }}p_A^0$
Given, vapour pressure of pure ethanol , $p_A^0$ = 168 mm Hg.
Mole fraction of ethanol in the solution, ${x_A}$ = 0.68
Thus, ${p_A} = 168 \times 0.68 = 114.24$ mm Hg.
Now, vapour pressure of methylcyclohexane (${p_B}$) is:
${p_B} = {x_B}{\text{ }}p_B^0$
Given, vapour pressure of pure methylcyclohexane,$p_B^0$= 280 mm Hg
Mole fraction of methylcyclohexane, ${x_B} = 1 - 0.68 = 0.32$
Thus, ${p_B} = 280 \times 0.32 = 89.6$ mm Hg.
Now, the total vapour pressure of the solution is the sum of the vapour pressure of ethanol and vapour pressure of methylcyclohexane.
Hence, ${P_T} = {p_A} + {p_B}$
$\therefore {P_T} = 114.24 + 89.6 = 203.84$ mm Hg.
But, the given total vapour pressure of the solution is 225 mm Hg which is higher than the predicted or above calculated total vapour pressure i.e., 203.84 mm Hg from Raoult’ law. Hence, according to Raoult’s law, the given solution is non-ideal and will show a positive deviation. When a non-ideal solution shows positive deviation, enthalpy change for the solution is greater than zero i.e., $\Delta H > 0$.

Hence, the given solution is formed from its components with the absorption of heat because $\Delta H > 0$. Thus, option B is correct.

Note: If the total vapour pressure of the solution is lower than the predicted total vapour pressure from Raoult’s law, then the solution exhibits negative deviation and $\Delta H < 0$. Hence, in this case, there is an evolution of heat.