Limiting reagent is $A$ so if $5$ mol of $A$ reacts then energy liberated $=10^{2} \,\mathrm{kJ}$ then for $3$ mole is $60\, \mathrm{kJ}$.
$\boxed{\Delta H = \Delta E + \Delta {n_g}RT}$
$\Delta E=-60\,kJ$
$\Delta n_{e}=-5$
$\Delta \mathrm{H}=-60+(-5) \,\mathrm{R} \times 300 \times 10^{-3}=-60-1500$
$\times 10^{-3} \,\mathrm{R}=-(60+1.5\, \mathrm{R})$
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A solution $\mathrm{M}$ is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is $0.9$ .
Given: Freezing point depression constant of water $\left(\mathrm{K}_{\mathrm{f}}^{\text {rate }}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
Freezing point depression constant of ethanol $\left(\mathrm{K}_{\mathrm{f}}^{\text {ethunol }}\right)=2.0 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
Boiling point elevation constant of water $\left(\mathrm{K}_{\mathrm{b}}^{\text {nate }}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
Boiling point elevation constant of ethanol $\left(\mathrm{K}_{\mathrm{b}}^{\text {ethanol }}\right)=1.2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$
Standard freezing point of water $=273 \mathrm{~K}$
Standard freezing point of ethanol $=155.7 \mathrm{~K}$
Standard boiling point of water $=373 \mathrm{~K}$
Standard boiling point of ethanol $=351.5 \mathrm{~K}$
Vapour pressure of pure water $=32.8 \mathrm{~mm} \mathrm{Hg}$
Vapour pressure of pure ethanol $=40 \mathrm{~mm} \mathrm{Hg}$
Molecular weight of water $=18 \mathrm{~g} \mathrm{~mol}^{-1}$
Molecular weight of ethanol $=46 \mathrm{~g} \mathrm{~mol}^{-1}$
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and nondissociative.
$1.$ The freezing point of the solution ${M}$ is
$(A)$ $268.7 \mathrm{~K}$ $(B)$ $268.5 \mathrm{~K}$
$(C)$ $234.2 \mathrm{~K}$ $(D)$ $150.9 \mathrm{~K}$
$2.$ The vapour pressure of the solution ${M}$ is
$(A)$ $39.3 \mathrm{~mm} \mathrm{Hg}$ $(B)$ $36.0 \mathrm{~mm} \mathrm{Hg}$
$(C)$ $29.5 \mathrm{~mm} \mathrm{Hg}$ $(D)$ $28.8 \mathrm{~mm} \mathrm{Hg}$
$3.$ Water is added to the solution ${M}$ such that the fraction of water in the solution becomes $0.9$ . The boiling point of this solution is
$(A)$ $380.4 \mathrm{~K}$ $(B)$ $376.2 \mathrm{~K}$
$(C)$ $375.5 \mathrm{~K}$ $(D)$ $354.7 \mathrm{~K}$
Give the answer question $1,2$ and $3.$