Thermodynamics

$\begin{aligned} & \mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{H}_2 \mathrm{O}(g) \\ & T=100 \Upsilon\mathrm{C} \Rightarrow p=1 \mathrm{~atm} \end{aligned}$

The process is an endothermic process, entropy increases during this change

$\begin{array}{ll} & \Delta S=+v e \\ \therefore \quad \quad & \Delta S_{\text {system }}>0 \\ & \Delta S_{\text {surrounding }}<0 . \end{array}$

Formula of kinetic energy $=\frac{3 n R T}{2}$

Total kinetic energy expression for $A$ and $B$ flask,

$\mathrm{KE}_A=\frac{3 n_A R T_A}{2} \text { and } \mathrm{KE}_B=\frac{3 n_B R T_B}{2} .$ ...... (i)

Let us consider common mass $=m$

$n_A=\frac{m}{2} \quad \text { and } \quad n_B=\frac{m}{44}$

Taking ratio (i) and (ii) we get,

$\begin{aligned} & \frac{\mathrm{KE}_A}{\mathrm{KE}_B}=\frac{n_A T_A}{n_B T_B} \\ & \frac{\mathrm{KE}_A}{\mathrm{KE}_B}=\frac{\frac{m}{2} \times 300}{\frac{m}{44} \times 600} \\ & {\left[\mathrm{KE}_A: \mathrm{KE}_B=11: 1\right]} \\ \end{aligned}$

Temperature of an ideal gas increased by $=20^{\circ} \mathrm{C}$ i.e. $T_2$

Initial temperature of gas, $T_1=0^{\circ} \mathrm{C}$

Number of moles, $n=2$

Formula of work done, $W=-n R\left(T_2-T_1\right)$

$\begin{aligned} & W=-2 R(20-0) \\ & W=-40 R \end{aligned}$

But work involved in the process, $W=+$ ve

$W=40 R$

Here, $R=$ Rate constant i.e. $8.314 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$

$W=40 \times 8.314=332.56 \mathrm{~JK}^{-1} \mathrm{~mol}^{-1}$

According to Gibb's free energy, $\Delta G=\Delta H-T \Delta S$

Reaction is non spontaneous i.e. $\Delta G > 0$ at $298 \mathrm{~K}$.

As the temperature increases from $298 \mathrm{~K}$ to $350 \mathrm{~K}$.

The reaction becomes spontaneous i.e. $\Delta G < 0$.

$\begin{gathered} \Delta G=\Delta H-T \Delta S \\ \Delta G < 0\end{gathered}$

When $\Delta H$ and $\Delta S$ are + ve then, $\Delta G$ will be positive till $\Delta H > T \Delta S$.

When the temperature is increased further $\Delta H$ becomes less than $T \Delta S$ i.e.

$\Delta H < T \Delta S$ and $\Delta G$ becomes $-$ve.

Thus, reaction becomes spontaneous.