Embibe Experts Solutions for Chapter: Equilibrium, Exercise 4: EXERCISE-4

The density of an equilibrium mixture of ${\mathrm{N}}_2{\mathrm{O}}_4$ and ${\mathrm{NO}}_2$ at $101.32 {\mathrm{KP}}_{\mathrm{a}}$ is $3.62 {\mathrm{gdm}}^{-3}$ at $288 \mathrm{K}$ and $1.84 {\mathrm{gdm}}^{-3}$ at $348 \mathrm{K}$. What is the heat of the reaction for ${\mathrm{N}}_2{\mathrm{O}}_4\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$.

The equilibrium constant for the following reaction at $1395 \mathrm{K}$.

$2{\mathrm{H}}_2\mathrm{O}\rightleftharpoons 2{\mathrm{H}}_2+{\mathrm{O}}_2 { \mathrm{K}}_1=2.1\times {10}^{-13}$

$\begin{array}{ll}2{\mathrm{CO}}_2\rightleftharpoons 2\mathrm{CO}+{\mathrm{O}}_2& { \mathrm{K}}_2=1.4\times {10}^{-12}\end{array}$

Calculate the value of $\mathrm{K}$ for the reaction : ${\mathrm{H}}_2+{\mathrm{CO}}_2\rightleftharpoons \mathrm{CO}+{\mathrm{H}}_2\mathrm{O}$

A saturated solution of iodine in water contains $0.33 {\mathrm{gI}}_2 {\mathrm{L}}^{-1}$. More than this can dissolve in a $\mathrm{KI}$ solution because of the equilibrium : ${\mathrm{I}}_2\left(\mathrm{aq}\right)+{\mathrm{I}}^{-}\left(\mathrm{aq}\right)\rightleftharpoons {\mathrm{I}}_3^{-}\left(\mathrm{aq}\right)$. A $0.10 \mathrm{MKI}$ solution $\left(0.10{\mathrm{MI}}^{-}\right)$ actually dissolves $12.5 \mathrm{g}$ of iodine $/\mathrm{L}$, most of which is converted to ${\mathrm{I}}_3^{-}$. Assuming that the concentration of ${\mathrm{I}}_2$ in all saturated solutions is the same, calculate the equilibrium constant for the above reaction. What is the effect of adding water to a clear saturated of ${\mathrm{I}}_2$ in the $\mathrm{KI}$ solution?

A mixture of ${\mathrm{N}}_2$ & ${\mathrm{H}}_2$ are in equilibrium at $600 \mathrm{K}$ at a total pressure of $80 \mathrm{atm}$. If the initial ratio of ${\mathrm{N}}_2$ and ${\mathrm{H}}_2$ are $3: 1$ and at equilibrium ${\mathrm{NH}}_3$ is $10\%$ by volume, calculate ${\mathrm{K}}_{\mathrm{p}}$ of reaction at given temperature.

$\mathrm{\Delta G}°(298 \mathrm{K})$ for the reaction $\frac{1}{2{ \mathrm{N}}_2}+3{\mathrm{H}}_2\rightleftharpoons {\mathrm{K}}_1{\mathrm{NH}}_3$ is $-16.5 \mathrm{kJ}{ \mathrm{mol}}^{-1}$. Find the equilibrium constant $\left({\mathrm{K}}_1\right)$ at $25°\mathrm{C}$. What will be the equilibrium constants ${\mathrm{K}}_2$ and ${\mathrm{K}}_3$ for the following reactions:

${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons {\mathrm{K}}_2\rightleftharpoons 2{\mathrm{NH}}_3$

${\mathrm{NH}}_3\rightleftharpoons {\mathrm{K}}_3\rightleftharpoons \frac{1}{2{ \mathrm{N}}_2}+\frac{3}{2{\mathrm{H}}_2}$

For the reaction ${\mathrm{SO}}_2\left(\mathrm{g}\right)+\frac{1}{2{\mathrm{O}}_2}\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{SO}}_3\left(\mathrm{g}\right){\mathrm{\Delta H}}_{298}°=\frac{-98.32 \mathrm{kJ}}{\mathrm{mole}}$ ${\mathrm{\Delta S}}_{298}°=-95.0 {\mathrm{JK}}^{-1} {\mathrm{mole}}^{-1}$. Find the ${\mathrm{K}}_{\mathrm{p}}$ for this reaction at $298 \mathrm{K}$.

For the reaction
${\mathrm{C}}_2{\mathrm{H}}_6\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{C}}_2{\mathrm{H}}_4\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$ ${{\mathrm{K}}_{\mathrm{p}}}^0$ is $0.05$ and ${\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}°$ is $22.384 \mathrm{kJ}{ \mathrm{mol}}^{-1}$ at $900 \mathrm{K}$. If an initial mixture comprising $20 \mathrm{mol}$ of ${\mathrm{C}}_2{\mathrm{H}}_6$ and $80 \mathrm{mol}$ of ${\mathrm{N}}_2$ (inert) is passed over a dehydrogenation catalyst at $900 \mathrm{K}$, what is the equilibrium percentage composition of the effluent gas mixture? The total pressure is kept at $0.5$ bar. Given : ${\mathrm{\Delta }}_{\mathrm{r}}\mathrm{S}°=135.143 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$ at $300 \mathrm{K}$. Calculate ${\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}°$ at $300 \mathrm{K}$. (Assume $\left.{\mathrm{\Delta }}_{\mathrm{r}}{\mathrm{C}}_{\mathrm{p}}=0\right)$.

Equimolar mixture of two gases ${\mathrm{A}}_2$ and ${\mathrm{B}}_2$ is taken in a container of volume $\mathrm{V}\text{'}$ at temperature $300 \mathrm{K}$. At constant temperature the gases reacts according to given equations :

${\mathrm{A}}_2\left(\mathrm{g}\right)\rightleftharpoons 2 \mathrm{A}\left(\mathrm{g}\right) {\mathrm{k}}_{\mathrm{p}}=?$

${\mathrm{B}}_2\left(\mathrm{g}\right)\rightleftharpoons 2 \mathrm{B}\left(\mathrm{g}\right) {\mathrm{K}}_{\mathrm{p}}=?$

${\mathrm{A}}_2\left(\mathrm{g}\right)+{\mathrm{B}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{AB}\left(\mathrm{g}\right) {\mathrm{k}}_{\mathrm{p}}=2$

If the initial pressure in the container was $2 \mathrm{atm}$ and final and final pressure developed at equilibrium is $2.75$ atm in which equilibrium partial pressure of gas $\mathrm{AB}$ was $0.5 \mathrm{atm}$, find equilibrium constant ${\mathrm{k}}_{\mathrm{p}}$ for the reaction.

$\mathrm{AB}\rightleftharpoons \mathrm{A}\left(\mathrm{g}\right)+\mathrm{B}\left(\mathrm{g}\right)$