Embibe Experts Solutions for Chapter: Equilibrium, Exercise 1: Exercise-1

Under what conditions a reversible process becomes irreversible?

What is the effect of temperature on ionic product of water?

What is common ion effect ?

A mixture of ${\mathrm{SO}}_3, {\mathrm{SO}}_2$ and ${\mathrm{O}}_2$ gases is maintained at equilibrium in $10$ litre flask at a temperature at which ${\mathrm{K}}_{\mathrm{C}}$ for the reaction, $2{\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{SO}}_3\left(\mathrm{g}\right)$ is $100 {\mathrm{mol}}^{-1} \mathrm{litre}$. At equilibrium.
(a) If no. of mole of ${\mathrm{SO}}_3$ and ${\mathrm{SO}}_2$ in flask are same, how many mole of ${\mathrm{O}}_2$ are present?
(b) If no. of mole of ${\mathrm{SO}}_3$ in flask are twice the no. of mole of ${\mathrm{SO}}_2$, how many mole of ${\mathrm{O}}_2$ are present?

$0.15$ mole of $\mathrm{CO}$ taken in a $2.5$ litre flask is maintained a $750 \mathrm{K}$ along with a catalyst so that the following reaction can take place.

$\mathrm{CO}\left(\mathrm{g}\right)+2{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{CH}}_3\mathrm{OH}\left(\mathrm{g}\right)$

Hydrogen is introduced until the total pressure of the system is $8.5 \mathrm{atm}$ at equilibrium and $0.08$ mole of methanol is formed. Calculate :
(i) ${\mathrm{K}}_{\mathrm{P}}$ and ${\mathrm{K}}_{\mathrm{C}}$
(ii) The final pressure, if the same mole of $\mathrm{CO}$ and ${\mathrm{H}}_2$ as before are used but without catalyst so that the reaction does not take place.

Calculate the equilibrium constant for the reaction ${\mathrm{H}}_2\left(\mathrm{g}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)$ at $1395 \mathrm{K}$, if the equilibrium constants at $1395 \mathrm{K}$ for the following are ;

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

$2{\mathrm{CO}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right) {\mathrm{K}}_2=1.4\times {10}^{-12}$

When $\mathrm{NO}$ and ${\mathrm{NO}}_2$ are mixed, the following equilibria are readily obtained;

$2{\mathrm{NO}}_2\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_4 {\mathrm{K}}_{\mathrm{P}}=6.8 {\mathrm{atm}}^{-1}$

and $\mathrm{NO}+{\mathrm{NO}}_2\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_3$

In an experiment when $\mathrm{NO}$ and ${\mathrm{NO}}_2$ are mixed in the ratio of $1:2$, the final total pressure was $5.05 \mathrm{atm}$  and the partial pressure of ${\mathrm{N}}_2{\mathrm{O}}_4$ was $1.7 \mathrm{atm}$. Calculate :
(a) the equilibrium partial pressure of $\mathrm{NO}$.
(b) ${\mathrm{K}}_{\mathrm{P}}$ for $\mathrm{NO}+{\mathrm{NO}}_2\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_3$.

Prove that degree of dissociation of a weak acid is given by: $\mathrm{\alpha }=\frac{1}{1+{10}^{\left({\mathrm{pK}}_{\mathrm{a}}-\mathrm{pH}\right)}}$ where ${\mathrm{K}}_{\mathrm{a}}$ is its dissociation constant.