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:

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

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

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.

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

A handbook states that the solubility of methylamine ${\mathrm{CH}}_3{\mathrm{NH}}_2\left(\mathrm{g}\right)$ in water at $1 \mathrm{atm}$ pressure at $25°\mathrm{C}$ is $959$ volumes of ${\mathrm{CH}}_3{\mathrm{NH}}_2\left(\mathrm{g}\right)$ per volume of water $\left({\mathrm{pk}}_{\mathrm{b}}=3.39\right)$:

(a) Estimate the max. $\mathrm{pH}$ that can be attained by dissolving methylamine in water.

(b) What molarity $\mathrm{NaOH}\left(\mathrm{aq}.\right)$ would be required to yield the same $\mathrm{pH}$?

Mixture of solutions. Calculate the $\mathrm{pH}$ of the following solutions,

For ${\mathrm{H}}_3{\mathrm{PO}}_4 ; {\mathrm{K}}_{{\mathrm{a}}_1}=7.5\times {10}^{-3}, {\mathrm{K}}_{{\mathrm{a}}_2}=6.2\times {10}^{-8}, {\mathrm{K}}_{{\mathrm{a}}_3}={10}^{-12}$

(a) $50\mathrm{mL}$ of $0.12\mathrm{M} {\mathrm{H}}_3{\mathrm{PO}}_4+20\mathrm{ML}$ of $0.15\mathrm{M} \mathrm{NaOH};$

(b) $50\mathrm{mL}$ of  $0.12\mathrm{M} {\mathrm{H}}_3{\mathrm{PO}}_4+20\mathrm{mL}$ of $0.15\mathrm{M} \mathrm{NaOH};$

(c) $40\mathrm{mL}$ of $0.12\mathrm{M} {\mathrm{H}}_3{\mathrm{PO}}_4+40\mathrm{mL}$ of $0.18\mathrm{M} \mathrm{NaOH}$

(d) $40\mathrm{mL}$ of $0.10\mathrm{M} {\mathrm{H}}_3{\mathrm{PO}}_4+40\mathrm{mL}$ of $0.25\mathrm{M} \mathrm{NaOH}$.

Mixtured of solutions. Calculate the $\mathrm{pH}$ of the following solution.

Use data of above question & For ${\mathrm{H}}_2{\mathrm{CO}}_3 ; {\mathrm{K}}_1=4.2\times {10}^{-7}, {\mathrm{K}}_2=4.8\times {10}^{-11}$

(a) $40\mathrm{mL}$ of $0.050\mathrm{M} {\mathrm{Na}}_2{\mathrm{CO}}_2+50\mathrm{mL}$ of $0.040\mathrm{M} \mathrm{HCl};$

(b) $40\mathrm{mL}$ of $0.020\mathrm{M} {\mathrm{Na}}_3{\mathrm{PO}}_4+40\mathrm{mL}$ of $0.040\mathrm{M} \mathrm{HCl};$

(c) $50\mathrm{mL}$ of $0.10\mathrm{M} {\mathrm{Na}}_3{\mathrm{PO}}_4+50\mathrm{mL}$ of $0.10\mathrm{M} {\mathrm{NaH}}_2{\mathrm{PO}}_4;$

(d) $40\mathrm{mL}$ of $0.10\mathrm{M} {\mathrm{H}}_3{\mathrm{PO}}_4+40\mathrm{mL}$ of $0.10\mathrm{M} {\mathrm{Na}}_3{\mathrm{PO}}_4$.