For a reaction at equilibrium

 $\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{B}\left(\mathrm{g}\right)+\frac{1}{2}\mathrm{C}\left(\mathrm{g}\right)$

 the relation between dissociation constant $\left(\mathrm{K}\right)$, degree of dissociation $\left(\mathrm{\alpha }\right)$ and equilibrium pressure $\left(\mathrm{p}\right)$ is given by :

$2{\mathrm{O}}_3\left(\mathrm{g}\right)\rightleftharpoons 3{\mathrm{O}}_2\left(\mathrm{g}\right)$

At $300 \mathrm{K}$, ozone is fifty percent dissociated. The standard free energy change at this temperature and $1 \mathrm{atm}$ pressure is $\left(-\right)......\mathrm{J} {\mathrm{mol}}^{-1}$. (Nearest integer)

[Given: $\ln 1.35=0.3$ and $\mathrm{R}=8.3 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}$]

The standard free energy change $\left(\mathrm{\Delta G}°\right)$ for $50\%$ dissociation of ${\mathrm{N}}_2{\mathrm{O}}_4$ into ${\mathrm{NO}}_2$ at $27 °\mathrm{C}$ and $1 \mathrm{atm}$ pressure is $-\mathrm{x} \mathrm{J}{ \mathrm{mol}}^{-1}$. The value of $\mathrm{x}$ is $-..... \mathrm{J}$. (Nearest Integer)

[Given : $\mathrm{R}=8.31 \mathrm{J}{ \mathrm{K}}^{-1}{ \mathrm{mol}}^{-1}, \log 1.33=0.1239 \ln 10=2.3$]

Assertion: The amphoteric behaviour of water is explained by Lewis acid base theory

Reason: water acts as acid with ${\mathrm{NH}}_3$ and base with ${\mathrm{H}}_2\mathrm{S}$

$50 \mathrm{mL}$ of $0.1 \mathrm{M} {\mathrm{CH}}_3\mathrm{COOH}$ is being titrated against $0.1 \mathrm{M} \mathrm{NaOH}$. When $25 \mathrm{mL}$ of $\mathrm{NaOH}$ has been added, the $\mathrm{pH}$ of the solution will be____$\times {10}^{-2}$. (Nearest integer)

(Given : ${\mathrm{pK}}_{\mathrm{a}}\left({\mathrm{CH}}_3\mathrm{COOH}\right)=4.76$)

$\log 2=0.30$

$\log 3=0.48$

$\log 5=0.69$

$\log 7=0.84$

$\log 11=1.04$

$2{\mathrm{NOCl}}_{\left(\mathrm{g}\right)}\rightleftharpoons 2{\mathrm{NO}}_{\left(\mathrm{g}\right)}+{{\mathrm{Cl}}_2}_{\left(\mathrm{g}\right)}$

In an experiment, $2.0$ moles of $\mathrm{NOCl}$ was placed in a one-litre flask and the concentration of $\mathrm{NO}$ after equilibrium established, was found to be $0.4 \mathrm{mol}/\mathrm{L}$. The equilibrium constant ${\mathrm{K}}_{\mathrm{c}}$ at $30 °\mathrm{C}$ is a$\times {10}^{-4}$. Calculate the value of $\mathrm{a}$ and give answer to the nearest integer value