Millimoles of calcium hydroxyide required to produce $100\mathrm{mL}$ of the aqueous solution of $\mathrm{pH} 12$ is $x\times {10}^{-1}$. The value of $x$ is _____ (Nearest integer).
Assume complete dissociation.

Consider the following reaction approaching equilibrium at $27°\mathrm{C}$ and $1$ atm pressure

$\mathrm{A}+\mathrm{B}\underset{{\mathrm{K}}_{\mathrm{r}}={10}^2}{\stackrel{{\mathrm{K}}_{\mathrm{t}}=0^3}{\rightleftharpoons }}\mathrm{C}+\mathrm{D}$

The standard Gibb's energy change $\left({\mathrm{\Delta }}_{\mathrm{r}}\mathrm{G}°\right)$ at $27°\mathrm{C}$ is $\left(-\right)$ _____ ${\mathrm{kJmol}}^{-1}$ (Nearest integer).

(Given : $\mathrm{R}=8.3\mathrm{J} {\mathrm{K}}^{-1} {\mathrm{mol}}^{-1}$ and $\ln 10=2.3$)

Water decomposes at $2300 \mathrm{K}$

${\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)$

The percent of water decomposing at $2300 \mathrm{K}$ and 1 bar is _____ (Nearest integer). Equilibrium constant for the reaction is $2\times {10}^{-3}$ at $2300 \mathrm{K}$

At $298 \mathrm{K}$

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right),{\mathrm{K}}_1=4\times {10}^5$

${\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right),{\mathrm{K}}_2=1.6\times {10}^{12}$

${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right),{\mathrm{K}}_3=1.0\times {10}^{-13}$

Based on above equilibria, the equilibrium constant of the reaction,

$2{\mathrm{NH}}_3\left(\mathrm{g}\right)+\frac{5}{2}{\mathrm{O}}_2( \mathrm{g})\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right)+3{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$
is _____ $\times {10}^{-33}$ (Nearest integer)

$600\mathrm{mL}$ of $0.01\mathrm{M} \mathrm{HCl}$ is mixed with $400\mathrm{mL}$ of $0.01\mathrm{M} {\mathrm{H}}_2{\mathrm{SO}}_4$. The $\mathrm{pH}$ of the mixture is _____$\times {10}^{-2}$. (Nearest integer)

[Given $\log 2=0.30, \log 3=0.48, \log 5=0.69, \log 7=0.84, \log 11=1.04$]

Consider the following equation:

$2{\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{SO}}_3\left(\mathrm{g}\right),\mathrm{\Delta H}=-190 \mathrm{kJ}$.

The number of factors which will increase the yield of ${\mathrm{SO}}_3$ at equilibrium from the following is _____ .

A. Increasing temperature
B. Increasing pressure
C. Adding more ${\mathrm{SO}}_2$
D. Adding more ${\mathrm{O}}_2$
E. Addition of catalyst

(i) $\mathrm{X}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{Y}\left(\mathrm{g}\right)+\mathrm{Z}\left(\mathrm{g}\right) {\mathrm{K}}_{\mathrm{p}1}=3$

(ii) $\mathrm{A}\left(\mathrm{g}\right)\rightleftharpoons 2 \mathrm{B}( \mathrm{g}) {\mathrm{K}}_{\mathrm{p}2}=1$

If the degree of dissociation and initial concentration of both the reactants $\mathrm{X}( \mathrm{g})$ and $\mathrm{A}\left(\mathrm{g}\right)$ are equal, then the ratio of the total pressure at equilibrium $\left(\frac{p_1}{p_2}\right)$ is equal to $\mathrm{x}: 1$. The value of $\mathrm{x}$ is (Nearest integer)