For reaction : $$\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g})$$
$$\mathrm{K}_{\mathrm{p}}=2 \times 10^{12}$$ at $$27^{\circ} \mathrm{C}$$ and $$1 \mathrm{~atm}$$ pressure. The $$\mathrm{K}_{\mathrm{c}}$$ for the same reaction is ____________ $$\times 10^{13}$$. (Nearest integer)
(Given $$\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$)
$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \Delta H=-190 \mathrm{~kJ}$
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
$$600 \mathrm{~mL}$$ 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 $$\log 2=0.30$$
$$\log 3=0.48$$
$$\log 5=0.69$$
$$\log 7=0.84$$
$$\log 11=1.04]$$
At 298 K
$$\mathrm{N_2~(g)+3H_2~(g)\rightleftharpoons~2NH_3~(g),~K_1=4\times10^5}$$
$$\mathrm{N_2~(g)+O_2~(g)\rightleftharpoons~2NO~(g),~K_2=1.6\times10^{12}}$$
$$\mathrm{H_2~(g)+\frac{1}{2}O_2~(g)\rightleftharpoons~H_2O~(g),~K_3=1.0\times10^{-13}}$$
Based on above equilibria, then equilibrium constant of the reaction, $$\mathrm{2NH_3(g)+\frac{5}{2}O_2~(g)\rightleftharpoons~2NO~(g)+3H_2O~(g)}$$ is ____________ $$\times10^{-33}$$ (Nearest integer).