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).

Water decomposes at 2300 K

$$\mathrm{H_2O(g)\to H_2(g)+\frac{1}{2}O_2(g)}$$

The percent of water decomposing at 2300 K and 1 bar is ___________ (Nearest integer).

Equilibrium constant for the reaction is $$2\times10^{-3}$$ at 2300 K.

Consider the following reaction approaching equilibrium at 27$$^\circ$$C and 1 atm pressure

$$\mathrm{A+B}$$ $$\mathrel{\mathop{\kern0pt\rightleftharpoons} \limits_{{k_r} = {{10}^2}}^{{k_f} = {{10}^3}}} $$ $$\mathrm{C+D}$$

The standard Gibb's energy change $$\mathrm{(\Delta_r G^\theta)}$$ at 27$$^\circ$$C is ($$-$$) ___________ kJ mol$$^{-1}$$ (Nearest integer).

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

At $$600 \mathrm{~K}, 2 \mathrm{~mol}$$ of $$\mathrm{NO}$$ are mixed with $$1 \mathrm{~mol}$$ of $$\mathrm{O}_{2}$$.

$$2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}_{2}(\mathrm{g})$$

The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that $$0.6 \mathrm{~mol}$$ of oxygen are present at equilibrium. The equilibrium constant for the reaction is ________. (Nearest integer)