For the reaction $SO_{2(g)} + 1/2 O_{2(g)} \rightleftharpoons SO_{3(g)}$,the equilibrium constant is $K_1$ at $298 \, K$. For the reaction $2SO_{3(g)} \rightleftharpoons 2SO_{2(g)} + O_{2(g)}$ at the same temperature,the equilibrium constant is $K_2$. Then,which of the following is correct?

Dihydrogen gas used in Haber's process is produced by reacting methane from natural gas with high temperature steam. The first stage of two stage reaction involves the formation of $CO$ and $H_2$. In second stage,$CO$ formed in first stage is reacted with more steam in water gas shift reaction,
$CO_{(g)} + H_2O_{(g)} \longleftrightarrow CO_{2(g)} + H_{2(g)}$
If a reaction vessel at $400^{\circ}C$ is charged with an equimolar mixture of $CO$ and steam such that $P_{CO} = P_{H_2O} = 4.0 \ bar,$ what will be the partial pressure of $H_2$ at equilibrium? $K_p = 10.1$ at $400^{\circ}C$

For the reaction: $H_{2(g)} + CO_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)}$,if the initial concentration of $[H_2] = [CO_2] = 1 \ M$ and $x \ mol/L$ of hydrogen is consumed at equilibrium,the correct expression for $K_c$ is:

In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,if at equilibrium there are $2 \ mol$ each of $PCl_5$,$PCl_3$,and $Cl_2$,and the total pressure is $3 \ atm$,then the value of the equilibrium constant $K_p$ is ....... $atm$.

Equilibrium constant for the reaction $H_2O_{(g)} + CO_{(g)} \rightleftharpoons H_{2(g)} + CO_{2(g)}$ is $81$. If the velocity constant of the forward reaction is $162 \ L \ mol^{-1} \ s^{-1}$,what is the velocity constant (in $L \ mol^{-1} \ s^{-1}$) for the backward reaction?

In a closed container of $1000\, cm^3$,$2\, mol$ of $PCl_5$,$2\, mol$ of $PCl_3$,and $3\, mol$ of $Cl_2$ are found to be at equilibrium at $27\, ^oC$. Then $K_P$ for the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$ at $27\, ^oC$ is $.....$ $atm$.