For the equilibrium reaction $CO + 2H_2 \rightleftharpoons CH_3OH$ at $427 \, ^\circ C$,the partial pressures of $CH_3OH$,$CO$,and $H_2$ are $2.0 \, atm$,$1.0 \, atm$,and $0.1 \, atm$ respectively. What is the value of $K_P$ for the decomposition of $CH_3OH$?

$1.1 \ mol$ of $A$ and $2.2 \ mol$ of $B$ are mixed in a $1 \ L$ flask until equilibrium is reached. At equilibrium,$0.2 \ mol$ of $C$ is formed. If the equilibrium reaction is $A + 2B \rightleftharpoons 2C + D$,the value of the equilibrium constant $K_C$ is:

For the reaction ${N_{2(g)}} + {O_{2(g)}} \rightleftharpoons 2NO_{(g)}$,the value of $K_c$ at $400 \ K$ is $4.0 \times 10^{-6}$. The value of $K_p$ for this reaction is .....

For the reaction $A + B \rightleftharpoons C + D$ at $298 \ K$,the equilibrium constant is $10.0$. If the initial concentration of all four species is $1 \ M$,what will be the equilibrium concentration of $D$ (in $mol \ L^{-1}$)?

For the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$,the equilibrium constant $K_p = 41$ at $400 \ K$. Calculate $K_c$ for the following reactions at $400 \ K$:
$(a)$ $2N_{2(g)} + 6H_{2(g)} \rightleftharpoons 4NH_{3(g)}$
$(b)$ $2NH_{3(g)} \rightleftharpoons N_{2(g)} + 3H_{2(g)}$
$(c)$ $\frac{1}{2}N_{2(g)} + \frac{3}{2}H_{2(g)} \rightleftharpoons NH_{3(g)}$

For the reaction $2NOCl_{(g)} \rightleftharpoons 2NO_{(g)} + Cl_{2_{(g)}}$ at $1060 \ K$,the equilibrium constant $K_p$ is $0.033 \ atm$. Find the value of $K_c$. (Given $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$)