For the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,$0.4 \ mol$ of $H_2$ and $I_2$ each are taken in a $2 \ L$ vessel. If $0.5 \ mol$ of $HI$ is formed at equilibrium,calculate the equilibrium constant $K_c$ and $K_p$.

If the equilibrium constant of a reaction is $20.0$ at equilibrium,and the rate constant of the forward reaction is $10.0$,then the rate constant for the backward reaction is:

For the following homogeneous gas reaction $4NH_3 + 5O_2 \rightleftharpoons 4NO + 6H_2O$,the equilibrium constant $K_c$ has the dimension of

The equilibrium constant for the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$ is $K.$ Then,the equilibrium constant for the equilibrium $NH_3 \rightleftharpoons \frac{1}{2}N_2 + \frac{3}{2}H_2$ is

At $1000 \ K$,the partial pressures of $CO_{2(g)}$ and $CO_{(g)}$ for the reaction $CO_{2(g)} + C_{(s)} \rightleftharpoons 2 CO_{(g)}$ in a closed vessel at equilibrium are $0.15 \ bar$ and $0.60 \ bar$ respectively. The $K_c$ for this reaction at the same temperature is approximately

$A_{(g)} \rightleftharpoons B_{(g)} + \frac{1}{2} C_{(g)}$. The correct relationship between $K_P$,$\alpha$,and equilibrium pressure $P$ is: