For the reaction $CuSO_4 \cdot 5H_2O_{(s)} \rightleftharpoons CuSO_4 \cdot 3H_2O_{(s)} + 2H_2O_{(g)}$,which of the following is a correct representation?

One mole of $N_2O_4(g)$ is taken in a closed container at $1 \ atm$ and $300 \ K$. When it is heated to $600 \ K$,$20 \%$ of $N_2O_4(g)$ dissociates into $NO_2(g)$. The resulting pressure is .......... $atm$.

For the reaction $H_{2(g)} + I_{2(g)} \rightleftharpoons 2HI_{(g)}$,the value of $K_c$ at $440 \ ^oC$ is $50$. If the reaction is initiated in a $1 \ L$ flask with $1 \ mol$ of $H_2$,$2 \ mol$ of $I_2$,and $3 \ mol$ of $HI$,then the equilibrium concentration of $HI$ will be .......... $M$.

The equilibrium constants $K_{p_1}$ and $K_{p_2}$ for the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$ are in the ratio of $1 : 4$. If the degree of dissociation of $X$ is $2$ times that of $Z$,then the ratio of total pressure $(P_1 : P_2)$ at these equilibria is: (Assume degree of dissociation for both reactions are very small)

$3.00 \, mol$ of $PCl_5$ kept in $1 \, L$ closed reaction vessel was allowed to attain equilibrium at $380 \, K$. Calculate the composition of the mixture at equilibrium. Given $K_c = 1.80$.

For a reaction $2 A \rightleftharpoons B + C$,$K_c$ is $2 \times 10^{-3}$. At a given time,the reaction mixture has $[A] = [B] = [C] = 3 \times 10^{-4} \ M$. Which of the following options is correct?