$15 \ mol$ of $H_2$ and $5.2 \ mol$ of $I_2$ are mixed and allowed to attain equilibrium at $773 \ K$. At equilibrium,the number of moles of $HI$ is found to be $10$. The equilibrium constant for the dissociation of $HI$ is

$5 \ \text{moles}$ of $SO_2$ and $5 \ \text{moles}$ of $O_2$ are allowed to react to form $SO_3$ in a closed vessel. At the equilibrium stage,$60\%$ of $SO_2$ is used up. The total number of moles of $SO_2$,$O_2$,and $SO_3$ in the vessel now is:

$(i) X(g) \rightleftharpoons Y(g) + Z(g), K_{p1} = 3$
$(ii) A(g) \rightleftharpoons 2B(g), K_{p2} = 1$
If the degree of dissociation and initial concentration of both the reactants $X(g)$ and $A(g)$ are equal,then the ratio of the total pressure at equilibrium $\left( \frac{p_1}{p_2} \right)$ is equal to $x : 1$. The value of $x$ is $......$ (Nearest integer)

At $T$ $(K)$,$K_c$ for the dissociation of $PCl_5$ is $2 \times 10^{-2} \ mol \ L^{-1}$. The number of moles of $PCl_5$ that must be taken in a $1.0 \ L$ flask at the same temperature to get $0.2 \ mol$ of chlorine at equilibrium is:

Write a relation between $\Delta G$ and $Q$ and define the meaning of each term and answer the following:
$(a)$ Why a reaction proceeds forward when $Q < K$ and no net reaction occurs when $Q = K$.
$(b)$ Explain the effect of increase in pressure in terms of reaction quotient $Q$.
For the reaction: $CO_{(g)} + 3H_{2(g)} \rightleftharpoons CH_{4(g)} + H_{2}O_{(g)}$

In the reaction $PCl_5 \rightleftharpoons PCl_3 + Cl_2$,one mole of $PCl_5$ is started in a $5 \ L$ vessel. If $0.3 \ mol$ of $PCl_5$ is present at equilibrium,find the concentration of $PCl_3$,total moles,and the value of $K_c$.