In a chemical reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times of $A$ but the equilibrium concentrations of $A$ and $B$ were found to be equal. The equilibrium constant $(K)$ for the aforesaid chemical reaction is

Air containing $79\%$ of nitrogen and $21\%$ of oxygen by volume is heated at $2200 \ K$ and $1 \ atm$ until equilibrium is established according to the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$. If the $K_p$ of the reaction is $1.1 \times 10^{-3}$,calculate the amount of nitric oxide produced in terms of volume percent.

For the reaction,$2SO_{2(g)} + O_{2(g)} \to 2SO_{3(g)}$
$\Delta H = -57.2 \ kJ \ mol^{-1}$ and $K_C = 1.7 \times 10^{16}$
Which of the following statement is $INCORRECT$?

Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per the following endothermic reaction:
$CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)}$
$(a)$ Write an expression for $K_p$ for the above reaction.
$(b)$ How will the values of $K_p$ and the composition of the equilibrium mixture be affected by:
$(i)$ increasing the pressure
$(ii)$ increasing the temperature
$(iii)$ using a catalyst?

In the reaction $PCl_{5(g)} \rightleftharpoons PCl_{3(g)} + Cl_{2(g)}$,initially $1 \text{ mole}$ each of $PCl_5$ and $PCl_3$ are present. At equilibrium,$x \text{ moles}$ of $PCl_5$ remain. What is the total number of moles at equilibrium (in $- x$)?

At $550 \ K$,the $K_c$ for the following reaction is $10^4 \ mol^{-1} \ L$: $X_{(g)} + Y_{(g)} \rightleftharpoons Z_{(g)}$. At equilibrium,it was observed that $[X] = \frac{1}{2}[Y] = \frac{1}{2}[Z]$. What is the value of $[Z]$ (in $mol \ L^{-1}$) at equilibrium?