At 1000 K , the equilibrium constant for the reaction, $\mathrm{CO}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ is 0.53 . In a one litre vessel, at equilibrium the mixture contains 0.25 mole of $\mathrm{CO}, 0.5$ mole of $\mathrm{CO}_2, 0.6$ mole of $\mathrm{H}_2$ and $x$ moles of $\mathrm{H}_2 \mathrm{O}$. The value of $x$ is

For the reaction $\mathrm{N}_2 \mathrm{O}_4(g) \rightleftharpoons 2 \mathrm{NO}_2(g)$, the correct relation between degree of dissociation $(\alpha)$ of $\mathrm{N}_2 \mathrm{O}_4(g)$ and equilibrium constant, $K_p$ is ( $p=$ total pressure of mixture)

At $T(K)$ the equilibrium constants for the following two reactions are given below

$ 2 A(g) \rightleftharpoons B(g)+C(g) ; K_{1}=16 $

$ 2 B(g)+C(g) \rightleftharpoons 2 D(g) ; K_{2}=25 $

What is the value of equilibrium constant $(K)$ for the reaction given below at $T(K)$ ?

$ A(g)+\frac{1}{2} B(g) \rightleftharpoons D(g) $