For the reversible reaction $2NO_2 \leftrightarrow[K_2]{K_1} N_2O_4$,the rate of disappearance of $NO_2$ is given by:

Consider the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$. The equilibrium constant of the above reaction is $K_p$. If pure ammonia is left to dissociate,the partial pressure of ammonia at equilibrium is given by (Assume that $P_{NH_3} \ll P_{total}$ at equilibrium and $P$ is the total pressure).

At $1000 \ K$,the equilibrium constant for the reaction $CO_{2(g)} + H_{2(g)} \rightleftharpoons CO_{(g)} + H_2O_{(g)}$ is $0.53$. In a one litre vessel,at equilibrium the mixture contains $0.25 \ mole$ of $CO$,$0.5 \ mole$ of $CO_2$,$0.6 \ mole$ of $H_2$ and $x \ moles$ of $H_2O$. The value of $x$ is

$A$ plot of $\ln \ K$ against $\frac{1}{T}$ (abscissa) is expected to be a straight line with an intercept on the ordinate axis equal to:

$K_{c}$ for the following reaction is $99.0$: $A_{2(g)} \rightleftharpoons B_{2(g)}$. In a $1 \ L$ flask,$2 \ moles$ of $A_{2}$ were heated to $T(K)$ and equilibrium was reached. The concentrations at equilibrium of $A_{2}$ and $B_{2}$ are $C_{1}(A_{2})$ and $C_{2}(B_{2})$ respectively. Now,$1 \ mole$ of $A_{2}$ was added to the flask and heated to $T(K)$ to establish equilibrium again. The concentrations of $A_{2}$ and $B_{2}$ are $C_{3}(A_{2})$ and $C_{4}(B_{2})$ respectively. What is the value of $C_{3}(A_{2})$ in $mol \ L^{-1}$?

For the reaction $A + B \rightleftharpoons 2C$,the value of equilibrium constant is $100$ at $298 \ K$. If the initial concentration of all the three species is $1 \ M$ each,then the equilibrium concentration of $C$ is $X \times 10^{-1} \ M$. The value of $X$ is $.....$ (Nearest integer)