The half-life of forward and reverse reactions are $400 \, sec$ and $100 \, sec$ respectively. If these half-lives are independent of the concentration of the reactant,find the equilibrium constant of the reaction.

One mole $H_2O_{(g)}$ and one mole $CO_{(g)}$ are taken in a $1 \ L$ flask and heated to $725 \ K$. At equilibrium,$40 \%$ (by mass) of water reacted with $CO_{(g)}$ as follows: $H_2O_{(g)} + CO_{(g)} \rightleftharpoons H_{2_{(g)}} + CO_{2_{(g)}}$. The value of $K_p$ is:

Explain why the partial pressure $p$ of a gas is proportional to its concentration $c$.

At $1000 \ K$,a vessel contains $CO_2$ at a pressure of $0.5 \ atm$. Some $CO_2$ is converted into $CO$ by the addition of graphite. If the total pressure at equilibrium is $0.8 \ atm$,what is the value of $K_p$ in $atm$?

The equilibrium constant for the reaction $N_{2(g)} + O_{2(g)} \rightleftharpoons 2NO_{(g)}$ at temperature $T$ is $4 \times 10^{-4}$. The value of $K_c$ for the reaction $NO_{(g)} \rightleftharpoons \frac{1}{2}N_{2(g)} + \frac{1}{2}O_{2(g)}$ at the same temperature is

For the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)}$ at $298 \ K$,the $K_c$ is $7 \times 10^{25}$. Calculate $K_c$ for the reaction $SO_{3(g)} \rightleftharpoons SO_{2(g)} + \frac{1}{2}O_{2(g)}$.