Write the equilibrium constant $K$ for the reaction $CH_3COOH + H_2O \rightleftharpoons H_3O^{+} + CH_3COO^{-}$

The rate of forward reaction is two times that of reverse reaction at a given temperature and identical concentration. $K_{equilibrium}$ is

For the reaction,$A_{(g)} + 2B_{(g)} \rightleftharpoons 2C_{(g)}$ at $25 \, ^oC$,$2 \, moles$ of $A$,$1 \, mole$ of $B$ and $1 \, mole$ of $C$ are present in a $1 \, L$ vessel. If $K_c$ for the reaction is $2$,then the reaction will proceed in:

Consider the following reactions in which all the reactants and products are in gaseous state:
$2PQ \rightleftharpoons P_2 + Q_2\,;\,K_1 = 2.5 \times 10^5$
$PQ + \frac{1}{2}R_2 \rightleftharpoons PQR\,;\,K_2 = 5 \times 10^{-3}$
The value of the equilibrium constant for the reaction:
$\frac{1}{2}P_2 + \frac{1}{2}Q_2 + \frac{1}{2}R_2 \rightleftharpoons PQR$ is

For the reaction $CO_{(g)} + 2H_{2_{(g)}} \rightleftharpoons CH_3OH_{(g)}$,the equilibrium constant $K_c$ is $0.5$. If the concentrations of $CO$ and $H_2$ at equilibrium are $0.18 \ M$ and $0.22 \ M$ respectively,what is the concentration of $CH_3OH$?

What is the equilibrium expression for the reaction $P_{4(s)} + 5O_{2(g)} \rightleftharpoons P_4O_{10(s)}$?