Fill in the blanks:
$a$. If a reaction is in equilibrium,then the rate of the forward reaction and the rate of the backward reaction will be ....... .
$b$. If $\Delta G$ is negative,then thermodynamically the reaction takes place in the ...... direction.
$c$. The equilibrium constant gives ........ information for a reaction.

The equilibrium constants of the following are
$N_2 + 3H_2 \rightleftharpoons 2NH_3 \,; \quad K_1$
$N_2 + O_2 \rightleftharpoons 2NO \,; \quad K_2$
$H_2 + \frac{1}{2} O_2 \rightleftharpoons H_2O \,; \quad K_3$
The equilibrium constant $(K)$ of the reaction:
$2NH_3 + \frac{5}{2} O_2 \rightleftharpoons 2NO + 3H_2O$ is:

Given below are two statements:
Statement $I$: $A$ catalyst cannot alter the equilibrium constant $(K_{C})$ of the reaction,temperature remaining constant.
Statement $II$: $A$ homogenous catalyst can change the equilibrium composition of a system,temperature remaining constant.
In the light of the above statements,choose the correct answer from the options given below:

For the reaction $CH_4(g) + 2O_2(g) \rightleftharpoons CO_2(g) + 2H_2O(l)$,the enthalpy change is $\Delta H_r = -170.8 \, kJ \, mol^{-1}$. Which of the following statements is $NOT$ true?

When the reaction $A + 2B \rightleftharpoons 2C + D$ was studied,it was observed that the initial concentration of $B$ was $1.5$ times that of $A$,and the equilibrium concentrations of $A$ and $C$ were equal. Then $K_C$ for the given equilibrium is equal to

Which of the following equations is incorrect?