Dihydrogen gas is obtained from natural gas by partial oxidation with steam as per the following endothermic reaction:
$CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)}$
$(a)$ Write an expression for $K_p$ for the above reaction.
$(b)$ How will the values of $K_p$ and the composition of the equilibrium mixture be affected by:
$(i)$ increasing the pressure
$(ii)$ increasing the temperature
$(iii)$ using a catalyst?

At $600 \ K$,$2 \ mol$ of $NO$ are mixed with $1 \ mol$ of $O_2$.
$2 \ NO_{(g)} + O_{2(g)} \rightleftarrows 2 \ NO_{2(g)}$
The reaction occurring as above comes to equilibrium under a total pressure of $1 \ atm$. Analysis of the system shows that $0.6 \ mol$ of oxygen are present at equilibrium. The equilibrium constant for the reaction is $.........$ (Nearest integer).

For the reaction $N_2 + 3H_2 \rightleftharpoons 2NH_3$,what is the relationship between $\Delta H$ and $\Delta E$?

Calculate:
$(a)$ $\Delta G^{\circ}$ and
$(b)$ the equilibrium constant for the formation of $NO_2$ from $NO$ and $O_2$ at $298 \, K$
$NO_{(g)} + 1/2 O_{2(g)} \longleftrightarrow NO_{2(g)}$
Given:
$\Delta G^{\circ}_f(NO_2) = 52.0 \, kJ/mol$
$\Delta G^{\circ}_f(NO) = 87.0 \, kJ/mol$
$\Delta G^{\circ}_f(O_2) = 0 \, kJ/mol$

Nitric oxide reacts with $Br_{2}$ and gives nitrosyl bromide as per the reaction given below:
$2 NO_{(g)} + Br_{2(g)} \longleftrightarrow 2 NOBr_{(g)}$
When $0.087 \ mol$ of $NO$ and $0.0437 \ mol$ of $Br_{2}$ are mixed in a closed container at constant temperature,$0.0518 \ mol$ of $NOBr$ is obtained at equilibrium. Calculate the equilibrium amount of $NO$ and $Br_{2}$.

Ethyl acetate is formed by the reaction between ethanol and acetic acid and the equilibrium is represented as:
$CH_3COOH_{(l)} + C_2H_5OH_{(l)} \longleftrightarrow CH_3COOC_2H_{5(l)} + H_2O_{(l)}$
$(i)$ Write the concentration ratio (reaction quotient),$Q_c$,for this reaction (note: water is not in excess and is not a solvent in this reaction).
$(ii)$ At $293 \ K$,if one starts with $1.00 \ mol$ of acetic acid and $0.18 \ mol$ of ethanol,there is $0.171 \ mol$ of ethyl acetate in the final equilibrium mixture. Calculate the equilibrium constant.
$(iii)$ Starting with $0.5 \ mol$ of ethanol and $1.0 \ mol$ of acetic acid and maintaining it at $293 \ K$,$0.214 \ mol$ of ethyl acetate is found after sometime. Has equilibrium been reached?