Consider the following reaction approaching equilibrium at $27^{\circ} C$ and $1 \ atm$ pressure. Given the rate constants for the forward and backward reactions are $K_{f} = 10^{3} \ s^{-1}$ and $K_{b} = 10^{2} \ s^{-1}$ respectively,calculate the standard Gibb's energy change $(\Delta_{r} G^{\circ})$ at $27^{\circ} C$ in $kJ \ mol^{-1}$ (Nearest integer). (Given: $R = 8.3 \ J \ K^{-1} \ mol^{-1}$ and $\ln 10 = 2.3$)

Using the data provided,find the value of the equilibrium constant for the following reaction at $298 \ K$ and $1 \ atm$ pressure: $NO_{(g)} + \frac{1}{2} O_{2(g)} \rightleftharpoons NO_{2(g)}$
$\Delta_{f} H^0(NO_{(g)}) = 90.4 \ kJ \cdot mol^{-1}$
$\Delta_{f} H^0(NO_{2(g)}) = 32.48 \ kJ \cdot mol^{-1}$
$\Delta S^{\circ} = -70.8 \ J \cdot K^{-1} \cdot mol^{-1}$
$\text{antilog}(6.4) = 2.51 \times 10^6$ (Note: Calculation based on standard thermodynamic relations)

Solid $NH_4HS$ is placed in a flask containing $NH_3$ gas at a certain temperature and a pressure of $0.50 \ atm$. The $NH_4HS$ decomposes to form $NH_3$ gas and $H_2S$ gas. When equilibrium is established in the flask,the total pressure increases to $0.84 \ atm$. What is the equilibrium constant $(K_p)$ for the decomposition of $NH_4HS$ at this temperature?

The equilibrium constants for the following three reactions $(i)$,$(ii)$,and $(iii)$ are given as:
$(i)$ $CO_{(g)} + H_2O_{(g)} \rightleftharpoons CO_{2(g)} + H_{2(g)} \quad K_1$
$(ii)$ $CH_{4(g)} + H_2O_{(g)} \rightleftharpoons CO_{(g)} + 3H_{2(g)} \quad K_2$
$(iii)$ $CH_{4(g)} + 2H_2O_{(g)} \rightleftharpoons CO_{2(g)} + 4H_{2(g)} \quad K_3$
Which of the following relations is correct?

In a closed vessel of $1 \ L$ capacity,$2 \ mol$ of $N_2$ and $6 \ mol$ of $H_2$ are mixed. If at equilibrium $50\% \ N_2$ is converted into $NH_3$,then the value of $K_c$ for the reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ will be:

$2SO_2 + O_2 \to$ product. If the pressure of the reaction increases $3$ times, then the rate will be (in $\times$)?