$1 \ mol$ of $N_2$ and $2 \ mol$ of $H_2$ are allowed to react in a $1 \ dm^3$ vessel. At equilibrium,$0.8 \ mol$ of $NH_3$ is formed. What is the concentration of $H_2$ at equilibrium (in $M$)?

The equilibrium constant $K_c$ for the following equilibrium:
$2 SO_{2(g)} + O_{2(g)} \rightleftharpoons 2 SO_{3(g)}$
at $563 \ K$ is $100$. At equilibrium,the number of moles of $SO_3$ in the $10 \ L$ flask is twice the number of moles of $SO_2$. Calculate the number of moles of oxygen.

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)

Consider a reaction that is first order in both directions: $A \underset{K_b}{\stackrel{K_f}{\rightleftharpoons}} B$. Initially only $A$ is present,and its concentration is $A_{0}$. Assume $A_{t}$ and $A_{\text{eq}}$ are the concentrations of $A$ at time $t$ and at equilibrium,respectively. The time $t$ at which $A_{t} = (A_{0} + A_{\text{eq}})/2$ is $....$

Match the items in List-$X$ with List-$Y$ and select the correct option.

List-$X$	List-$Y$
$(A)$ $A_{(g)} \rightleftharpoons B_{(g)} + \text{Heat}$	$(i)$ Equilibrium constant
$(B)$ $r_b/r_f$	$(ii)$ Favored at low temperature
$(C)$ $r_f/r_b$	$(iii)$ [Equilibrium constant]$^{-1}$
$(D)$ $2A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)}$	$(iv)$ $A_{(g)} + B_{(g)} \rightleftharpoons C_{(g)} + D_{(g)}$
$(E)$ Effect of pressure	$(V)$ $\Delta n < 0$

The equilibrium constant at $298 \ K$ for a reaction $A + B \rightleftharpoons C + D$ is $100$. If the initial concentration of all the four species were $1 \ M$ each,then the equilibrium concentration of $D$ (in $mol \ L^{-1}$) will be: