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The standard free energy change \( (\Delta G^\circ) \) for \( 50\% \) dissociation of \( \mathrm{N_2O_4} \) into \( \mathrm{NO_2} \) at \( 27^\circ \text{C} \) and \( 1 \, \text{atm} \) pressure is \( -x \, \text{J mol}^{-1} \). The value of \( x \) is __________.(Nearest Integer)
[Given : \( R = 8.31 \, \text{J K}^{-1} \text{mol}^{-1} \) , \( \log 1.33 = 0.1239 \) \( \ln 10 = 2.3 \)]

For a reaction at equilibrium
\( \mathrm{A(g)} \rightleftharpoons \mathrm{B(g)} + \tfrac{1}{2}\mathrm{C(g)} \)
The relation between dissociation constant \( (K) \), degree of dissociation \( (\alpha) \) and equilibrium pressure \( (p) \) is given by:

\( 2\, \mathrm{NOCl}\,(g) \rightleftharpoons 2\mathrm{NO}\,(g) + \mathrm{Cl_2}\,(g) \)
In an experiment, \( 2.0 \) moles of \( \mathrm{NOCl} \) was placed in a one-litre flask and the concentration of \( \mathrm{NO} \) after equilibrium established, was found to be \( 0.4 \; \mathrm{mol/L} \). The equilibrium constant at \( 30^\circ \mathrm{C} \) is ________ \( \times 10^{-4} \).

\( 4.0 \) moles of argon and \( 5.0 \) moles of \( \mathrm{PCl_5} \) are introduced into an evacuated flask of \( 100 \) litre capacity at \( 610 \, \text{K} \). The system is allowed to equilibrate. At equilibrium, the total pressure of mixture was found to be \( 6.0 \) atom. The \( K_p \) for the reaction is [Given: \( R = 0.082 \, \text{L atm K}^{-1} \text{ mol}^{-1} \) ]

At \( 298 \, \text{K} \), the equilibrium constant is \( 2 \times 10^{15} \) for the reaction:
\( \mathrm{Cu(s)} + 2\mathrm{Ag^+(aq)} \rightleftharpoons \mathrm{Cu^{2+}(aq)} + 2\mathrm{Ag(s)} \)
The equilibrium constant for the reaction \( \dfrac{1}{2}\mathrm{Cu^{2+}(aq)} + \mathrm{Ag(s)} \rightleftharpoons \dfrac{1}{2}\mathrm{Cu(s)} + \mathrm{Ag^+(aq)} \) is \( x \times 10^{-8} \). The value of \( x \) is _______________. (Nearest Integer)

$\text{PCl}_5$ dissociates as

$\text{PCl}_5(\text{g}) \rightleftharpoons \text{PCl}_3(\text{g}) + \text{Cl}_2(\text{g})$

5 moles of $\text{PCl}_5$ are placed in a 200 litre vessel which contains 2 moles of $\text{N}_2$ and is maintained at 600 K. The equilibrium pressure is 2.46 atm. The equilibrium constant $\text{K}_\text{p}$ for the dissociation of $\text{PCl}_5$ is $\underline{\qquad} \times 10^{-3}$. (nearest integer)

(Given : $\text{R} = 0.082 \text{ L atm K}^{-1}\text{ mol}^{-1}$; Assume ideal gas behaviour)

At \( 600 \, \text{K} \), \( 2 \, \text{mol} \) of \( \text{NO} \) are mixed with \( 1 \, \text{mol} \) of \( \text{O}_2 \). The reaction occurring as above comes to equilibrium under a total pressure of \( 1 \, \text{atm} \). Analysis of the system shows that \( 0.6 \, \text{mol} \) of oxygen are present at equilibrium. The equilibrium constant for the reaction is __________. (Nearest integer)