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For the given hypothetical reactions, the equilibrium constants are as follows:

$X \rightleftharpoons Y; K_1 = 1.0$
$
$$Y \rightleftharpoons Z; K_2 = 2.0$
$
$$Z \rightleftharpoons W; K_3 = 4.0$
The equilibrium constant for the reaction $X \rightleftharpoons W$ is:

For the reaction \( \mathrm{N_2O_4(g)} \rightleftharpoons 2\mathrm{NO_2(g)}, \ K_p = 0.492 \, \mathrm{atm} \) at \( 300 \, \mathrm{K} \). \( K_c \) for the reaction at same temperature is __________ \( \times 10^{-2} \). (Given : \( r = 0.082 \, \mathrm{L \, atm \, mol^{-1} \, K^{-1}} \) )

\( \mathrm{A(g)} \rightleftharpoons \mathrm{B(g)} + \dfrac{\mathrm{C}}{2}(g) \). The correct relationship between \( K_p \), \( \alpha \) and equilibrium pressure \( P \) is:

For a certain reaction at \( 300 \, \text{K} \), \( K = 10 \), then \( \Delta G^\circ \) for the same reaction is __________ \( \times 10^{-1} \, \text{kJ mol}^{-1} \). (Given \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \) )

The ratio \( \frac{K_P}{K_C} \) for the reaction: \( \mathrm{CO(g)} + \tfrac{1}{2}\mathrm{O_2(g)} \rightleftharpoons \mathrm{CO_2(g)} \) is:

The equilibrium constant for the reaction \( \mathrm{SO_3(g)} \rightleftharpoons \mathrm{SO_2(g)} + \tfrac{1}{2}\mathrm{O_2(g)} \) is \( K_c = 4.9 \times 10^{-2} \). The value of \( K_c \) for the reaction given below is \( 2\mathrm{SO_2(g)} + \mathrm{O_2(g)} \rightleftharpoons 2\mathrm{SO_3(g)} \) is:

The following concentrations were observed at \( 500 \, \mathrm{K} \) for the formation of \( \mathrm{NH_3} \) from \( \mathrm{N_2} \) and \( \mathrm{H_2} \). At equilibrium: \( [\mathrm{N_2}] = 2 \times 10^{-2} \, \mathrm{M} \), \( [\mathrm{H_2}] = 3 \times 10^{-2} \, \mathrm{M} \) and \( [\mathrm{NH_3}] = 1.5 \times 10^{-2} \, \mathrm{M} \). Equilibrium constant for the reaction is __________.

The following reaction occurs in the blast furnace where iron ore is reduced to iron metal
$\text{Fe}_2\text{O}_{3(s)} + 3\text{CO}_{(g)} \rightleftharpoons \text{Fe}_{(\ell)} + 3\text{CO}_{2(g)}$
Using the Le-Chatelier’s principle, predict which one of the following will not disturb the equilibrium.

At \( -20^\circ \text{C} \) and \( 1 \, \text{atm} \) pressure, a cylinder is filled with equal number of \( \mathrm{H_2} \), \( \mathrm{I_2} \) and \( \mathrm{HI} \) molecules for the reaction:
\( \mathrm{H_2(g)} + \mathrm{I_2(g)}\rightleftharpoons
2\mathrm{HI(g)} \),
the \( K_p \) for the process is \( x \times 10^{-1} \), \( x = \) _____. [Given: \( R = 0.082 \, \text{L atm K}^{-1} \text{ mol}^{-1} \)]

The equilibrium \( \mathrm{Cr_2O_7^{2-}} \rightleftharpoons 2\mathrm{CrO_4^{2-}} \) is shifted to the right in:

For the given reaction, choose the correct expression of \( K_c \) from the following:-
$\text{Fe}^{3+}_{\text{(aq)}} + \text{SCN}^-_{\text{(aq)}} \rightleftharpoons \text{(FeSCN)}^{2+}_{\text{(aq)}}$

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JEE Main 2024 1st Feb Evening Shift

For a certain reaction at \( 300 \, \text{K} \), \( K = 10 \), then \( \Delta G^\circ \) for the same reaction is __________ \( \times 10^{-1} \, \text{kJ mol}^{-1} \). (Given \( R = 8.314 \, \text{J K}^{-1} \text{mol}^{-1} \) )