1
JEE Main 2023 (Online) 29th January Morning Shift
Numerical
+4
-1

Consider the following reaction approaching equilibrium at 27$$^\circ$$C and 1 atm pressure

$$\mathrm{A+B}$$ $$\mathrel{\mathop{\kern0pt\rightleftharpoons} \limits_{{k_r} = {{10}^2}}^{{k_f} = {{10}^3}}}$$ $$\mathrm{C+D}$$

The standard Gibb's energy change $$\mathrm{(\Delta_r G^\theta)}$$ at 27$$^\circ$$C is ($$-$$) ___________ kJ mol$$^{-1}$$ (Nearest integer).

(Given : $$\mathrm{R=8.3~J~K^{-1}~mol^{-1}}$$ and $$\mathrm{\ln 10=2.3}$$)

2
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1 At $$600 \mathrm{~K}, 2 \mathrm{~mol}$$ of $$\mathrm{NO}$$ are mixed with $$1 \mathrm{~mol}$$ of $$\mathrm{O}_{2}$$.

$$2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2}(\mathrm{g}) \rightleftarrows 2 \mathrm{NO}_{2}(\mathrm{g})$$

The reaction occurring as above comes to equilibrium under a total pressure of 1 atm. Analysis of the system shows that $$0.6 \mathrm{~mol}$$ of oxygen are present at equilibrium. The equilibrium constant for the reaction is ________. (Nearest integer)

3
JEE Main 2022 (Online) 26th July Morning Shift
Numerical
+4
-1 At $$298 \mathrm{~K}$$, the equilibrium constant is $$2 \times 10^{15}$$ for the reaction :

$$\mathrm{Cu}(\mathrm{s})+2 \mathrm{Ag}^{+}(\mathrm{aq}) \rightleftharpoons \mathrm{Cu}^{2+}(\mathrm{aq})+2 \mathrm{Ag}(\mathrm{s})$$

The equilibrium constant for the reaction

$$\frac{1}{2} \mathrm{Cu}^{2+}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s}) \rightleftharpoons \frac{1}{2} \mathrm{Cu}(\mathrm{s})+\mathrm{Ag}^{+}(\mathrm{aq})$$

is $$x \times 10^{-8}$$. The value of $$x$$ is _____________. (Nearest Integer)

4
JEE Main 2022 (Online) 29th June Evening Shift
Numerical
+4
-1 A box contains 0.90 g of liquid water in equilibrium with water vapour at 27$$^\circ$$C. The equilibrium vapour pressure of water at 27$$^\circ$$C is 32.0 Torr. When the volume of the box is increased, some of the liquid water evaporates to maintain the equilibrium pressure. If all the liquid water evaporates, then the volume of the box must be __________ litre. [nearest integer]

(Given : R = 0.082 L atm K$$-$$1 mol$$-$$1)

(Ignore the volume of the liquid water and assume water vapours behave as an ideal gas.)

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