1
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1 At 298 K

$$\mathrm{N_2~(g)+3H_2~(g)\rightleftharpoons~2NH_3~(g),~K_1=4\times10^5}$$

$$\mathrm{N_2~(g)+O_2~(g)\rightleftharpoons~2NO~(g),~K_2=1.6\times10^{12}}$$

$$\mathrm{H_2~(g)+\frac{1}{2}O_2~(g)\rightleftharpoons~H_2O~(g),~K_3=1.0\times10^{-13}}$$

Based on above equilibria, then equilibrium constant of the reaction, $$\mathrm{2NH_3(g)+\frac{5}{2}O_2~(g)\rightleftharpoons~2NO~(g)+3H_2O~(g)}$$ is ____________ $$\times10^{-33}$$ (Nearest integer).

2
JEE Main 2023 (Online) 29th January Morning Shift
Numerical
+4
-1

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is $$x\times10^{-1}$$. The value of $$x$$ is ___________ (Nearest integer).

Assume complete dissociation.

3
JEE Main 2023 (Online) 29th January Morning Shift
Numerical
+4
-1

Solid Lead nitrate is dissolved in 1 litre of water. The solution was found to boil at 100.15$$^\circ$$C. When 0.2 mol of NaCl is added to the resulting solution, it was observed that the solution froze at $$-0.8^\circ$$ C. The solubility product of PbCl$$_2$$ formed is __________ $$\times$$ 10$$^{-6}$$ at 298 K. (Nearest integer)

Given : $$\mathrm{K_b=0.5}$$ K kg mol$$^{-1}$$ and $$\mathrm{K_f=1.8}$$ K kg mol$$^{-1}$$. Assume molality to the equal to molarity in all cases.

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

Water decomposes at 2300 K

$$\mathrm{H_2O(g)\to H_2(g)+\frac{1}{2}O_2(g)}$$

The percent of water decomposing at 2300 K and 1 bar is ___________ (Nearest integer).

Equilibrium constant for the reaction is $$2\times10^{-3}$$ at 2300 K.

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