At 298K N _ 2 (g) + 3 H _ 2 (g) ⇌ 2 NH _ 3 (g), K _ 1 = 4 × 10 ^ 5 N _ 2 (g) + O _ 2 (g) ⇌ 2NO(g), K _ 2 = 1 . 6 × 10 ^ 12 H _ 2 (g) + (1)/(2) O _ 2 (g) ⇌ H _ 2 O ( g ) , K _ 3 = 1 . 0 × 10 ^ - 13 Based on above

Correct answer: 0 Given, N _ 2 (g) 3 H _ 2 (g) ⇌ 2 NH _ 3 (g) , K _ 1 = 4 × 10 ^ 5 (1) N _ 2 (g) + O _ 2 (g) ⇌ 2NO (g) , K _ 2 = 1 . 6 × 10 ^ 12 (2) H _ 2 (g) + (1)/(2) O _ 2 (g) ⇌ H _ 2 O (g) , K _ 3 = 1 . 0 × 10 ^ - 13 (3) Using properties of equilibrium constant: (2) + 3 × (3) - (1) 2 NH _ 3 (g) + (5)/(2) O _ 2 (g) ⇌ 2N O(g) + 3 H _ 2 O (g) K _ eq = K _ 2 × K _ 3 ^ 3 K _ 1 = 1 . 6 × 10 ^ 12 × ( 10 ^ - 13 ) ^ 3 4 × 10 ^ 5 = (1 . 6)/(4) × 10 ^ - 32 = 4 × 10 ^ - 33

JEE Main 202329 JanuaryEvening Shift

Exam: JEE Main
Year: 2023
Date: 29 January
Shift: Evening Shift
Subject: Chemistry
Chapter: Chemical Equilibrium

JEE Main 2023 · 29 January · Evening Shift · Chemistry · Chemical Equilibrium

At 298K N _ 2 (g) + 3 H _ 2 (g) ⇌ 2 NH _ 3 (g), K _ 1 = 4 × 10 ^ 5...

At $298K$

${N}_{2}\left(g\right) + 3{H}_{2}\left(g\right) ⇌ 2{NH}_{3}\left(g\right), {K}_{1} = 4 \times {10}^{5}$

${N}_{2}\left(g\right) + {O}_{2}\left(g\right) ⇌ 2NO\left(g\right), {K}_{2} = 1 . 6 \times {10}^{12}$

${H}_{2}\left(g\right) + \dfrac{1}{2}{O}_{2}\left(g\right) ⇌ {H}_{2}O ( g ) , {K}_{3} = 1 . 0 \times {10}^{- 13}$

Based on above equilibria, the equilibrium constant of the reaction,

$2{NH}_{3}\left(g\right) + \dfrac{5}{2}{O}_{2} ( g ) ⇌ 2NO\left(g\right) + 3{H}_{2}O\left(g\right)$
is _____ $\times {10}^{- 33}$ (Nearest integer)

Correct answer

Step-by-step solution

Given,
${N}_{2}$ \left(g\right) $3{H}_{2}\left(g\right)$ ⇌ 2{NH}_{3} $\left(g\right)$ , {K}_{1} = 4 \times {10}^{5} \ldots \left(1\right) $$ {N}_{2}\left(g\right) $+ {O}_{2}$ \left(g\right) $⇌ 2NO$ \left(g\right) $, {K}_{2} = 1 . 6 \times {10}^{12} \ldots \left(2\right)$

${H}_{2}\left(g\right) + \dfrac{1}{2}{O}$ _{2}\left(g\right) $⇌ {H}_{2}O \left(g\right)$ , {K}_{3} = 1 . 0 \times {10}^{- 13} \ldots \left(3\right) $ Using properties of equilibrium constant:\left(2\right) + 3 \times$ \left(3\right) - \left(1\right)

$2{NH}_{3}\left(g\right)$ + $\dfrac{5}{2}$ {O}_{2} $\left(g\right) ⇌ 2N$ O\left(g\right) $+ 3{H}_{2}O \left(g\right)$

${K}_{eq} = \dfrac{{K}_{2} \times {K}_{3}^{3}}{{K}_{1}} = \dfrac{1 . 6 \times {10}^{12} \times {\left({10}^{- 13}\right)}^{3}}{4 \times {10}^{5}}$

$= \dfrac{1 . 6}{4} \times {10}^{- 32} = 4 \times {10}^{- 33}$

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