Chemical Equilibrium: Step-by-Step Worked Examples (8)

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Tags Equilibrium

Question

For the reaction N2(g)+3H2(g)⇌2NH3(g)N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g), Kc=1.7×102K_c = 1.7 \times 10^2 at 500500 K. If initial concentrations are [N2]=0.50[N_2] = 0.50 M, [H2]=1.50[H_2] = 1.50 M, [NH3]=0.20[NH_3] = 0.20 M, predict the direction of reaction and find QcQ_c. JEE Main 2023 pattern.

Solution — Step by Step

Qc=[NH3]2[N2][H2]3Q_c = \frac{[NH_3]^2}{[N_2][H_2]^3}

This has the same form as KcK_c but uses initial (not equilibrium) concentrations.

Qc=(0.20)2(0.50)(1.50)3=0.040.50×3.375=0.041.6875Q_c = \frac{(0.20)^2}{(0.50)(1.50)^3} = \frac{0.04}{0.50 \times 3.375} = \frac{0.04}{1.6875}

Qc≈0.0237≈2.37×10−2Q_c \approx 0.0237 \approx 2.37 \times 10^{-2}

Qc=2.37×10−2Q_c = 2.37 \times 10^{-2} and Kc=1.7×102=170K_c = 1.7 \times 10^2 = 170. Clearly Qc≪KcQ_c \ll K_c.

When Q<KQ < K, the reaction proceeds in the forward direction (left to right) to produce more products. When Q>KQ > K, it proceeds backward. When Q=KQ = K, the system is at equilibrium.

Final answer: Qc≈2.37×10−2Q_c \approx 2.37 \times 10^{-2}. Since Qc<KcQ_c < K_c, the reaction proceeds forward (more NH3NH_3 is produced).

Why This Works

The reaction quotient QQ is a snapshot of the reaction’s “progress ratio” at any instant — built using the same algebra as KK. Comparing QQ to KK tells us how far the system is from equilibrium and which direction it must shift.

If QQ is small, products are scarce relative to equilibrium — reaction goes forward to make more. If QQ is large, products are excess — reaction reverses. This is just Le Chatelier’s principle quantified.

Alternative Method

Use ICE (Initial, Change, Equilibrium) table approach if you also need equilibrium concentrations. Set up an ICE table with xx as extent of reaction, plug into KcK_c expression, solve for xx. For predicting direction alone, the QQ vs KK comparison is much faster.

A frequent error: comparing QQ and KK but forgetting that “small QQ → forward reaction” only because QQ is at the bottom of the equilibrium fraction. Always remember: Q<KQ < K means we need more of what’s in the numerator (products), so reaction goes forward.

Whenever a JEE question gives initial concentrations and a KK value, the first thing to check is QQ vs KK. This 10-second comparison decides the direction and often the answer to MCQ-style questions.

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