Chemistry • Year 12 • Module 5 • Lesson 12
Reaction Quotient Q
Build HSC Band 5–6 extended-response and multi-step quantitative technique using Q to synthesise, evaluate and justify.
1. Data-driven extended response — Haber process reactor monitoring (Band 5–6)
8 marks Band 5–6
Stimulus — Incitec Pivot reactor data. The Haber process reaction is N2(g) + 3H2(g) ⇌ 2NH3(g), Keq = 977 at 300 °C and Keq = 0.500 at 400 °C. A process engineer at Incitec Pivot’s Gibson Island (Brisbane) ammonia plant monitors Q in real time. The table below shows the measured concentrations inside the reactor at three different moments during the same operating run at a constant temperature of 400 °C.
| Time point | [N2] (mol/L) | [H2] (mol/L) | [NH3] (mol/L) |
|---|---|---|---|
| T1 (start) | 0.800 | 2.400 | 0.000 |
| T2 (mid-run) | 0.450 | 1.350 | 0.420 |
| T3 (late run) | 0.200 | 0.300 | 0.150 |
Q1a. Calculate Q at T1, T2 and T3. Show all working. 3 marks
Q1b. For each time point, compare Q to Keq = 0.500 and state the direction the reaction is shifting (or whether it has reached equilibrium). 3 marks
Q1c. Analyse and evaluate the following claim made by a junior operator: “At T3, Q < Keq = 0.500, so the reactor still needs to produce more NH3. The best action is to increase the temperature to speed up the forward reaction.” Use your Q value from Q1a to evaluate whether the Q-based direction prediction is correct. Then evaluate whether the temperature recommendation is correct. Justify both using Q reasoning and Keq temperature dependence. 2 marks
2. Multi-step calculation and interpretation — H2 + I2 ⇌ 2HI disturbance (Band 5–6)
7 marks Band 5–6
The reaction H2(g) + I2(g) ⇌ 2HI(g) has Keq = 54.3 at 430 °C. A sealed flask is brought to equilibrium with the following concentrations: [H2] = 0.020 mol/L, [I2] = 0.020 mol/L, [HI] = 0.148 mol/L.
Q2a. Verify that this mixture is at equilibrium by calculating Q and comparing it to Keq. Show full working. 2 marks
Q2b. 0.040 mol/L of I2 is injected into the flask. Calculate the new Q immediately after injection and state the direction of shift. Show working. 2 marks
Q2c. Describe, step by step, how Q changes as the system moves from the disturbed state (after I2 injection) back to the new equilibrium. Refer specifically to which concentrations change and how each change affects the numerator and denominator of Q. 2 marks
Q2d. State one assumption made when applying Q analysis to a real gas-phase reaction in a sealed flask that may limit the accuracy of the prediction. 1 mark
Q1a — Q calculations at T1, T2, T3 (3 marks)
Expression: Q = [NH3]² / ([N2][H2]³)
T1: Q = (0.000)² / (0.800)(2.400)³ = 0 / (0.800 × 13.824) = 0. [Pure reactants → Q = 0]
T2: Q = (0.420)² / (0.450)(1.350)³ = 0.1764 / (0.450 × 2.460) = 0.1764 / 1.107 = 0.159 (3 s.f.)
T3: Q = (0.150)² / (0.200)(0.300)³ = 0.0225 / (0.200 × 0.0270) = 0.0225 / 0.00540 = 4.17 (3 s.f.)
[1 mark per correct Q with working shown]
Q1b — Direction of shift (3 marks)
T1: Q = 0 < Keq = 0.500. System shifts right (forward) — NH3 forms from N2 and H2. [1]
T2: Q = 0.159 < Keq = 0.500. System still shifts right (forward) — more NH3 is needed. [1]
T3: Q = 4.17 > Keq = 0.500. System shifts left (reverse) — NH3 decomposes back to N2 and H2. [1]
Q1c — Evaluation of the operator’s claim (2 marks)
Q-direction prediction: The operator is wrong about Q. From the table data at T3, Q = 4.17 > Keq = 0.500 (as calculated in Q1a/Q1b). The operator’s quoted value of Q = 0.188 does not match the given concentrations and is incorrect. Because Q > Keq, the system must shift left (not right) — NH3 is actually in excess of equilibrium at T3, and the reactor needs to decompose NH3, not produce more of it. [1]
Temperature recommendation: The operator is also wrong about the temperature strategy. The Haber process is exothermic in the forward direction (NH3 synthesis, ΔH = −92 kJ/mol). Increasing temperature shifts the equilibrium left (Le Chatelier’s Principle: system opposes added heat by reversing the exothermic forward reaction), which decreases Keq. At 400 °C, Keq = 0.500; at 300 °C, Keq = 977. Increasing temperature would decrease Keq further, making the equilibrium even less favourable for NH3 production — the opposite of what is needed. [1]
Q2a — Verify equilibrium (2 marks)
Q = [HI]² / ([H2][I2]) = (0.148)² / (0.020)(0.020) = 0.021904 / 0.000400 = 54.76 ≈ 54.3.
Q ≈ Keq = 54.3 (within rounding of given data — 3 significant figures). The mixture is verified to be at (or very close to) equilibrium. [1 correct calculation; 1 explicit comparison and conclusion]
Q2b — New Q after I2 injection (2 marks)
New [I2] = 0.020 + 0.040 = 0.060 mol/L. [H2] and [HI] are momentarily unchanged at 0.020 and 0.148 mol/L respectively.
New Q = (0.148)² / (0.020)(0.060) = 0.021904 / 0.001200 = 18.25.
Q = 18.25 < Keq = 54.3. System shifts right (forward direction). [1 correct new Q; 1 Q < Keq → shift right]
Q2c — How Q changes during approach to new equilibrium (2 marks)
After I2 injection, Q < Keq, so the system shifts right: H2 and I2 are consumed and HI is produced. As [HI] increases, the numerator of Q (= [HI]²) increases. As [H2] decreases and [I2] decreases, the denominator (= [H2][I2]) decreases. Both effects cause Q to increase progressively. This continues until Q has risen back to equal Keq = 54.3, at which point the new equilibrium is established. Q does not overshoot Keq; it approaches asymptotically from below. [1 correct direction of change in each concentration with effect on Q expression; 1 Q increases toward Keq asymptotically until Q = Keq]
Q2d — Assumption / limitation (1 mark)
Accept any one of: (i) Q analysis assumes ideal gas behaviour (activity = concentration in mol/L); real gases at high pressures deviate from ideal behaviour, so the actual Q may differ from the calculated value. (ii) Q analysis assumes the temperature remains constant; in practice, the injection of I2 and the subsequent exothermic shift right may slightly raise the temperature, which would alter Keq. (iii) The model assumes instantaneous mixing of the added I2 before any reaction occurs; in practice mixing and reaction are simultaneous.