Reversible Reactions and Equilibrium: Question 9

Syllabus 6.3

Structured Extended 8 marks

The Contact process manufactures sulfur trioxide from sulfur dioxide and oxygen, using a vanadium(V) oxide catalyst:

2SO2(g)+O2(g)2SO3(g)2\text{SO}_2(g) + \text{O}_2(g) \rightleftharpoons 2\text{SO}_3(g)

The forward reaction is exothermic. Industrially, the Contact process operates at a temperature of 450 °C and a pressure of only about 200 kPa (roughly 2 atmospheres). Much lower than the 20 000 kPa used in the Haber process for ammonia,

N2(g)+3H2(g)2NH3(g)\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)

even though both reactions have fewer gas molecules on the product side than on the reactant side.

(a) For each reaction, state the number of moles of gas molecules on the reactant side and on the product side, and hence the overall decrease in the number of moles of gas molecules as the forward reaction proceeds. [2]

(b) Use your answer to part (a) to suggest why increasing the pressure has a smaller effect on the position of equilibrium, and therefore on the percentage yield, in the Contact process than in the Haber process. [2]

(c) The Contact process already achieves a very high percentage yield of sulfur trioxide at only 200 kPa. Using your answer to part (b), explain why it would not be economically sensible to increase the pressure further. [2]

(d) State and explain the effect that raising the temperature above 450 °C would have on the equilibrium yield of sulfur trioxide in the Contact process. [2]

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Worked solution

Part (a): Counting moles of gas on each side

Contact process:

2SO2(g)2 mol+O2(g)1 mol2SO3(g)2 mol\underbrace{2\text{SO}_2(g)}_{2\text{ mol}} + \underbrace{\text{O}_2(g)}_{1\text{ mol}} \rightleftharpoons \underbrace{2\text{SO}_3(g)}_{2\text{ mol}}

Reactant side: 2+1=32 + 1 = 3 mol of gas. Product side: 22 mol of gas. Decrease =32=1= 3 - 2 = 1 mol.

Haber process:

N2(g)1 mol+3H2(g)3 mol2NH3(g)2 mol\underbrace{\text{N}_2(g)}_{1\text{ mol}} + \underbrace{3\text{H}_2(g)}_{3\text{ mol}} \rightleftharpoons \underbrace{2\text{NH}_3(g)}_{2\text{ mol}}

Reactant side: 1+3=41 + 3 = 4 mol of gas. Product side: 22 mol of gas. Decrease =42=2= 4 - 2 = 2 mol.

Part (b): Why pressure has a smaller effect in the Contact process

Increasing pressure shifts the position of equilibrium towards the side with fewer gas molecules, since that partly relieves the increase in pressure.

In the Haber process, the forward reaction decreases the number of gas moles by 2 (from 4 to 2). In the Contact process, the forward reaction only decreases the number of gas moles by 1 (from 3 to 2). Because the Contact process’s forward reaction reduces the total number of gas particles by a smaller amount, increasing pressure can only relieve the pressure increase by a correspondingly smaller amount there. This means increasing pressure shifts the Contact process’s equilibrium, and therefore its percentage yield of SO3\text{SO}_3, by a smaller amount than it does for the Haber process’s equilibrium.

Part (c): Why it is not worth increasing the pressure further

Because pressure has only a small effect on the Contact process’s position of equilibrium (part (b)), and the percentage yield is already very high at 200 kPa, increasing the pressure further could only add a small additional amount of yield.

Building and maintaining high-pressure equipment is expensive (thicker vessel walls, stronger pipework, more powerful compressors, greater safety precautions for a mixture of corrosive gases). Since the extra yield gained would be small, this extra cost is not economically justified, unlike in the Haber process, where the equilibrium yield without high pressure is much lower, so the large investment in high-pressure equipment is worthwhile there.

Part (d): Effect of raising the temperature above 450 °C

The forward reaction (formation of SO3\text{SO}_3) is exothermic. By Le Chatelier’s principle, increasing the temperature always shifts the position of equilibrium in the endothermic direction. Here, that is the reverse reaction (breakdown of SO3\text{SO}_3 back into SO2\text{SO}_2 and O2\text{O}_2).

So raising the temperature above 450 °C would decrease the equilibrium yield of sulfur trioxide, even though it would make equilibrium be reached faster (since particles collide more frequently and with more of the collisions exceeding the activation energy).

Final answers

  • (a) Contact process: 323 \to 2 mol (decrease of 11); Haber process: 424 \to 2 mol (decrease of 22).
  • (b) The Contact process loses fewer gas moles overall, so pressure shifts its equilibrium, and its yield, by a smaller amount than in the Haber process.
  • (c) The extra yield from higher pressure would be small, so it does not justify the much higher cost of high-pressure equipment.
  • (d) Yield decreases above 450 °C, since the forward reaction is exothermic and higher temperature favours the reverse (endothermic) direction.