Haber's Process: MDCAT Chemistry notes
Haber's Process MDCAT notes: ammonia synthesis conditions from Le Chatelier's principle, yield versus rate, iron catalyst and the contact process.
The reaction
$$\mathrm{N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)}\qquad \Delta H = -92.4\ \mathrm{kJ\,mol^{-1}}$$
The Haber process makes ammonia from nitrogen and hydrogen. Two features decide the conditions:
- The forward reaction is exothermic.
- It goes from 4 moles of gas to 2, so volume decreases ($\Delta n = -2$).
$$K_c = \frac{[\mathrm{NH_3}]^2}{[\mathrm{N_2}][\mathrm{H_2}]^3}\qquad \text{unit: } \mathrm{dm^6\,mol^{-2}}$$
Applying Le Chatelier's principle
| Condition | Effect on yield of $\mathrm{NH_3}$ | Reason |
|---|---|---|
| High pressure | Increases | Favours fewer gas molecules |
| Low temperature | Increases | Forward reaction is exothermic |
| Removing $\mathrm{NH_3}$ continuously | Increases | Pulls the equilibrium forward |
| Adding more $\mathrm{N_2}$ or $\mathrm{H_2}$ | Increases | More reactant drives it forward |
| Increasing volume | Decreases | Lowers pressure |
| Catalyst | No change in yield | Only speeds up attainment of equilibrium |
So the maximum yield needs high pressure, low temperature and continual removal of ammonia.
Industrial conditions: a compromise
- Pressure: about 200 to 300 atm. High pressure gives a better yield; still higher pressures are costly and hazardous.
- Temperature: about 400 to 450 °C. A low temperature favours yield but makes the reaction too slow. This optimum temperature balances a reasonable yield with a workable rate.
- Catalyst: finely divided iron, with promoters, to reach equilibrium quickly.
- Ammonia is removed by cooling it to a liquid, and the unreacted $\mathrm{N_2}$ and $\mathrm{H_2}$ are recycled.
At these temperatures $\mathrm{N_2}$, $\mathrm{H_2}$ and $\mathrm{NH_3}$ are all in the gaseous state.
Contact process (related industrial equilibrium)
$$\mathrm{2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)}\qquad \Delta H \text{ negative}$$
- Exothermic and decreases gas moles (3 to 2), so the same reasoning applies.
- Catalyst: vanadium pentoxide, $\mathrm{V_2O_5}$.
- Optimum temperature: about 400 to 500 °C; pressure only slightly above atmospheric, because the yield is already high.
- $\mathrm{SO_3}$ is absorbed in concentrated $\mathrm{H_2SO_4}$ to form oleum, $\mathrm{H_2S_2O_7}$. Adequate water is then added to oleum to give sulphuric acid: $\mathrm{H_2S_2O_7 + H_2O \rightarrow 2H_2SO_4}$.
- $\mathrm{SO_3}$ is not dissolved directly in water because it forms a mist of acid that is hard to condense.
Key formulas
- $K_p = K_c(RT)^{\Delta n}$ with $\Delta n = -2$ for ammonia, so $K_p \lt K_c$.
Common MDCAT traps
- Continual removal of ammonia raises yield; addition of ammonia lowers it.
- Low temperature favours yield; the moderate industrial temperature is chosen for rate, not yield.
- High pressure (about 200 atm) is used for better yield, not for a lower rate or lower cost.
- Catalyst for Haber is iron; for the contact process it is $\mathrm{V_2O_5}$. Do not swap them.
- In the contact process water is added to $\mathrm{H_2S_2O_7}$, not directly to $\mathrm{SO_3}$.
Quick revision
- Haber: $\mathrm{N_2 + 3H_2 \rightleftharpoons 2NH_3}$, $\Delta H = -92.4$ kJ/mol.
- Conditions: 200 to 300 atm, about 450 °C, iron catalyst.
- High pressure and low temperature favour ammonia.
- Contact process uses $\mathrm{V_2O_5}$ at 400 to 500 °C.
- Oleum is $\mathrm{H_2S_2O_7}$.