Chemical equilibrium
Le Chatelier says that ammonia is best made cold, and kinetics says that cold is never how it is made. Almost every industrial process lives in the negotiation between those two answers.
01Reactions that come back
Many reactions do not go to completion: they reach a point at which the forward and reverse reactions occur at the same rate and the concentrations stop changing. That is chemical equilibrium, and it is dynamic: underneath everything keeps happening, but the net balance is zero.
The reaction quotient \( Q \) has the same form but is calculated with the concentrations at that moment. Comparing \( Q \) with \( K \) tells you which way the system will move: if \( Q \lt K \), toward the products; if \( Q \gt K \), toward the reactants; and if they are equal, it is already at equilibrium.
It speeds up the forward and reverse reactions in the same proportion, so the end point does not move: what changes is how long it takes to get there. That is why the iron catalyst of the Haber-Bosch process does not increase the theoretical yield; it makes it possible to reach it in a reasonable time at a temperature at which, without it, the reaction would be unworkable.
02Le Chatelier's principle
If a system at equilibrium is disturbed, the system shifts in the direction that partially counteracts the disturbance. There are three possible disturbances and each has its own rule:
| Disturbance | The system responds | Does \( K \) change? |
|---|---|---|
| Adding a reactant | By consuming it: it shifts toward products | No |
| Increasing the pressure | Toward the side with fewer moles of gas | No |
| Increasing the temperature | Toward the endothermic side | Yes |
The third row is the only one that really changes \( K \); the other two move the concentrations within a \( K \) that keeps the same value. The dependence on temperature has its own equation:
Four gas-phase equilibria, chosen to cover the four possible cases. Move temperature and pressure and the composition is recalculated. Pay attention to the last one: it has the same number of moles on both sides.
03The trade-off in every industrial process
Ammonia synthesis is exothermic and goes from four moles of gas to two. Le Chatelier then says that high pressure and low temperature are favorable. But at low temperature the reaction, although favorable, is so slow that it does not occur: kinetics rules over equilibrium.
Haber and Bosch resolved the conflict from both sides: an iron catalyst so that the kinetics suffices at moderate temperature, about 200 atmospheres to push the equilibrium, and recycling of what did not react. Neither the thermodynamic optimum nor the kinetic one is chosen: what is chosen is the point where the product of the two yields the most per hour.
The growth of the gate oxide is exothermic, so thermodynamics would prefer to do it cold. But at room temperature the oxide grows two nanometers and stops. That is why thermal oxidation is done at 1000 °C, where the equilibrium is less favorable but the kinetics allows finishing in hours instead of centuries. It is exactly the same trade-off.
04In the lab
With a sealed tube of NO₂ in equilibrium with N₂O₄, immerse it alternately in hot water and in ice. Record the color and deduce the sign of \( \Delta H \) from the direction in which the equilibrium shifts.
On the iron(III) thiocyanate equilibrium, separately add iron(III) ion, thiocyanate and an agent that complexes iron. Predict with \( Q \) and \( K \) the direction of the shift before each addition, and compare with the color.
Determine \( K \) of the thiocyanate equilibrium by colorimetry at two temperatures and obtain \( \Delta H^{\circ} \) with van 't Hoff. Discuss the uncertainty of calculating a slope with only two points.
05Common mistakes
- Believing that everything stops at equilibrium. It is dynamic: both reactions continue, at the same rate.
- Including pure solids and liquids in \( K \). Their activity is 1 and they do not appear.
- Thinking that pressure changes \( K \). It changes the concentrations, not the constant.
- Applying the pressure effect when \( \Delta n = 0 \). If there is the same number of moles of gas on both sides, compressing shifts nothing.
- Expecting a catalyst to improve the yield. It improves the time, not the end point.
- Confusing a large \( K \) with a fast reaction. They are different things: one is equilibrium, the other kinetics.
06Self-assessment
What does the equilibrium constant depend on?
Only on temperature. Neither pressure, nor the initial amounts, nor a catalyst modifies it.
Which way does an equilibrium shift when compressed?
Toward the side with fewer moles of gas. If there is the same number on both sides, it does not shift.
What happens to \( K \) of an exothermic reaction when heated?
It decreases: the system shifts toward the endothermic side, which is the reactant side.
What is the use of comparing \( Q \) with \( K \)?
To know in which direction the system will evolve. If \( Q \lt K \), toward products.
Why does the Haber-Bosch process use 200 atmospheres?
Because the reaction goes from four moles of gas to two, and pressure shifts the equilibrium toward ammonia.
Why is it not carried out at low temperature, since it is exothermic?
Because there the kinetics is impractically slow. The chosen point is a compromise between equilibrium and rate.
07Further reading
- Raymond Chang and Kenneth A. Goldsby. Chemistry. 12th ed. (Spanish edition, “Química”), McGraw-Hill, 2017. Chapter 14: equilibrium constant, reaction quotient and Le Chatelier, with the Haber process worked out.
- Peter Atkins and Julio de Paula. Physical Chemistry. 10th ed. (Spanish edition, “Química física”), Editorial Médica Panamericana, 2018. Equilibrium from the Gibbs free energy, which is where van 't Hoff comes from.
- Ralph H. Petrucci et al. General Chemistry. 11th ed. (Spanish edition, “Química general”), Pearson, 2017. Worked gas-phase equilibrium problems, with the ICE-table method.