Higher or lower temperature to produce maximum yield of NH3(g) in Haber process

Question

Question: In order to get the highest yield of NH3(g) in Haber process, should you use high or low temperature?

The answer in the textbook says lower temperature produces more yield of NH3(g) in Haber process since it is exothermic. Doesn't lower the temperature also lower the reaction rate which results lower yield? My teacher says higher temperature produces more NH3(g) even though the the reaction shifts to the reactant side.

Answer 1

The book is right, and so is your teacher.

• The reaction is exothermic, $\ce {N2 + 3 H2 -> 2 NH3}$, ΔH° = -91.8 ~kJ/mol, so higher temperature leads to decomposition, i.e., makes $\ce{2 NH3 -> N2 + 3H2}$ the preferred reaction.
• The rate of reaction would be rather slow at STP (i.e., not coming to equilibrium within the lifetime of the universe), so even at high pressure (commonly 20 MPa), using a good catalyst, it is run at ~775 K because that optimizes profitable throughput.

Think also of carbon: at STP, graphite is more stable than diamond, but have no fear your gems and jewelry will change allotrope in your lifetime.

Answer 2

The oversimplified and probably expected answer is the higher yield is provided at lower temperature, as the reaction is exothermic and its equilibrium constant decreases with temperature.

But the scenario is more complicated and there are multiple factors to consider, as the Haber-Bosch process is more than just the reaction $\ce{3 H2 + N2 -> 2 NH3}$. (Considering temperature, pressure, flow, production rate, gas flow cost, catalyst efficiency, production loopbacks..)

• The initial reaction rate of synthesis of $\ce{NH3}$ exponentially raises with T.
• The reaction rate constant of $\ce{NH3}$ decomposition raises with T faster than the reaction rate constant of its synthesis.
• Above some reaction yield, the net reaction rate (initially faster) becomes slower for higher T than for lower T.
• Above some even higher reaction yield, the net reaction rate becomes slower for higher T due progressively fast backward reaction.
• As the Haber process is about $\ce{NH3}$ production, lower reaction yield with higher gas flow leads to higher production rate.
• For a given pressure, there exists such a "neutral gas flow" passing the catalyst providing a product "neutral yield" that more or less does not depend on T.
• If there is chosen gas flow lower than "neutral gas flow", the yield is higher than the "neutral yield" and than lower temperature leads to the higher yield.
• If there is chosen gas flow higher than "neutral gas flow", the yield is lower than the "neutral yield" and than higher temperature leads to the higher yield.
• Overall, tuning up parameters to optimize Haber-Bosch process is not a trivial task.