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Why are many exothermic reactions, like Haber process, conducted at high temperature, thus their unfavourable equilibrium position?

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There are two competing problems in the Haber Bosch process: the equilibrium position and the reaction rate. The reaction: $\ce{N_2 + 3H_2 -> 2NH3}\ (\Delta H = -92.4 \mathrm{\ kJ/mol})$ is exothermic and the equilibrium is actually favourable at room temperature, but the rate is very slow due to the large energy barrier to breaking the triple bond in $\ce{N2}$. To increase the reaction rate, a catalyst is used at high temperature. As you say, the high temperature pushes the equilibrium towards the reactants (by the Van 't Hoff equation) so there is a competition between yield and rate.

In practice, high pressure is also used to increase the yield (since the products side of the equation has fewer molecules), and like many industrial processes, it's run as a recirculating process. At manageable pressures and temperatures, they may only get 10 or 15% yield after one pass, but the ammonia is removed and the unreacted gases passed back into the reactor, giving quite high overall yield.

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