Which property of a reversible reaction can be used to predict the effect of a change in temperature on the value of the equilibrium constant? The change in entropy, the change in enthalpy, the change in Gibbs free energy, the current value of the equilibrium constant, or the reaction stoichiometry.
Let’s start by reviewing what we know about reversible reactions and equilibrium constants. If we have a reaction where A plus B are in equilibrium with C plus D, we can calculate the equilibrium constant by multiplying the concentrations of C and D, both raised to the power of their stoichiometric coefficient, all divided by the same for what’s on the left-hand side, the concentration of A raised to its coefficient multiplied by the concentration of B raised to its coefficient.
It’s important to remember that at a constant temperature, 𝐾, our equilibrium constant, is also constant. And we’re being asked, what happens if we change the temperature? What happens to the value of 𝐾? And how can we predict what happens to the value of 𝐾? Let’s remind ourselves of Le Chatelier’s principle. Le Chatelier’s principle states that when a change is made to a system, which is at equilibrium, the position of equilibrium moves in order to counteract that change.
You can think of this a bit like a seesaw with the reactants on one end and the products on the other. If we change something in the system, for example, the temperature, this will affect the equilibrium. By increasing the temperature, this means our system is no longer balanced. So the system itself will move the position of equilibrium to bring things back to the balance. So what we have to decide is what effect changing the temperature has on our equilibrium constant.
If we increase the temperature, Le Chatelier’s principle says that the reaction needs to shift to counteract that change. So if we add more heat, we need a reaction which takes away heat. And that’s our endothermic reaction. Remember that in reversible reactions, one of the directions is exothermic and one is endothermic. If we decrease the temperature, the system is going to change to produce more heat to counteract our initial change. And that means the exothermic reaction is favoured.
But how does this affect the equilibrium constant 𝐾? The answer is it depends on whether it’s the forward reaction or the backward reaction which is endo- or exothermic. Let’s use an example. Let’s imagine that we increase the temperature of our reaction. We know that an increase in temperature favours the endothermic reaction. In example number one, the endothermic reaction is the backwards reaction. In example number two, the endothermic reaction is the forward reaction. Remember that this is how we calculate the equilibrium constant 𝐾.
If we’re favouring the backwards reaction, then we’re going to have lots of A and B. And we’re going to deplete our reserves of C and D. We can approximate this as having a small numerator and a large denominator. When you divide a small number by a large number, you get a small number. So by increasing the temperature, we favour the backwards reaction which means that 𝐾 has decreased. We can do the same for equation two. In equation two, the forwards reaction is the endothermic reaction. And this is the one we favour. We’re going to produce lots of C and D and reduce how much A and B we have.
This means, relatively speaking, we’ll end up with a large number on the top and a small number on the bottom. And when you divide a large number by a small number, roughly speaking, you keep a large number. So when the forward reaction is endothermic and we increase the temperature, we also increase the equilibrium constant. We could do the same thing for a decrease in temperature. But actually, we already have enough information to answer our question. The question was, which property of a reversible reaction can we use to predict what happens to the equilibrium constant when we change the temperature?
We’ve seen that the property we’ve been using to predict what happens to 𝐾 is, which reaction is exothermic and which is endothermic, whether that’s forwards or backwards? So how can you tell whether a reaction is exo- or endothermic? Which value is it that we’re looking for? The answer, of course, is Δ𝐻 enthalpy. If Δ𝐻 is negative, that means that reaction is exothermic. If the Δ𝐻 is positive, that means your reaction is endothermic. So it’s Δ𝐻, the change in enthalpy that we’re using to predict what happens to the equilibrium constant. So the change in enthalpy is our answer.