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you can think about it this way... the equilibrium constant k is basically products/reactants. If the activation energy is super high, then it's harder to form products since we have to first overcome this barrier. So when the numerator is smaller, k is smaller.
You can see the relationship by looking at the equation: k=Ae^(-Ea/RT); an e to a small number will give you a small k, whereas an e to a big number will give you a large k. In other words, the bigger Ea is, the smaller the value of k will be and vice versa.
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