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Suppose two different nucleophiles react with a single substrate via SN1. Would the energy of activation for the second transition state (nucleophile reacts with carbocation) be less for the better nucleophile? Would the products be of equal energy and produce a 1:1 mixture for both nucleophiles?

I know SN1 is unimolecular so changing the nucleophile would not change the reaction rate. Additionally, since the activation energy for the rate determing step was already surpassed, I believe the products will form in 1:1 mixture where both nucleophiles react equally and both products are of equal energy.

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