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When looking at the reverse rate (k') of a reaction, why is a lower rate constant required for a higher energy barrier? Visa versa for forward reaction (k), why is a higher rate constant required for a lower energy barrier?
Well the rate constant is part of what determines the rate of the reaction. A larger rate constant corresponds to a faster reaction. If the energy barrier is lower then less energy is required for the reaction to occur, so the reaction will be faster and thus k must be larger.
This can be explained with the Arrhenius equation: k=A*Exp(-EA/(R*T)), which is determined through experiments. A higher energy level means reactants must collide with higher energy, which is harder to achieve. Therefore the rate is lower and the rate constant is smaller.
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