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Chapter 59: Problem 16

What is the mathematical relationship between \(E_{\mathrm{a}}\) (forward), \(E_{\mathrm{a}}\) (reverse), and \(\Delta H\) ?

Short Answer

Expert verified
\(E_{\mathrm{a}}\) (reverse) = \(E_{\mathrm{a}}\) (forward) + \(\Delta H\).

Step by step solution

01

Understanding the relationship between activation energy and change in enthalpy

The energy of activation in the forward direction, \(E_{\mathrm{a}}\) (forward), is the energy barrier that must be overcome for a reaction to proceed. The change in enthalpy, \(\Delta H\), represents the difference in the energy of the reactants and the products. If the reaction is exothermic (\(\Delta H < 0\)), the products have lower energy than the reactants. If the reaction is endothermic (\(\Delta H > 0\)), the products have higher energy than the reactants.
02

Understanding the relationship between the forward and reverse activation energies

The energy of activation in the reverse direction, \(E_{\mathrm{a}}\) (reverse), is the energy barrier that must be overcome for the reaction to proceed in the opposite direction. In an exothermic reaction (\(\Delta H < 0\)), \(E_{\mathrm{a}}\) (reverse) is higher than \(E_{\mathrm{a}}\) (forward), because it's harder to convert low-energy products back into high-energy reactants. In an endothermic reaction (\(\Delta H > 0\)), \(E_{\mathrm{a}}\) (reverse) is lower than \(E_{\mathrm{a}}\) (forward), because it's easier to convert high-energy products back into low-energy reactants.
03

Diagramming the relationship

From the given descriptions in Step 1 and Step 2, we can summarize these relationships into a formula: \(E_{\mathrm{a}}\) (reverse) = \(E_{\mathrm{a}}\) (forward) + \(\Delta H\). In this formula, the activation energy in the reverse direction equals the activation energy in the forward direction plus the change in enthalpy.

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