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Is it necessary that all endothermic reactions be slow and all exothermic reactions fast? This is based on the fact that endothermic reactions require more activation energy than exothermic reactions to initiate a chemical reaction. Or are there some endothermic reactions that can be fast without the presence of a catalyst?

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    $\begingroup$ Why should endothermic reactions have a higher activation energy? $\endgroup$ – bon Aug 17 '15 at 20:58
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A reaction being endothermic or exothermic depends on thermochemistry while the rate of a reaction depends on its chemical kinetics. Hence, there is no relationship between the activation energy of a reaction and its enthalpy change. Also there is no relationship between the change enthalpy and the rate of a reaction. A rate of reaction is dependent on the concentration of the reactants which are to a certain power which is multiplied by a certain constant, k, which is called the reaction rate constant. For example, for the general reaction: $$\ce{A + B -> C}$$ the rate of the reaction is given by the following equation: $$ rate = k[A]^a[B]^b$$ The reaction rate constant is not dependent on whether a reaction is exothermic or endothermic. However is does depend on the temperature and and also the activation energy of the reaction, given by the equation: $$k = Ae^\frac{-E_a}{RT}$$ So you are right to say that a reaction will be slower if it has a higher activation energy, but you are wrong to say that endothermic reactions have a higher activation energy than exothermic reactions.

There are actually several endothermic reactions that are fast, for example, dissolving common table salt (NaCl) occurs pretty quickly, but it is actually a endothermic reaction. Meanwhile, the spontaneously decomposition of diamond to graphite is actually a exothermic reaction, however it is extremely slow. It is so slow that it not even observed after several decades.

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The activation barrier is cause by energy needed to form the transition state between reactants and products. While it is generally true that the activation energy, and hence rate constant, is not related to how exothermic or endothermic the reaction is that is not the whole story.

If a reaction is endothermic by $+ \Delta E$ then the activation barrier has always to be at least this large for the products to be reached. Of course the barrier could be larger. (Although complicated protein unfolding is an example of a reaction in which the overall activation energy is large and only slightly greater than the endothermicity. Since many proteins spontaneously fold, the barrier to folding is small.)

In an exothermic reaction (by $-\Delta E$), while there can be, and often there is, a large barrier it is possible for there to be no barrier, i.e. the reaction can be activationless. In this case, in solution or gas, the rate constant is limited by how fast the reactants can diffuse together. Many electron transfer reactions are barrierless.

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