Activation energy

  1. In a typical General Chemistry textbook, quantitative treatments of activation energies begin with the Arrhenius equation, which is given (not derived). When R and T values are properly inserted with the given units, the activation energy comes out with the unit of J/mole.

    My Question 1: Suppose that the reaction in question is mA + nB -> pC + qD (two reactants and two products). If the activation energy involved in this reaction is determined to be xJ/mole, what does it mean? xJ per mole of which substance(s)?

    Typically, a schematic energy diagram accompanies such calculations, indicating an energy “mount” that represents the activation energy; and the same diagram usually indicates that the difference between the energy levels of the reactants and products is equal to the enthalpy change (delta H) of the reaction.

    Delta H of a reaction always carries the unit of J (not J/mole) – this is usually found in a different chapter of a book.

    My Question 2: I ran into a question that asks the following about a given reaction:
    (i) What is the activation energy of the forward reaction? (This was easily calculated; the answer came out with the unit of J/mole).
    (ii) What is the heat of reaction (delta H)? (This was also easily calculated from a table of standard heat of formation, by multiplying them with the number of moles, which yields a final answer bearing the unit of J (not J/mole)
    (iii) What is the activation of the reverse reaction? Here, it appears that the person who made the question is expecting students to simply add the forward activation energy and delta H, but I am having difficulty with the unit (and the meaning of “per mole” which I mentioned above).

    Clarification by an expert will be very much appreciated. Thank you.
  2. jcsd
  3. Ygggdrasil

    Ygggdrasil 1,612
    Science Advisor

    Activation energies make sense only when considering elementary reaction steps and not overall reaction equations. Typically elementary steps involve only a small amount of species, so we'll consider the reaction A + BC -> AB + C (similar to a SN2 reaction in organic chemistry where A reacts with BC to displace C from BC).

    In this case, the activation energy represents the energy needed to break the B-C bond, offset by the energy gained from the partial A-B bond. Thus the activation energy is a property of the specific reaction, and not any particular substance in the reaction. (In fact, the activation energy is specific to the pathway the reaction takes. If, for example, you change the pathway from reactants to products by adding a catalyst, the activation energy will change.)

    Energies given in units of joules actually represent energies per molecule. For example, in the reaction A + B -> C, a ΔH of 5J would mean that 5J of heat are absorbed when one molecule of C is produced. Therefore, to convert from energies per molecule to energies per mole, all you need to do is multiply by Avogadro's number (6.02x1023 mol-1).

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