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After thinking about it, I'm confused by what the reaction barrier of an enzyme actually means.
Imagine a reactor containing enzyme and substrate.
If the enzyme in the reactor has a reaction barrier of 15 kcal/mol,
a) then when 1 mole of product has formed, that means 15 kcal have been consumed, independent of how much enzyme is present in the reactor.
b) then when 1 mole of enzyme is present in the reactor and 1 mole of product is formed, 15 kcal have been consumed.
Is it option a), b) or otherwise?
Let us imagine two companies A and B. Both companies use very similar technical equipment to carry out a biotechnological process where a chemical reaction is catalyzed by an enzyme. Company A uses an enzyme with a reaction barrier of, say, 15 kcal/mol, while company B uses an enzyme to catalyze the same reaction but this enzyme has an activation energy of only, say 12 kcal/mol. For every Mole of product, company B saves 3 kcal worth of energy needed to drive the factory.
Does that make sense?
The reaction barrier (also termed activation energy) is the energy that is needed for the reaction to take place. An enzyme is "only" a catalysator which lowers the necessary energy (and/or makes the reaction possible under the conditions) but some energy to start a chemical reaction is still needed. See this image (from here):
To your questions: A and B are essentially the same - but the reaction time necessary with small amounts of enzyme is much longer than when 1 mole of enzyme is present. The amount of energy needed to catalyze the production of 1 mole of product stays the same.
The activation energy for a reaction is given for a given extent of reaction, typically per mole of product formed. In general, the amount of enzyme present in the reactor is irrelevant with respect to the activation energy. So option a) is closest to correct. However, note that the activation energy does not tell you how much energy is consumed taken up during the reaction, only how much energy is needed for the activation energy to be exceeded and the reaction to proceed. The kinetics of a reaction, is a separate issue from the thermodynamics of the reaction, which determines the equilibrium concentrations of substrate and product. What the enzyme does is lowering the activation energy, thus speeding up the kinetics of the reaction and allowing equilibrium to be reached. In practice, the activation energy in the absence of the enzyme may be so high that the reaction would not proceed at all, and thus equilibrium would not be reached.
To better understand the activation energy concept my teacher had given us an excellent example. Suppose you are driving a car and want to cross a mountain. You could either go to the mountain summit and then come down or you could directly cross it through a tunnel. What enzyme does is to construct a tunnel for the reaction to proceed.