Reaction Rate and the Reaction Coordinate Diagram

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When dissecting chemical reactions presented on the MCAT, we’re often interested in how fast the reaction occurs. The reaction rate is the rate at which reactants are converted to products. We can measure this rate using either of two methods: measuring either the rate of product production or the rate of reactant consumption. The rate at which a reaction occurs depends on energetic barriers intrinsic to the reaction, something which we can represent visually on a reaction coordinate diagram.
Determining Reaction Rate
A formula for reaction rate can be extrapolated from a reaction formula. Consider the reaction of nitrogen and hydrogen gas, forming ammonia. Note that over any amount of time, if 2 moles of ammonia are produced, 3 moles of hydrogen gas and 2 moles of nitrogen gas must have been consumed. Notice correspondingly that in the reaction rate, each term has a unique coefficient denoting the relative amount of change. In the rate shown below, “1/2 NH3” means that the concentration of ammonia is increasing half as fast as nitrogen gas is decreasing. The reaction rate can thus be understood as the net change in concentration of any of the reactants or products, divided by the total reaction time. A negative reaction rate, such as with hydrogen gas, implies that the concentration of hydrogen is decreasing. In other words, hydrogen is being subtracted from the reaction mixture.
Measuring the change in concentration of any of the reactants or products over a period of time, and plugging those numbers into the reaction rate formula, will produce the same value for rate. For instance, you could measure 10 moles of nitrogen gas disappearing over 10 minutes, or 20 moles of ammonia being produced over 10 minutes. Regardless, plugging empirical measurements into the formula for rate derived from the reaction formula will yield the same final value.
Reaction Coordinate Diagrams
A reaction coordinate diagram depicts the energy of molecules during the course of a chemical reaction. There are several key points on the reaction coordinate diagram to take note of. The very beginning of the diagram denotes the reactants, while the very end of the diagram denotes the products. A “peak” in between the reactants and products denotes the transition state of a reaction. A transition state is a very short lived, highly unstable structure that is intermediate between the reactants and products. It requires a great amount of energy to convert the reactants or products into the transition state. The energy required to do so is known as the “activation energy” of a reaction. Without a large amount of energy dumped into a reaction to force the reactants into the transition state, the reaction will not proceed. Thus, this peak can be thought of as a barrier to the reaction proceeding.
If the products of a reaction were located higher up on the reaction diagram than the reactants, the reactants must have undergone a net increase in energy over the course of the reaction. This, by definition, would mean the reaction was endergonic, taking up energy from the environment. On the other hand, if the products of a reaction were located lower on the diagram than the reactants, the reactants must have undergone a net decrease in energy. A reaction like that would be correspondingly called exergonic, releasing energy into the environment.
Some reactions can have two transition states. This appears on a reaction coordinate diagram as two “peaks” in between the reactants and diagrams. But if there are two peaks, what’s in between the two transition states? The low energy trough in between two transition states is known as an intermediate state. An intermediate state of a reaction is relatively unstable, but not quite as unstable as a transition state. Within a reaction mixture, we might expect to be able to isolate an intermediate state structure before it turns into the product state. Within a given reaction, if there are multiple transition states, the one that requires the largest amount of energy to form (the most prominent “peak” on the reaction diagram) is the slowest step. Being the slowest step, it limits the rate of the reaction.
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