General Chemistry Review – Chemical Kinetics

Chemical kinetics is the study of the rates of chemical reactions.  It can be essential for determining the mechanisms of chemical reactions. Here are the fundamentals of chemical kinetics that you must remember as you progress from general chemistry to organic chemistry.

1. Reaction rates are proportional to concentration and to temperature.

First and foremost, chemical reactions occur when atoms or molecules collide and the arrangement of their chemical bonds changes as a result. Therefore, the rate of a chemical reaction is proportional to the number of molecular collisions.  Not every collision will result in a chemical reaction; only a certain percentage of the total number of collisions will occur at the appropriate energy to allow the processes of chemical bond breaking and forming to occur. Consider a telemarketer selling Ginsu knives; only a small percentage of his calls will result in a sale, but the total number of sales will be proportional to the number of calls.

Anything that increases the collision rate in chemical reactions will increase the reaction rate. Increasing concentration is one way to achieve this. You may recall that what we refer to as "temperature" is a measure of atomic and molecular motion. Increasing the temperature is another method.

2. First and Second order reactions

Depending on the type of reaction, the transformation can involve either one or two chemical species. Due to the impossibility of three species colliding with the correct energy, reactions involving more than two chemical species are almost never observed.

The order of a reaction is determined by the number of species involved.

The rate of a chemical reaction is the number of molecules produced per unit volume per second, expressed as M/L•s. If we take the proportionality relationship, rate [fish] conc, and change it into an equation by introducing a constant k called the rate constant, we can write an equation for this. Each reaction has a unique rate constant that is valid at constant temperature, which makes sense given that an increase in temperature will increase the number of collisions and result in a different rate.

For a reaction involving a single species A, the rate is k[A], where [A] is the concentration of A in mol/L. For a bimolecular reaction A+B, the rate is k[A][B], where [A] and [B] are the concentrations of A and B, respectively.

In the SN1 reaction, which you will learn about in Org 1, the first step involves the breaking of a weak bond to produce a halide (in this case, bromide) and a carbocation. This is a unimolecular, first-order reaction. This reaction's rate constant can be expressed as rate = k [A].

In the second step, the carbocation reacts with a molecule of solvent (such as methanol) to produce an ether. This is a reaction of the second order. Note, however, that since the concentration of methanol is extremely high (it is the solvent), the small amount of methanol consumed in this reaction will have no effect on its concentration. Therefore, the reaction rate will depend solely on the concentration of C4H9 carbocation. This represents a pseudo-first order reaction.

Although there are many examples of reactions that involve a single overall transformation (such as HCl + NaOH giving water, for example), you will quickly discover in organic chemistry that multi-step reactions like the SN1 are far more prevalent. The sequence of chemical reactions that result in a specific product is known as the reaction mechanism.

3. The rate of a reaction is determined by the slowest step.

The rate of the slowest step determines the rate of the reaction. Since the first reaction in the preceding SN1 example is the slowest step, we can approximate the rate of the reaction using the rate law for this step. Therefore, the overall rate law of the SN1 reaction would be expressed as rate [C4H9OCH3] = k [C4H9Br]. In other words, at a given temperature, the rate of formation of C4H9OCH3 will be directly proportional to the concentration of C4H9Br and will not depend at all on the concentration of CH3OH.

4. Rate laws can give insight into the mechanism:

Here's a helpful hint: rate laws can actually provide information about mechanisms. The SN1 reaction, for instance, belongs to a class of reactions known as substitution reactions. The SN2 reaction is the second type of substitution mechanism. SN1's rate-determining step is unimolecular, whereas SN2's rate-determining step is bimolecular.

5. The barrier to reaction is called the activation energy.

My second-year physical chemistry professor once made the concept of activation energy shockingly clear by stating that, in thermodynamic terms, the combustion of human flesh to CO2 and water was extremely thermodynamically favourable, but our continued presence in his classroom was evidence of activation barriers. The point he was attempting to make was that the thermodynamics of a process provides no information regarding the rate.

The rate of a chemical reaction is dependent on the activation energy, which is the amount of energy required to reach a transition state that will result in the formation of a product.

In this equation, k represents the rate constant, T represents the temperature, R represents the gas constant, Ea represents the activation energy, and the mysterious letter A represents the so-called pre-exponential constant.

The rate constant k is the number of collisions per second that result in a reaction, A is the total number of collisions per second, and e(Ea/rt) is the probability that any particular collision will result in a reaction.

A baseball analogy follows. Suppose you are tasked with formulating an equation that will provide an estimate of the number of home runs hit in a specific ballpark. You could create an equation that resembled the following:

Number of home runs equals total number of balls hit. [likelihood ball has sufficient energy for a home run]

In this instance, the "activation energy" would be the distance from home plate to the outfield fences, which would be included in the "percentage" term (presumably along with the height of the fence). As the outfield fences are moved back, the amount of home runs will inevitably decrease. If you knew the number of balls hit and the energy required to clear the fence, you could possibly rearrange this equation to calculate the distance to the fence.

The Arrhenius equation is a potent tool for calculating the activation energy and rate constant at different temperatures. It is unlikely that you will be required to delve too deeply into the Arrhenius equation in your course, but it is still important to understand its subtleties.

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