General Chemistry/Introduction to Kinetics

Chemical kinetics is the study of the rates of chemical reactions. You may know if a reaction is capable of happening, and you may know how far the reaction will proceed, but you don't know fast it will happen. Consider two reactions: the rusting of an iron nail and the combustion of propane. Both reactions will occur, and both will occur to completion. The rusting will take years to complete, but propane will combust in an instant. Furthermore, the nail will rust faster when it's moist, and slower in the presence of less oxygen. Obviously, there are factors that affect the rates of chemical reactions. The study of these factors and rates is chemical kinetics.

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  This iron wire has taken years to become rusty.
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  This fire took only a moment to start.

Reaction Rate

$a{\hbox{A}}+b{\hbox{B}}\to c{\hbox{C}}+d{\hbox{D}}$	Consider this generic chemical reaction. (Lower case letters represent the molar coefficients.)
$r=-{\frac {1}{a}}{\frac {d[{\hbox{A}}]}{dt}}=-{\frac {1}{b}}{\frac {d[{\hbox{B}}]}{dt}}={\frac {1}{c}}{\frac {d[{\hbox{C}}]}{dt}}={\frac {1}{d}}{\frac {d[{\hbox{D}}]}{dt}}$	The reaction rate $r$ is defined as the rate of change of the concentration of the substances. Remember that a substance written inside brackets is its concentration, and it is always raised to the power of its coefficient in the reaction (just like equilibrium expressions). The reaction rate involves Calculus, but in non-mathematical terms it is simply the rate of change of the concentrations.
$r=k[{\hbox{A}}]^{a}[{\hbox{B}}]^{b}$	Actually measuring the rate of change of the reactants and products is difficult. Instead, the reaction rate can be accurately modeled by a rate equation. This is an example of a rate equation that might model the above reaction, where $k$ is a constant.

In summary, the reaction rate can be determined using a rate equation, which depends on (among other things) the concentration of the reactants. The reaction rate essentially measures the speed at which a reaction proceeds.

Collision Theory

All reactions have activation energy regardless of being endothermic or exothermic.

Collision theory predicts that reactions occur when molecules collide. In order for reactants to form products, the reactant molecules must physically collide so that they can rearrange themselves into product molecules. Only some collisions are effective because the collision must involve enough energy to allow the reaction to occur. This is called activation energy, the energy needed to begin a reaction.

Activation energy explains why gasoline will not spontaneously ignite. First, a small spark or flame must be present. The heat generated by the spark gives the gasoline molecules enough energy to activate the reaction. Being highly exothermic, the combustion of gasoline releases a large amount of heat—more than enough to activate further reactions and create a fire.

Collision theory allows us to predict the rate constant $k$ for a rate equation (see above). At a given temperature $T$, the rate constant is:

$k=Z\rho e^{-E_{a}/(RT)}$,

where $R$ is the Universal Gas Constant, $E_{a}$ is the activation energy for the reaction, $\rho$ is a predicted-to-actual correction factor, and $Z$ is the collision factor. The collision factor can also be calculated mathematically. It is the average number of reactant particle collisions per unit time.

Factors Affecting Rate

The rate of a reaction is affected by many factors. These effects can be measured empirically or explained by collision theory.

Concentration

This is the most obvious factor affecting rate. Increasing the concentration of the reactants will increase the rate they react. This is the main purpose of writing a rate equation; the concentrations can be plugged in like variables and the rate can be solved mathematically. In a rate equation in the form $r=k[{\hbox{A}}]^{a}[{\hbox{B}}]^{b}$, the concentrations are the variables (raised to the powers of their coefficients in the reaction). All other factors that can affect rate are lumped into $k$, which is considered a constant.

Collision theory explains this. Higher concentrations means more molecules packed into a given space. Therefore, there will be more collisions and thus a faster reaction.

Pressure

In a reaction of gaseous reactants, the partial pressure of the gases has the same function as the concentration.

Adding an inert gas like argon will not affect the rate because the partial pressures of the reacting gases remain the same.

However, increasing the overall pressure (or decreasing the volume if you remember the gas laws) will also result in a greater reaction rate. The increased pressure causes the molecules to collide with more force. More collisions will be effective and therefore products will form faster.

Temperature

As you should already know, a molecule's kinetic energy is directly proportional to its temperature. By increasing the temperature, molecules collide more vigorously, and more collisions will be effective.

Stirring

In a heterogeneous reaction there are two or more phases of matter interacting, such as a solid dissolving into a liquid. Stirring or shaking the mixture will speed up the reaction rate. This is common sense. When you add sugar to a drink, you stir it because you know it will dissolve faster. Collision theory would predict this because the stirring would increase the number of collisions between reactant molecules.

In a similar manner, increasing the surface area of a solid reactant will increase the reaction rate.

Catalysts/Enzyme

The activation energy E_a is decreased by a catalyst, but the overall reaction does not change.

A catalyst is a substance that helps a reaction proceed without being consumed. Catalysts have already been explored in this book. A Catalyst provides a reaction pathway with lower activation energy.

In biochemistry, an enzyme is a protein that serves as a catalyst.