Chemistry for Liberal Studies - Forensic Academy / Dr. Stephanie R. Dillon

# The Rates of Chemical Reactions

As we saw in the previous lecture, the speed at which a reaction takes place can be very important to the results of the reaction. Within the area of forensic investigation, the part of the investigation most concerned with the speed of reactions is the investigation of death. Both the time of death and the chemical processes that take place after a person dies are of great interest to an investigator. A chemist can use his or her knowledge of what happens chemically to a body after death to assist in pinpointing both the method and time of death. For this lecture we will be discussing those chemical processes that take place in the body immediately and over time after death. We will start with a general explanation of how chemists study the rates of reactions.

### Reaction Rates

Chemical reactions require varying lengths of time for completion, depending upon the characteristics of the reactants and products and the conditions under which the reaction is taking place. Chemical Kinetics is the study of reaction rates, how reaction rates change under varying conditions and by which mechanism the reaction proceeds.

Factors that affect the rate of a reaction

There are five general properties that can affect the rate of a reaction:

• The concentration of the reactants. The more concentrated the faster the rate.
• Temperature. Usually reactions speed up with increasing temperature.
• Physical state of reactants. Powders react faster than blocks - greater surface area and since the reaction occurs at the surface we get a faster rate.
• The presence (and concentration/physical form) of a catalyst (or inhibitor). A catalyst speeds up a reaction, an inhibitor slows it down.
• Light. Light of a particular wavelength may also speed up a reaction

How does temperature affect the rate of a chemical reaction?

For two chemicals react, their molecules have to collide with each other with sufficient energy and in the correct orientation for the reaction to take place. The two molecules will only react if they have enough energy. By heating the mixture, you are raising the energy levels of the molecules involved in the reaction. Increasing temperature also means the molecules are moving around faster and will therefore "bump" into each other more often. More collisions afford more opportunities for reaction.

How do catalysts affect the rate of a reaction?

Catalysts speed up chemical reactions. Only very minute quantities of the catalyst are required to produce a dramatic change in the rate of the reaction. This is really because the reaction proceeds by a different pathway when the catalyst is present essentially lowering the activation energy required for the reaction to take place.

How does concentration affect the rate of a reaction?

Increasing the concentration of the reactants will increase the frequency of collisions between the two reactants. When collisions occur, they do not always result in a reaction (atoms misaligned or insufficient energy, etc.). Higher concentrations mean more collisions and more opportunities for reaction.

What affect does pressure have on the reaction between two gasses?

You should already know that the atoms or molecules in a gas are very spread out. For the two chemicals to react, there must be collisions between their molecules. By increasing the pressure, you squeeze the molecules together so you will increase the frequency of collisions between them. You can easily increase the pressure by simply reducing the volume of the reaction vessel the gases are in.

How does surface area affect a chemical reaction?

If one of the reactants is a solid, the surface area of the solid will affect how fast the reaction goes. This is because the two types of molecule can only bump into each other at the liquid solid interface, i.e. on the surface of the solid. So the larger the surface area of the solid, the faster the reaction will be. In a chemical reaction, you can’t just keep making the solid bigger and bigger to give more surface area since you would quickly be unable to fit it in your reaction vessel. But you can increase the surface area of a solid by cutting it up. Think of it this way, if you have a loaf of bread you have 6 sides of surface area, correct? What if you sliced it in half? Then you would have 12 sides of surface area, right? Now some of the sides would be slightly smaller than the original loaf but overall the surface area has increased. If you keep cutting the bread up, you keep increasing the surface area and provide more and more locations for a reaction to take place.

Which would react faster?

Reaction Rates

The rate of a reaction is defined at the change in concentration over time:

$$\text{rate} = { \text{change in concentration} \over \text{change in time} }$$

Rate Expressions describe reactions in terms of the change in reactant or product concentrations over the change in time. The rate of a reaction can be expressed by any one of the reactants or products in the reaction.

There are a couple of rules to writing rate expressions:

1. Expressions for reactants are given a negative sign. This is because the reactant is being used up or decreasing.
2. Expressions for products are positive. This is because they are increasing.
3. All of the rate expressions for the various reactants and products must equal each other to be correct. (This means that the stoichiometry of the reaction must be compensated for in the expression)

Example

In an equation that is written: 2X + 3Y → 5Z, the Rate Expression would be:

$$- {1 \over 2} { d[X] \over dt } = - {1 \over 3} { d[Y] \over dt } = {1 \over 5} { d[Z] \over dt }$$

This expression means that the rate at which the molecule X is disappearing is 2/3 as fast as the rate at which Y is appearing and 2/5 as fast as Z is appearing based on the stoichiometry (balance) of the reaction. This relationship is determined mathematically by multiplying both sides of each equation by 2.

Example:

$$2 (- {1 \over 2} { d[X] \over dt }) = 2 (- {1 \over 3} { d[Y] \over dt })$$

= $$- { d[X] \over dt } = - {2 \over 3} { d[Y] \over dt }$$

The lower case d in from of both [X] and t means "the change in". The brackets themselves mean the "concentration" of whatever molecule is inside of them. So the rate expression means the change in concentration over the change in time.

Experimentally, chemists measure the concentration of a reactant or product over a period of time to see the rate at which the molecules disappear or appear.