# Chemical Kinetics and Chemical Equilibrium

## Chemical kinetics is the study of how quickly a chemical reaction occurs and what factors affect its rate.

#### Key Points

• The reaction time is the interval required for a reaction to occur. Every reaction has a reaction time and therefore a rate. Reaction rates are not usually constant over a given reaction time. The reaction reaches equilibrium when its rate is constant.

• The rate at which products are formed and reactants are used up determines the speed of the reaction. It can be expressed as the ratio of the change in the concentration of a reactant (or product) to the change in time. The unit of this rate is usually M/second.

• Actually measuring the rate of a reaction is difficult. Instead, it is modeled by a rate equation or rate law. The rate law depends on the concentrations of the reactants.

#### Terms

• a process wherein a fuel is combined with oxygen, usually at high temperature, releasing heat

• an equation involving the derivatives of a function

#### Figures

1. ##### Change in Concentration of Chemicals Over Time

Plot of time versus concentration for two species in chemical equilibrium

Consider two reactions: the rusting of an iron nail and the combustion of propane. Both reactions can 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 is moist, and it will rust more slowly in the presence of less oxygen.

Obviously, there are factors that affect the rates of chemical reactions. Knowing how quickly a chemical reaction occurs is a crucial factor in how the reaction affects its surroundings and vice versa. The study of these factors and rates is known as chemical kinetics.

The interval required for a chemical change or reaction to occur is called the reaction time. Every reaction has its own unique reaction time. Each reaction also has a reaction rate. Reaction rates are not usually constant over a given reaction time. As described in previous sections, the reaction reaches equilibrium when its rate is constant, as seen in Figure 1.

Consider this generic chemical reaction:

$aA + bB \rightarrow cC + dD$

The rate at which products are formed and reactants are used up determines the speed of the reaction. This rate can be expressed as the ratio of the change in the concentration of a reactant (or product) to the change in time.

$r = -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$

The reaction rate involves differential equations, but in non-mathematical terms it is simply the rate of change in the concentrations. Since it is customary to define rates as positive quantities and the change in the concentration of the reactants is negative, the values of [A] and [B] are preceded by minus signs so that the final result will be positive. The unit of this rate is usually M/second.

Actually measuring the rates of change in 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:

$r = k[A]^a[B]^b$

where k is a constant. The reaction rate can be determined using a rate law, which depends on the concentrations of the reactants, among other things. You can read more about reaction rates and rate laws in the Kinetics unit.

#### Key Term Glossary

chemical reaction
A process involving the breaking or making of interatomic bonds, in which one or more substances are changed into others.
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combustion
a process wherein a fuel is combined with oxygen, usually at high temperature, releasing heat
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concentration
the proportion of a substance in a mixture
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constant
Consistently recurring over time; persistent
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differential equation
an equation involving the derivatives of a function
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equilibrium
the state of a reaction in which the rates of the forward and reverse reactions are the same
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kinetics
The branch of chemistry that is concerned with the rates of chemical reactions.
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oxygen
a chemical element (symbol O) with an atomic number of 8 and relative atomic mass of 15.9994
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product
a chemical substance formed as a result of a chemical reaction
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Rate law
The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with concentrations or pressures of reactants and constant parameters (normally rate coefficients and partial reaction orders).
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ratio
The relative magnitudes of two quantities (usually expressed as a quotient).
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reactant
Any of the participants present at the start of a chemical reaction. Also a molecule before it undergoes a chemical change.
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reaction rate
how fast or slowly a reaction takes place
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surroundings
All parts of the universe that are not within the thermodynamic system of interest.