# Structural Biochemistry/Rate Laws

When studying Chemistry, it is important to consider both the chemical properties of the reactants and the conditions under which the reaction occurs, the mechanism by which it takes place, the rate at which it occurs and the equilibrium toward which it proceeds. The law of mass action states that the rate of a chemical reaction at a constant temperature depends only on the concentrations of the substances that influence the rate, which are usually one or more of the reactants, but can occasionally be a product. Another influence on the rate can be caused by the presence of a catalyst that does not appear in the balances chemical equation. The rate law can only be experimentally determined and can be used to predict the relationship between the rate of a reaction and the concentrations of reactants.

## Rate Equation

For almost all forward and irreversible reactions, the rate is proportional to the product of the concentrations of the reactants, each raised to some degree. For example, for the reaction aA+bB-> cC +dD, the rate is proportional to [A]^m[B]^n, that is: rate = k[A]^m[B]^n The k is the rate constant. Multiplying the units of k by the concentration factors raised to the appropriate powers give the rate in units of: concentration/time. The proportionality factor, k called the rate constant, is a constant at a certain temperature. There are dimensions in the constant and it can be easily determined by using dimensional analysis of a particular rate law.. It is commonly known that as the value of the k value increases, the reaction speed increases.

## Rate Law Determination through Experiment

The value of k (constant), x and y in the rate law equation (rate= [A]^m[B]n) must be determined experimentally for a given reaction at given temperature. the rate is measured as a function of the initial concentrations of the reactants A and B.

## Order or Reactions

Chemical reactions are often classified on the basis of kinetics as zero-order, first-order, second-order, mixed order, or higher-order reactions. The general reaction aA + bB → cC + dD will be used in the discussion next. First lets note what each of these orders means in terms of initial rate of reaction effect:

1. Zero-order in the reactant—there is no effect on the initial rate of reaction
2. First-order in the reactant—there initial rate of reaction doubles
3. Second order in the reactant—the initial rate of the reaction quadruples
4. Third order in the reactant—the initial rate of reaction increases eightfold

The equation of rate law

${\displaystyle -r_{A}=k_{A}(T)fn(C_{A},C_{B},...)}$

${\displaystyle k_{A}}$  is the specific rate of reaction, which also called the rate constant.

Generally, four reactions are involved with rate laws. The homogeneous reactions include only one phase. The Heterogeneous reactions include two or more phases, and usually appear at the interface between the phases. The reversible reactions depend on the concentrations of reactants and products that can react in both directions. The irreversible reactions react in only one direction until one of the reactants is exhausted.

Generally, there are four types of reaction order. The most common form is

${\displaystyle -r_{A}=k_{A}C_{A}^{a}C_{B}^{b}}$

The units of the specific reaction rate constant are

${\displaystyle k=(Concentration)^{1-n}/Time}$

The four types of reaction order:

• Zero-order (n=0): ${\displaystyle -r_{A}=k_{A}}$

The unit of k of zero-order is ${\displaystyle mol/dm^{3}/s}$

• First-order (n=1): ${\displaystyle -r_{A}=k_{A}C_{A}}$

The unit of k of first-order is ${\displaystyle s^{-1}}$

• Second-order (n=2): ${\displaystyle -r_{A}=k_{A}C_{A}^{2}}$

The unit of k of second-order is ${\displaystyle dm^{3}/mol/s}$

• Third-order (n=3): ${\displaystyle -r_{A}=k_{A}C_{A}^{3}}$

The unit of k of third-order is ${\displaystyle (dm^{3}/mol)^{2}/s}$

## References

Fogler, H. Scott. "Chapter 3." Essentials of Chemical Reaction Engineering. Upper Saddle River, NJ: Prentice Hall, 2011. N. pag. Print.