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First Order Reaction

A general unimolecular reaction

where A is a reactant and P is a product is called a first-order reaction.

The rate is proportional to the concentration of a single reactant raised to the first power.

The decrease in the concentration of A over time can be written as:

Equation (2) represents the differential form of the rate law. Integration of this equation and determination of the integration constant C produces the corresponding integrated law.

Integrating equation (2) yields:

The constant of integration C can be evaluated by using boundary conditions. When t = 0, [A] = [A]₀. [A]₀ is the original concentration of A.

Substituting into equation (3) gives:

Therefore the value of the constant of integration is:

Substituting (5) into (4) leads to:

Plotting ln[A] or ln[A] / [A]₀ against time

creates a straight line with slope -k. The plot

should be linear up to a conversion of about

90%.

Equation (6) can also be written as:

This means that the concentration of A decreases exponentially as a function of time.

The rate constant k can also be determined from the half-life t_1/2. Half-life is the time it takes for the concentration to fall from [A]₀ to [A]₀ / 2.

According to equation (6) is obtained:

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