Derivation of Time Required for Zero Order Reaction & Half-Life Calculation

Zero-order reactions are chemical reactions that proceed at a constant rate independent of the concentration of the reactants. In this guide, we will derive the expression for the time required for a zero-order reaction and calculate its half-life.

Derivation of Time Required for Zero Order Reaction:

The rate law for a zero-order reaction is given by:

rate = k[R]^0 = k

where [R] is the concentration of the reactant and k is the rate constant.

We can integrate this rate law to obtain the expression for the time required for a zero-order reaction:

[R]t = [R]0 - kt

where [R]t is the concentration of the reactant at time t, [R]0 is the initial concentration of the reactant, and k is the rate constant.

To solve for time, we can rearrange this equation as:

t = ([R]0 - [R]t) / k

This is the expression for the time required for a zero-order reaction.

Half-Life Calculation:

The half-life of a zero-order reaction is the time required for the concentration of the reactant to decrease by half. We can calculate the half-life of a zero-order reaction using the expression we derived earlier:

[R]t = [R]0 - kt

Let's assume that the initial concentration of the reactant is [A]0 and the concentration of the reactant at the half-life is [R]1/2.

Then, we can write:

[R]1/2 = [R]0 / 2

Substituting this into the above equation and solving for t, we get:

t1/2 = [R]0 / 2k

This is the expression for the half-life of a zero-order reaction.