Question

Write the rate equations for a first-order and a second-order reaction.

Short answer

The rate equation for a first-order reaction is $\text{k =}\frac{\text{1}}{\text{t}}\text{ln}\frac{{\left[\text{A}\right]}_{\text{0}}}{\left[\text{A}\right]}$and the rate equation for a second-order reaction is $\text{k =}\frac{\text{1}}{\text{t}}\left(\frac{\text{1}}{\left[\text{A}\right]}\text{-}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\right)$.

Step-by-step solution

Rate equation

A chemical reaction's rate law (also known as the rate equation) is an expression that establishes a link between the reaction's pace and the concentrations of the reactants involved.

The pace at which reactants are consumed or products are created is known as the rate of a chemical reaction.

First-order reaction

The rate equation for first-order reaction is,

$\text{k}=\frac{\text{1}}{\text{t}}\text{ln}\frac{{\left[\text{A}\right]}_{\text{0}}}{\left[\text{A}\right]}$

where,

k= Rate constant

Second-order reaction

The rate equation for second-order reaction is,

$\text{k}=\frac{\text{1}}{\text{t}}\left(\frac{\text{1}}{\left[\text{A}\right]}\text{-}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\right)$

where,

k=Rate constant

As a result, we may assume that raising a substance's concentration will increase the reaction rate.