Question

What is the rate law for a first order reaction?

Answer 1

We know that a first-order reaction refers to a reaction which proceeds at a rate that depends only on one reactant concentration linearly. You should have at-least basic knowledge about differential rate laws which are usually utilized to explain what is actually occurring on a molecular level while a reaction is occurring.

Complete answer:
In a chemical reaction, it is important to consider not only the chemical properties of the reactants, but also the conditions under which the reaction occurs, the mechanism through which it takes place, the rate at which it occurs, and the equilibrium toward which it is proceeding. On the other hand, integrated rate laws are employed for identifying the reaction order as well as the value of the rate constant from the experimental measurements.
A first-order reaction has a rate law in which the sum of the exponents is equal to $1.~$ In a first–order reaction, the reaction rate is directly proportional to the concentration of one of the reactants. A first–order reaction depends on the concentration of one reactant, and the rate law is $r=-\left( dAdt \right)=k\left[ A \right]r=-\text{ }\left( dAdt \right)=\text{ }k\left[ A\text{ } \right].$ For a first–order reaction, a plot of the natural logarithm of the concentration of a reactant versus time is a straight line with a slope of $-k.$

Note:
Remember that the expression of the rate law for a specific reaction can only be determined experimentally. The rate law expression is not determined by the balanced chemical equation. If the reaction is of zero-order, doubling the reactant concentration will have no effect on the reaction rate. A zero-order reaction means that the rate of the reaction is independent of the concentration of the reactants.