Short Answer

The reaction rate law is expressed as a mathematical equation that shows how the rate of a reaction depends on the concentration of its reactants. It relates reaction speed to the amount of each reactant present at a given time.

The rate law is usually written as: Rate = k[A]^m[B]^n, where k is the rate constant and m and n show how each reactant affects the reaction rate. These values are determined through experiments, not from the balanced chemical equation.

Detailed Explanation :

Reaction Rate Law Expression

The reaction rate law is a mathematical relationship that explains how the rate of a chemical reaction changes with the concentration of reactants. It is one of the most important concepts in chemical kinetics because it shows the exact dependence of reaction speed on the amount of reactants present in the reaction mixture. Rate laws help chemists understand reaction behaviour, predict how fast reactions will occur, and design practical applications in laboratories and industries.

The rate law must always be determined through experiments. It cannot be predicted simply by looking at the chemical equation because the visible equation does not show the actual steps of the reaction mechanism. Instead, scientists measure how the reaction speed changes when they vary reactant concentrations one by one.

1. General Form of the Rate Law

The rate law for a reaction is usually expressed in the form:

Rate = k[A]^m[B]^n

Here:

• Rate is the speed of the reaction.
• k is the rate constant, which changes with temperature.
• [A] and [B] are the concentrations of reactants.
• m and n are the powers showing how each reactant affects the rate. These are called orders with respect to reactants.

The sum m + n gives the overall order of the reaction.

This general form explains how rate depends on concentration. If the concentration of a reactant is doubled, the rate will change according to its power in the rate law.

2. How Rate Law is Determined

Rate law is always determined experimentally, usually by:

• Measuring reaction rate at different concentrations
• Keeping one reactant concentration constant while changing the other
• Observing how the rate increases or decreases

From these observations, chemists write the rate law that best matches the experimental data.

3. Types of Rate Laws

1. a) Differential Rate Law

This expresses how the instantaneous reaction rate depends on concentrations.

Example:
Rate = k[A]²

This form is used to understand how fast the reaction proceeds at any moment.

1. b) Integrated Rate Law

This relates concentration to time and helps calculate how long a reaction takes.

Examples:

• First-order: ln[A] = –kt + ln[A]₀
• Second-order: 1/[A] = kt + 1/[A]₀

Integrated laws help plot graphs and find half-life of reactions.

4. Role of the Rate Constant (k)

The rate constant k is a specific value for each reaction. It depends on:

• Temperature
• Presence of catalysts
• Nature of reactants

Higher k means a faster reaction. When temperature increases, k also increases because particles gain more energy.

5. Importance of Exponents m and n

The powers m and n are very important because they show:

• How strongly each reactant influences reaction speed
• Whether doubling a reactant concentration doubles, triples, or does not change the rate
• The reaction pathway or mechanism

These exponents cannot be taken from the balanced chemical equation. They must be discovered through rate experiments.

6. Examples of Rate Law Expression

Example 1: First-Order Reaction

Rate = k[A]
Rate doubles when concentration of A doubles.

Example 2: Second-Order Reaction

Rate = k[A]²
If A is doubled, rate becomes four times faster.

Example 3: Zero-Order Reaction

Rate = k
Rate does not depend on concentration.

These examples show how rate laws capture the behaviour of different reactions.

7. Why Expression of Rate Law is Important

The way the rate law is written helps chemists:

• Predict reaction speed under different conditions
• Calculate required reactant amounts
• Understand reaction mechanisms
• Improve efficiency in industrial chemical processes
• Control reactions safely in laboratories

Without rate laws, it would be difficult to study or use chemical reactions in real life.

Conclusion

The reaction rate law is expressed as an equation that relates the reaction rate to the concentration of reactants. It is usually written as Rate = k[A]^m[B]^n, where k is the rate constant and m and n are experimentally determined powers. Rate laws help understand reaction speed, reaction mechanisms, and the influence of concentration on chemical processes. This makes the rate law an essential tool in studying and applying chemical reactions.