Rate Law Calculating M & N

Understanding rate laws is fundamental to chemical kinetics. This guide explains how to determine the reaction orders (m and n) for reactants in a chemical reaction using experimental data.

What is Rate Law?

The rate law of a chemical reaction describes how the reaction rate depends on the concentrations of the reactants. It's typically expressed as:

Rate = k[A]^m[B]ⁿ

Where:

Rate is the reaction rate (often in mol/L·s)
k is the rate constant
[A] and [B] are the concentrations of reactants A and B
m and n are the reaction orders for reactants A and B

The reaction order (m or n) indicates how much the reaction rate changes when the concentration of a reactant changes. The sum of the reaction orders (m + n) gives the overall reaction order.

Calculating m & n

To determine the reaction orders (m and n), you need experimental data showing how the reaction rate changes with different concentrations of reactants. Here's the general method:

Measure the initial rates of reaction at different concentrations of reactant A, keeping [B] constant
Plot ln(rate) vs ln([A]) to determine m
Repeat the process for reactant B to determine n
The slope of each plot gives the reaction order

Note: This method assumes that the reaction is first order with respect to each reactant. For more complex reactions, additional experiments may be needed.

Example Calculation

Consider the reaction: 2A + B → Products. We measure the following initial rates at different concentrations:

[A] (M)	[B] (M)	Initial Rate (M/s)
0.10	0.20	0.0050
0.20	0.20	0.0200
0.30	0.20	0.0450

To determine m (the order with respect to A):

Plot ln(rate) vs ln([A]) using the data above
The slope of the line will be equal to m
From the data, we find m = 2

This indicates the reaction is second order with respect to A.

Common Reaction Orders

Reaction orders can be zero, first, or second, depending on the reaction mechanism. Here are some common cases:

Order	Description	Example
Zero order	Rate is independent of concentration	Decomposition of N₂O at high pressures
First order	Rate depends linearly on concentration	Radioactive decay, hydrolysis of esters
Second order	Rate depends on the square of concentration	Reaction between two molecules (A + B → Products)

FAQ

What if my reaction has more than two reactants?

For reactions with more than two reactants, you would need to perform additional experiments to determine the order with respect to each reactant separately.

How do I know if my reaction is elementary or complex?

An elementary reaction has a rate law that matches its stoichiometry. A complex reaction has a rate law that doesn't match its stoichiometry and may involve intermediate steps.

What if my data doesn't fit a straight line on a log-log plot?

If your data doesn't fit a straight line, the reaction may not be elementary, or you may need to collect more precise data points.