Physical chemistry

Rates and reaction order

Chemical kinetics studies concentration-change rates and their dependence on reactant concentrations. Reaction order is determined experimentally and need not equal stoichiometric coefficients.

For v=k[A]^m[B]^n, the overall order is m+n. Integrated laws relate concentration to time; half-life depends on reaction order.

Model and quantities

Read the relation together with assumptions about state, experimental conditions, and sign conventions. Keep units consistent and check dimensions before interpreting a result.

t_{1/2}^{(1)}=\frac{\ln 2}{k}, \qquad t_{1/2}^{(0)}=\frac{[A]_0}{2k}

Definition: Reaction order

Exponents in an empirical rate law are partial orders; their sum is the overall order. Units of k vary with order so the rate remains concentration per time.

Quantities in the relation are defined for the reaction or system at hand. In particular, distinguish standard-state quantities from actual conditions and do not infer a mechanism from a general expression alone.

Example: Worked example

A first-order reaction has k=0.20 min⁻¹. Find its half-life.

Solution

Use $t_{1/2}=\ln2/k=0.693/0.20=3.47$ min. For first order, it is independent of initial concentration.

Concept summary
Concept	Description	Unit / note
Key relation	Use under stated conditions	Check units and sign convention
Measured quantity	Relates a state or process	Compare data with model
Scope	Model specific conditions	Check assumptions first

For a second-order reaction in one reactant, $1/[A]-1/[A]_0=kt$ and $t_{1/2}=1/(k[A]_0)$ . The appropriate linear plot helps distinguish orders.

In the worked example, which result follows from the given data?

Which statement is consistent with this lesson?

References

Peter Atkins, Julio de Paula (2014). Physical Chemistry