Chemistry · Lesson
Rate laws, reaction order and rate constants
Infer concentration dependence from controlled initial-rate comparisons. Keep empirical reaction orders separate from overall stoichiometric coefficients.
Back to the Chemistry mapBy the end, you can
- Determine orders by comparing one concentration at a time.
- Calculate k with units appropriate to the rate law.
- State the conditions and range in which an empirical law applies.
A rate law summarizes a tested dependence
A common empirical form is r = k[A]^m[B]^n. The exponents m and n are the orders with respect to A and B, and their sum is the overall order for this form. Experiments determine them for a specified reaction regime. The coefficients in an overall balanced equation do not automatically supply these exponents.
Orders can be zero, fractional or negative as well as positive integers. A zero order means the rate is approximately independent of that concentration within the tested regime. It does not erase the species from the chemistry or guarantee the same rate at every concentration, including zero.
Change one concentration while holding the rest fixed
Our original hypothetical initial-rate table keeps temperature, medium and other relevant conditions the same. Doubling [A] from 0.100 to 0.200 mol L⁻¹ at fixed [B] makes r rise from 0.00100 to 0.00400 mol L⁻¹ s⁻¹. Thus 2^m = 4 and m = 2.
In a separate comparison, doubling [B] from 0.100 to 0.200 mol L⁻¹ at fixed [A] doubles r to 0.00200 mol L⁻¹ s⁻¹. Therefore 2^n = 2 and n = 1. These clean values are supplied exercise data; an actual experiment would include measurement uncertainty and check repeatability.
| Trial | [A] / mol L⁻¹ | [B] / mol L⁻¹ | Initial r / mol L⁻¹ s⁻¹ |
|---|---|---|---|
| 1 | 0.100 | 0.100 | 0.00100 |
| 2 | 0.200 | 0.100 | 0.00400 |
| 3 | 0.100 | 0.200 | 0.00200 |
Original hypothetical initial rates under identical temperature, medium and other conditions. Compare rows 1–2 for A and rows 1–3 for B. Values are invented exact-pattern exercise data, not a real experiment.
The units of k depend on the law
For this table r = k[A]²[B], with overall order 3. Inserting the first row gives k = 0.00100/(0.100² × 0.100) = 1.00 L² mol⁻² s⁻¹. Multiplying those units by three powers of concentration returns mol L⁻¹ s⁻¹.
A first-order law for a concentration rate instead has k in s⁻¹. Rate constants with different units cannot be ranked simply by their numerical values. Always retain whether r is a species depletion rate or a stoichiometrically normalized reaction rate.
A fitted constant belongs to stated conditions
A useful k is constant with respect to the concentrations in its stated law, while temperature, solvent, catalyst and other relevant conditions are held fixed. Changing those conditions or moving outside the tested range can change k or the form of the law.
A successful fit is evidence for a concentration dependence, not unique proof of a molecular mechanism. Multiple mechanisms can produce the same empirical law. Additional kinetic, spectroscopic or other evidence can help distinguish them.
Worked examples
Obtain the law and its constant
Use the three hypothetical initial-rate trials to determine m, n and k in r = k[A]^m[B]^n.
- Rows 1 and 2: A doubles while B stays fixed; rate becomes four times as large, giving m = 2.
- Rows 1 and 3: B doubles while A stays fixed; rate doubles, giving n = 1.
- Use row 1: k = 0.00100/(0.100² × 0.100) = 1.00.
- Rate units divided by concentration cubed give L² mol⁻² s⁻¹.
r = k[A]²[B], with k = 1.00 L² mol⁻² s⁻¹ for this stipulated regime.
Try it yourself
May overall balanced-equation coefficients automatically become empirical rate exponents?
Show the answer and reasoning
No.
Overall order must be established for the regime; an explicitly elementary step has a separate molecular interpretation.
Doubling A alone makes rate four times as large in a power-law model. What order in A follows?
Show the answer and reasoning
Second order.
2² = 4.
What overall order has r = k[A]²[B]?
Show the answer and reasoning
Third order.
Add the exponents: 2 + 1 = 3.
Does zero order in B prove B can be removed without affecting the chemistry at every concentration?
Show the answer and reasoning
No.
The observed independence is limited to the stated regime.
What to carry forward
- Infer orders using controlled comparisons.
- Keep empirical order separate from overall stoichiometry.
- Derive k’s units from the defined rate and concentration powers.
- Retain the conditions and tested range of the law.
References
Teaching resources and reference material supporting this lesson’s explanations and examples.