Library / Foundations: Chemistry / FCH-21

Foundations: Chemistry

Rate equation

How the speed of a reaction depends on the concentrations of the reactants.

Ref: FCH-21
Rev: v1
Field: Foundations: Chemistry
Result: rate [mmol/(dm³ s)]

rate = k {[A]}^{m} {[B]}^{n}

k is the rate constant (its units depend on the overall order), [A] and [B] are concentrations in mol/dm³ and m and n are the orders with respect to A and B. Orders are found by experiment, not from the balanced equation.

The rate depends on how concentrated each reactant is, and the orders tell you how strongly.

Calculator

Solve for

rateRateComputed

mmol/(dm³ s)

kRate constant

dm⁶ mol⁻² s⁻¹

1e-61,000,000

[A]Concentration of A

mol/dm³

0.0015

mOrder with respect to A

[B]Concentration of B

mol/dm³

0.0015

nOrder with respect to B

Rate in mol dm⁻³ s⁻¹0.002 mol/(dm³ s)
Overall order3

What drives the result

Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.

Rate (mmol/(dm³ s)) current value 2 mmol/(dm³ s)

kRate constantKey driver

4e-64,000,000

[B]Concentration of B

5e-51,250

[A]Concentration of A

0.02100

nOrder with respect to B

0.450

mOrder with respect to A

0.0220

Second order in B means doubling [B] quadruples the rate; zero order means the rate does not depend on that reactant.
k rises with temperature (Arrhenius), whereas the concentrations only change the multiplier.

Chart data as tables

Ranked variables

Variable	Typical range	Lowest result	Highest result	Swing (mmol/(dm³ s))	Local step	Change in result
k Rate constant	1e-6 to 1,000,000 dm⁶ mol⁻² s⁻¹	4e-6	4,000,000	4,000,000	+10%	+10 %
[B] Concentration of B	0.001 to 5 mol/dm³	5e-5	1,250	1,250	+10%	+21 %
[A] Concentration of A	0.001 to 5 mol/dm³	0.02	100	99.98	+10%	+10 %
n Order with respect to B	0 to 3	0.4	50	49.6	+10%	−27.5 %
m Order with respect to A	0 to 3	0.02	20	19.98	+10%	−20.6 %

Sweep of Concentration of B

Concentration of B (mol/dm³)	Rate (mmol/(dm³ s))
0.001	5e-5
0.0029	4.204e-4
0.008409	0.003536
0.02438	0.02973
0.07071	0.25
0.205	2.102
0.5946	17.68
1.724	148.7
5	1,250

Sweep one variable

Vary

Rate (mmol/(dm³ s))Hover, touch, or use the arrow keys on the chart

Variables and how each one contributes

rate

Rate

Result · mmol/(dm³ s)

What the equation gives you. Everything else feeds it.

Rate constant

dm⁶ mol⁻² s⁻¹ · typical 1e-6 to 1,000,000

Rate constant for the reaction at the given temperature. Directly proportional.

[A]

Concentration of A

mol/dm³ · typical 0.001 to 5

Concentration of A. Raised to the power m.

Order with respect to A

· typical 0 to 3

Order with respect to A. A higher order makes the rate more sensitive to [A].

[B]

Concentration of B

mol/dm³ · typical 0.001 to 5

Concentration of B. Raised to the power n.

Order with respect to B

· typical 0 to 3

Order with respect to B. A higher order makes the rate more sensitive to [B].

Worked example with the values above

[A]¹ = 0.1; [B]² = 0.04.
rate = k × 0.1 × 0.04 = 0.002 mol dm⁻³ s⁻¹.
Rate = 2 mmol dm⁻³ s⁻¹.

Assumptions and limits

Constant temperature.
Orders determined experimentally.

Common mistakes

Using the coefficients in the balanced equation as the orders.
Giving k without checking the units.

Statistics and uncertainty

Orders determined from experiments are usually integers or halves, and rate measurements carry 5–10% error, so choose the order that fits several runs.

Where it is used

Predicting reaction times.
Mechanism studies and shelf-life.

Maths you need

Concentration: mol/dm³
Powers: indices

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