# What is the reaction rate?

Finds the average rate of a reaction from a concentration change over time and the stoichiometric coefficient, the rate or the rate constant k from the rate law rate = k[A]^m[B]^n, or a reaction order from two trials.

- Page: https://www.acalculator.org/chemistry/reaction-rate-calculator
- JSON spec: https://www.acalculator.org/chemistry/reaction-rate-calculator.json
- Version: 3d71e1b2440c

## Default answer

Example with the default inputs (Find Average rate, The substance is a Reactant, Its coefficient in the equation 1, Concentration at the start (mol/L) 1, Concentration at the end (mol/L) 0.5, Start time 0, End time 6, Time unit h): Rate = 0.0833333 mol/(L·h).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | The average rate, the rate from the rate law, the rate constant k, or a reaction order. |
| role | The substance is a | A reactant is used up; a product is made. |
| co | Its coefficient in the equation | The number in front of the substance in the balanced equation: 2 for H₂O₂ in 2H₂O₂ → 2H₂O + O₂. |
| c1 | Concentration at the start (mol/L) | The concentration at the start time. |
| c2 | Concentration at the end (mol/L) | The concentration at the end time. |
| t1 | Start time | The time of the first concentration. |
| t2 | End time | The time of the second concentration. |
| tu | Time unit | The time unit of the times and rates: seconds, minutes or hours. |
| k | Rate constant k | The rate constant, in the unit that matches the orders and time unit. |
| r | Rate (mol/(L·time)) | The measured reaction rate. |
| a | [A] (mol/L) | The concentration of reactant A. |
| m | Order in A (m) | The reaction order with respect to A, from experiment: often 0, 1 or 2. |
| b | [B] (mol/L), optional | The concentration of reactant B; leave empty for a rate law in A only. |
| n | Order in B (n) | The reaction order with respect to B; used only when [B] is given. |
| ku | Time unit | The time unit of the times and rates: seconds, minutes or hours. |
| oc1 | Trial 1: [A] (mol/L) | The concentration of A in the first trial. |
| or1 | Trial 1: rate | The initial rate in the first trial. |
| oc2 | Trial 2: [A] (mol/L) | The concentration of A in the second trial; other concentrations unchanged. |
| or2 | Trial 2: rate | The initial rate in the second trial, in the same unit. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The rate, the rate constant with its unit, or the order. |
| rateValue | Reaction rate | The rate of the reaction, in mol/(L·time). |
| change | Δ[ ] ÷ Δt | How fast the substance’s concentration changes: negative for a reactant. |
| kValue | Rate constant k | The rate constant, in the unit shown. |
| unit | Unit of k | L^(x−1) mol^(1−x) per time for an overall order x. |
| overall | Overall order | m + n, the sum of the orders. |
| orderValue | Reaction order | ln(rate₂ ÷ rate₁) ÷ ln([A]₂ ÷ [A]₁). |

## Method

Average rate = −(1/a) × Δ[reactant] ÷ Δt = (1/b) × Δ[product] ÷ Δt; rate = k[A]^m[B]^n; k = rate ÷ ([A]^m[B]^n), in L^(x−1) mol^(1−x) per time for x = m + n; order m = ln(rate₂ ÷ rate₁) ÷ ln([A]₂ ÷ [A]₁).

## Assumptions

- Orders come from experiment: they need not match the coefficients of the balanced equation.
- In the order mode only [A] changes between the two trials; every other concentration and the temperature stay the same.

## Worked examples

1. find = avg, role = reactant, co = 1, c1 = 1, c2 = 0.5, t1 = 0, t2 = 6, tu = h gives rateValue = 0.0833333, change = −0.0833333, result = Rate = 0.0833333 mol/(L·h). Source: OpenStax, Chemistry 2e, §12.1 Chemical Reaction Rates (rate = −Δ[A]/Δt; for aA → bB, rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt; H₂O₂ table), https://openstax.org/books/chemistry-2e/pages/12-1-chemical-reaction-rates, Figure 12.2 table: 0.0833 mol/(L·h).
2. find = avg, role = reactant, co = 2, c1 = 0.25, c2 = 0.125, t1 = 12, t2 = 18, tu = h gives rateValue = 0.0104167, change = −0.0208333. Source: OpenStax, Chemistry 2e, §12.1 Chemical Reaction Rates (rate = −Δ[A]/Δt; for aA → bB, rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt; H₂O₂ table), https://openstax.org/books/chemistry-2e/pages/12-1-chemical-reaction-rates: Figure 12.2 gives −Δ[H₂O₂]/Δt = 0.0208 mol/(L·h).
3. find = k, r = 0.000066, a = 0.000001, m = 1, b = 0.000003, n = 1, ku = s gives kValue = 22,000,000, unit = L/(mol·s), result = k = 2.2 × 10⁷ L/(mol·s). Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.4 Determining a Rate Law from Initial Rates: k = 2.20 × 10⁷ L mol⁻¹ s⁻¹.
4. find = k, r = 0.003, a = 0.1, m = 2, b = 0.1, n = 1, ku = s gives kValue = 3, unit = L²/(mol²·s), overall = 3. Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.5 Determining Rate Laws from Initial Rates: k = 3.0 mol⁻² L² s⁻¹.
5. find = k, r = 0.00184, a = 0.004, m = 2, b = 0.002, n = 1, ku = s gives kValue = 57,500. Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.5 Check Your Learning: k = 5.75 × 10⁴ mol⁻² L² s⁻¹.
6. find = k, r = 0, a = 0.00175, m = 2, n = 1, ku = s gives kValue = 0.00000672653, unit = L/(mol·s). Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.4 Check Your Learning: k = 6.73 × 10⁻⁶ L/mol/s.
7. find = rate, k = 22,000,000, a = 0.000002, m = 1, b = 0.000009, n = 1, ku = s gives rateValue = 0.000396, result = Rate = 3.96 × 10⁻⁴ mol/(L·s). Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.4: trial 4 rate 3.96 × 10⁻⁴ mol L⁻¹ s⁻¹.
8. find = order, oc1 = 0.1, or1 = 0.003, oc2 = 0.15, or2 = 0.00675 gives orderValue = 2, result = Order = 2. Source: OpenStax, Chemistry 2e, §12.3 Rate Laws (rate = k[A]^m[B]^n; units of k), https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws, Example 12.5: m = 2.

## FAQ

### How do I calculate the average rate of a reaction?

Divide the change in concentration by the time it took, and make it positive: rate = −Δ[A]/Δt for a reactant. H₂O₂ falls from 1.000 to 0.500 mol/L in 6.00 h, so its rate of decrease is 0.500 ÷ 6.00 = 0.0833 mol/(L·h) (OpenStax).

### Why divide by the coefficient?

So that every substance gives the same rate for the reaction. For aA → bB, rate = −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt. In 2H₂O₂ → 2H₂O + O₂, H₂O₂ disappears twice as fast as O₂ appears, so the reaction rate is half of H₂O₂’s rate of decrease.

### How do I calculate the rate constant?

Divide the rate by the concentration terms of the rate law: k = rate ÷ ([A]^m[B]^n). For NO + O₃ with rate = k[NO][O₃]: k = 6.60 × 10⁻⁵ ÷ (1.00 × 10⁻⁶ × 3.00 × 10⁻⁶) = 2.20 × 10⁷ L/(mol·s).

### What are the units of the rate constant?

They depend on the overall order x = m + n: mol/(L·s) for zero order, s⁻¹ for first order, L/(mol·s) for second order, L²/(mol²·s) for third order; in general L^(x−1) mol^(1−x) s⁻¹.

### How do I find the order of a reaction from data?

Compare two trials where only one concentration changes: m = ln(rate₂ ÷ rate₁) ÷ ln([A]₂ ÷ [A]₁). Raising [NO] from 0.10 to 0.15 M raised the rate from 0.00300 to 0.00675: ln 2.25 ÷ ln 1.5 = 2, so the reaction is second order in NO.

### Do the orders come from the balanced equation?

No. Orders are found by experiment and need not match the coefficients; they are usually 0, 1 or 2 but can be fractions or negative (OpenStax). The rate law of 2NO + Cl₂ → 2NOCl happens to be rate = k[NO]²[Cl₂].

## Sources

- OpenStax, Chemistry 2e, §12.1 Chemical Reaction Rates: rate = −Δ[A]/Δt, the relative rates −(1/a)Δ[A]/Δt = (1/b)Δ[B]/Δt, and the H₂O₂ table at 40 °C (1.000, 0.500, 0.250, 0.125 mol/L every 6.00 h; rates 0.0833, 0.0417, 0.0208 mol L⁻¹ h⁻¹). https://openstax.org/books/chemistry-2e/pages/12-1-chemical-reaction-rates (retrieved 2026-10-19)
- OpenStax, Chemistry 2e, §12.3 Rate Laws: rate = k[A]^m[B]^n, the units of k (Table 12.1), Example 12.4 (NO + O₃: k = 2.20 × 10⁷ L mol⁻¹ s⁻¹; CH₃CHO: 6.73 × 10⁻⁶ L/mol/s) and Example 12.5 (2NO + Cl₂: m = 2, n = 1, k = 3.0 mol⁻² L² s⁻¹; OCl⁻ + I⁻: 5.75 × 10⁴). https://openstax.org/books/chemistry-2e/pages/12-3-rate-laws (retrieved 2026-10-19)