{
  "id": "reaction-rate",
  "version": "3d71e1b2440c",
  "status": "published",
  "name": "Reaction Rate Calculator",
  "question": "What is the reaction rate?",
  "summary": "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.",
  "category": "chemistry",
  "subcategory": "stoichiometry",
  "url": "https://www.acalculator.org/chemistry/reaction-rate-calculator",
  "markdown": "https://www.acalculator.org/chemistry/reaction-rate-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "The average rate, the rate from the rate law, the rate constant k, or a reaction order.",
        "type": "string",
        "enum": [
          "avg",
          "rate",
          "k",
          "order"
        ]
      },
      "role": {
        "title": "The substance is a",
        "description": "A reactant is used up; a product is made.",
        "type": "string",
        "enum": [
          "reactant",
          "product"
        ]
      },
      "co": {
        "title": "Its coefficient in the equation",
        "description": "The number in front of the substance in the balanced equation: 2 for H₂O₂ in 2H₂O₂ → 2H₂O + O₂.",
        "type": "integer",
        "minimum": 1,
        "maximum": 20
      },
      "c1": {
        "title": "Concentration at the start (mol/L)",
        "description": "The concentration at the start time.",
        "type": "number",
        "minimum": 0,
        "maximum": 100
      },
      "c2": {
        "title": "Concentration at the end (mol/L)",
        "description": "The concentration at the end time.",
        "type": "number",
        "minimum": 0,
        "maximum": 100
      },
      "t1": {
        "title": "Start time",
        "description": "The time of the first concentration.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000
      },
      "t2": {
        "title": "End time",
        "description": "The time of the second concentration.",
        "type": "number",
        "minimum": 0,
        "maximum": 1000000000000
      },
      "tu": {
        "title": "Time unit",
        "description": "The time unit of the times and rates: seconds, minutes or hours.",
        "type": "string",
        "enum": [
          "s",
          "min",
          "h"
        ]
      },
      "k": {
        "title": "Rate constant k",
        "description": "The rate constant, in the unit that matches the orders and time unit.",
        "type": "number",
        "minimum": 1e-100,
        "maximum": 1e+100
      },
      "r": {
        "title": "Rate (mol/(L·time))",
        "description": "The measured reaction rate.",
        "type": "number",
        "minimum": 1e-100,
        "maximum": 1e+100
      },
      "a": {
        "title": "[A] (mol/L)",
        "description": "The concentration of reactant A.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 100
      },
      "m": {
        "title": "Order in A (m)",
        "description": "The reaction order with respect to A, from experiment: often 0, 1 or 2.",
        "type": "number",
        "minimum": -3,
        "maximum": 3
      },
      "b": {
        "title": "[B] (mol/L), optional",
        "description": "The concentration of reactant B; leave empty for a rate law in A only.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 100
      },
      "n": {
        "title": "Order in B (n)",
        "description": "The reaction order with respect to B; used only when [B] is given.",
        "type": "number",
        "minimum": -3,
        "maximum": 3
      },
      "ku": {
        "title": "Time unit",
        "description": "The time unit of the times and rates: seconds, minutes or hours.",
        "type": "string",
        "enum": [
          "s",
          "min",
          "h"
        ]
      },
      "oc1": {
        "title": "Trial 1: [A] (mol/L)",
        "description": "The concentration of A in the first trial.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 100
      },
      "or1": {
        "title": "Trial 1: rate",
        "description": "The initial rate in the first trial.",
        "type": "number",
        "minimum": 1e-100,
        "maximum": 1e+100
      },
      "oc2": {
        "title": "Trial 2: [A] (mol/L)",
        "description": "The concentration of A in the second trial; other concentrations unchanged.",
        "type": "number",
        "minimum": 1e-15,
        "maximum": 100
      },
      "or2": {
        "title": "Trial 2: rate",
        "description": "The initial rate in the second trial, in the same unit.",
        "type": "number",
        "minimum": 1e-100,
        "maximum": 1e+100
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The rate, the rate constant with its unit, or the order.",
      "format": "text"
    },
    "rateValue": {
      "label": "Reaction rate",
      "description": "The rate of the reaction, in mol/(L·time).",
      "format": "number"
    },
    "change": {
      "label": "Δ[ ] ÷ Δt",
      "description": "How fast the substance’s concentration changes: negative for a reactant.",
      "format": "number"
    },
    "kValue": {
      "label": "Rate constant k",
      "description": "The rate constant, in the unit shown.",
      "format": "number"
    },
    "unit": {
      "label": "Unit of k",
      "description": "L^(x−1) mol^(1−x) per time for an overall order x.",
      "format": "text"
    },
    "overall": {
      "label": "Overall order",
      "description": "m + n, the sum of the orders.",
      "format": "number"
    },
    "orderValue": {
      "label": "Reaction order",
      "description": "ln(rate₂ ÷ rate₁) ÷ ln([A]₂ ÷ [A]₁).",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "avg",
      "role": "reactant",
      "co": 1,
      "c1": 1,
      "c2": 0.5,
      "t1": 0,
      "t2": 6,
      "tu": "h",
      "k": 22000000,
      "r": 0.000066,
      "a": 0.000001,
      "m": 1,
      "b": 0.000003,
      "n": 1,
      "ku": "s",
      "oc1": 0.1,
      "or1": 0.003,
      "oc2": 0.15,
      "or2": 0.00675
    },
    "outputs": {
      "result": "Rate = 0.0833333 mol/(L·h)",
      "rateValue": 0.08333333333333333,
      "change": -0.08333333333333333
    },
    "text": "Rate = 0.0833333 mol/(L·h)."
  },
  "examples": [
    {
      "given": {
        "find": "avg",
        "role": "reactant",
        "co": 1,
        "c1": 1,
        "c2": 0.5,
        "t1": 0,
        "t2": 6,
        "tu": "h"
      },
      "expect": {
        "rateValue": 0.08333333333333333,
        "change": -0.08333333333333333,
        "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); Python 3"
    },
    {
      "given": {
        "find": "avg",
        "role": "reactant",
        "co": 2,
        "c1": 0.25,
        "c2": 0.125,
        "t1": 12,
        "t2": 18,
        "tu": "h"
      },
      "expect": {
        "rateValue": 0.010416666666666666,
        "change": -0.020833333333333332
      },
      "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); rate = (1/2) of it; Python 3"
    },
    {
      "given": {
        "find": "k",
        "r": 0.000066,
        "a": 0.000001,
        "m": 1,
        "b": 0.000003,
        "n": 1,
        "ku": "s"
      },
      "expect": {
        "kValue": 22000000,
        "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; Python 3"
    },
    {
      "given": {
        "find": "k",
        "r": 0.003,
        "a": 0.1,
        "m": 2,
        "b": 0.1,
        "n": 1,
        "ku": "s"
      },
      "expect": {
        "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; Python 3"
    },
    {
      "given": {
        "find": "k",
        "r": 0.00184,
        "a": 0.004,
        "m": 2,
        "b": 0.002,
        "n": 1,
        "ku": "s"
      },
      "expect": {
        "kValue": 57500
      },
      "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; Python 3"
    },
    {
      "given": {
        "find": "k",
        "r": 2.06e-11,
        "a": 0.00175,
        "m": 2,
        "n": 1,
        "ku": "s"
      },
      "expect": {
        "kValue": 0.000006726530612244898,
        "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; Python 3"
    },
    {
      "given": {
        "find": "rate",
        "k": 22000000,
        "a": 0.000002,
        "m": 1,
        "b": 0.000009,
        "n": 1,
        "ku": "s"
      },
      "expect": {
        "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; Python 3"
    },
    {
      "given": {
        "find": "order",
        "oc1": 0.1,
        "or1": 0.003,
        "oc2": 0.15,
        "or2": 0.00675
      },
      "expect": {
        "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; Python 3",
      "tolerance": 1e-12
    }
  ],
  "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)"
  ],
  "related": [
    "half-life",
    "equilibrium-constant",
    "stoichiometry",
    "molarity"
  ],
  "changelog": []
}