{
  "id": "enthalpy",
  "version": "2da35c0aac21",
  "status": "published",
  "name": "Enthalpy Calculator",
  "question": "What is the enthalpy change?",
  "summary": "Finds the enthalpy change ΔH of a reaction from coffee-cup calorimetry (mass, specific heat, temperature change and moles) or from standard enthalpies of formation of the products and reactants.",
  "category": "chemistry",
  "subcategory": "stoichiometry",
  "url": "https://www.acalculator.org/chemistry/enthalpy-calculator",
  "markdown": "https://www.acalculator.org/chemistry/enthalpy-calculator.md",
  "kind": "function",
  "method": "Calorimetry: q_solution = m × c × (T_final − T_start); q_rxn = −q_solution; ΔH = q_rxn ÷ moles. Formation: ΔH° = Σ n × ΔH°f(products) − Σ n × ΔH°f(reactants).",
  "assumptions": [
    "Calorimetry: a coffee-cup calorimeter at constant pressure that loses no heat, so q_rxn = −q_solution and equals ΔH.",
    "Formation: ΔH°f values are standard (25 °C, 1 bar); elements in their standard state have ΔH°f = 0."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "From",
        "description": "A calorimeter measurement, or standard enthalpies of formation.",
        "type": "string",
        "enum": [
          "calorimetry",
          "formation"
        ]
      },
      "m": {
        "title": "Mass of solution",
        "description": "The mass of the solution that warms or cools (about 1 g per mL for dilute water solutions).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 1e-9,
        "maximum": 1000000
      },
      "c": {
        "title": "Specific heat, J/(g·°C)",
        "description": "The specific heat of the solution; 4.184 for water.",
        "type": "number",
        "minimum": 0.000001,
        "maximum": 1000
      },
      "t1": {
        "title": "Starting temperature",
        "description": "The starting temperature of the solution.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0.000001,
        "maximum": 10000
      },
      "t2": {
        "title": "Final temperature",
        "description": "The final temperature of the solution.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0.000001,
        "maximum": 10000
      },
      "n": {
        "title": "Moles reacted",
        "description": "The moles of the reaction as written, usually of the limiting reactant.",
        "type": "number",
        "minimum": 1e-12,
        "maximum": 1000000000
      },
      "species": {
        "title": "Reactants and products",
        "description": "One row per substance: product or reactant, its coefficient, and its standard enthalpy of formation in kJ/mol.",
        "type": "array",
        "items": {
          "type": "object",
          "properties": {
            "s": {
              "title": "Side",
              "description": "Whether the substance is a product or a reactant.",
              "type": "string",
              "enum": [
                "p",
                "r"
              ]
            },
            "k": {
              "title": "Coefficient",
              "description": "The coefficient in the balanced equation.",
              "type": "number",
              "exclusiveMinimum": 0,
              "maximum": 1000
            },
            "h": {
              "title": "ΔH°f, kJ/mol",
              "description": "The standard enthalpy of formation in kJ/mol.",
              "type": "number",
              "minimum": -100000,
              "maximum": 100000
            }
          }
        }
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Enthalpy change",
      "description": "ΔH per mole of reaction, to 6 significant figures.",
      "format": "text"
    },
    "flow": {
      "label": "Heat flow",
      "description": "Whether the reaction gives off heat (exothermic) or takes it in (endothermic).",
      "format": "text"
    },
    "dH": {
      "label": "ΔH (kJ/mol of reaction)",
      "description": "The enthalpy change per mole of reaction as written.",
      "format": "number"
    },
    "qSolution": {
      "label": "Heat taken in by the solution (J)",
      "description": "q = m × c × ΔT; negative when the solution cools.",
      "format": "number"
    },
    "qReaction": {
      "label": "Heat of the reaction (kJ)",
      "description": "q_rxn = −q_solution, for the amount that reacted.",
      "format": "number"
    },
    "products": {
      "label": "Σ n·ΔH°f of products (kJ)",
      "description": "The products’ coefficients times their enthalpies of formation.",
      "format": "number"
    },
    "reactants": {
      "label": "Σ n·ΔH°f of reactants (kJ)",
      "description": "The reactants’ coefficients times their enthalpies of formation.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "calorimetry",
      "m": "100 g",
      "c": 4.184,
      "t1": "22 °C",
      "t2": "28.9 °C",
      "n": 0.05,
      "species": [
        {
          "side": "p",
          "n": 2,
          "hf": -207.4
        },
        {
          "side": "p",
          "n": 1,
          "hf": 90.25
        },
        {
          "side": "r",
          "n": 3,
          "hf": 33.2
        },
        {
          "side": "r",
          "n": 1,
          "hf": -285.83
        }
      ]
    },
    "outputs": {
      "result": "ΔH = −57.7392 kJ/mol",
      "flow": "exothermic, gives off heat",
      "dH": -57.7392,
      "qSolution": 2886.96,
      "qReaction": -2.88696
    },
    "text": "The enthalpy change is ΔH = −57.7392 kJ/mol: exothermic, gives off heat."
  },
  "examples": [
    {
      "given": {
        "from": "calorimetry",
        "m": 0.1,
        "c": 4.184,
        "t1": 295.15,
        "t2": 302.04999999999995,
        "n": 0.05
      },
      "expect": {
        "qSolution": 2886.96,
        "qReaction": -2.88696,
        "dH": -57.7392
      },
      "source": "OpenStax, Chemistry 2e, §5.2 Calorimetry (q = c × m × ΔT; q_rxn = −q_solution), https://openstax.org/books/chemistry-2e/pages/5-2-calorimetry, Example 5.5 Heat Produced by an Exothermic Reaction: about 2.9 × 10³ J; hand calculation in content.mdx: 0.0500 mol reacted"
    },
    {
      "given": {
        "from": "calorimetry",
        "m": 0.05321,
        "c": 4.184,
        "t1": 298.04999999999995,
        "t2": 293.45,
        "n": 0.0401
      },
      "expect": {
        "qReaction": 1.024100944,
        "dH": 25.53867690773067
      },
      "source": "OpenStax, Chemistry 2e, §5.2 Calorimetry (q = c × m × ΔT; q_rxn = −q_solution), https://openstax.org/books/chemistry-2e/pages/5-2-calorimetry, Example 5.6 Heat Flow in an Instant Ice Pack: q_rxn = +1.0 kJ; Python 3"
    },
    {
      "given": {
        "from": "formation",
        "species": [
          {
            "side": "p",
            "n": 2,
            "hf": -207.4
          },
          {
            "side": "p",
            "n": 1,
            "hf": 90.25
          },
          {
            "side": "r",
            "n": 3,
            "hf": 33.2
          },
          {
            "side": "r",
            "n": 1,
            "hf": -285.83
          }
        ]
      },
      "expect": {
        "products": -324.55,
        "reactants": -186.23,
        "dH": -138.32
      },
      "source": "OpenStax, Chemistry 2e, §5.3 Enthalpy (ΔH° = Σ n × ΔH°f(products) − Σ n × ΔH°f(reactants)), https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy, Example 5.15 Using Hess’s Law, ΔH°f values from the example; hand calculation in content.mdx (the book prints −136.80 kJ)"
    }
  ],
  "sources": [
    "OpenStax, Chemistry 2e, section 5.2 Calorimetry: q = c × m × ΔT, q_rxn = −q_solution; Examples 5.5 and 5.6. CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/chemistry-2e/pages/5-2-calorimetry",
    "OpenStax, Chemistry 2e, section 5.3 Enthalpy: ΔH°reaction = Σ n × ΔH°f(products) − Σ n × ΔH°f(reactants); Example 5.15. CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/chemistry-2e/pages/5-3-enthalpy",
    "OpenStax, Chemistry 2e, Appendix G Standard Thermodynamic Properties for Selected Substances (ΔH°f values). CC BY 4.0, retrieved 2026-10-03. https://openstax.org/books/chemistry-2e/pages/g-standard-thermodynamic-properties-for-selected-substances"
  ],
  "related": [
    "stoichiometry",
    "limiting-reactant",
    "mole"
  ],
  "changelog": []
}