# What is the enthalpy change?

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.

- Page: https://www.acalculator.org/chemistry/enthalpy-calculator
- JSON spec: https://www.acalculator.org/chemistry/enthalpy-calculator.json
- Version: 2da35c0aac21

## Default answer

Example with the default inputs (From Calorimetry, Mass of solution 100 g, Specific heat, J/(g·°C) 4.184, Starting temperature 22 °C, Final temperature 28.9 °C, Moles reacted 0.05): The enthalpy change is ΔH = −57.7392 kJ/mol: exothermic, gives off heat.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| from | From | A calorimeter measurement, or standard enthalpies of formation. |
| m | Mass of solution | The mass of the solution that warms or cools (about 1 g per mL for dilute water solutions). |
| c | Specific heat, J/(g·°C) | The specific heat of the solution; 4.184 for water. |
| t1 | Starting temperature | The starting temperature of the solution. |
| t2 | Final temperature | The final temperature of the solution. |
| n | Moles reacted | The moles of the reaction as written, usually of the limiting reactant. |
| species | Reactants and products | One row per substance: product or reactant, its coefficient, and its standard enthalpy of formation in kJ/mol. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Enthalpy change | ΔH per mole of reaction, to 6 significant figures. |
| flow | Heat flow | Whether the reaction gives off heat (exothermic) or takes it in (endothermic). |
| dH | ΔH (kJ/mol of reaction) | The enthalpy change per mole of reaction as written. |
| qSolution | Heat taken in by the solution (J) | q = m × c × ΔT; negative when the solution cools. |
| qReaction | Heat of the reaction (kJ) | q_rxn = −q_solution, for the amount that reacted. |
| products | Σ n·ΔH°f of products (kJ) | The products’ coefficients times their enthalpies of formation. |
| reactants | Σ n·ΔH°f of reactants (kJ) | The reactants’ coefficients times their enthalpies of formation. |

## 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.

## Worked examples

1. from = calorimetry, m = 0.1, c = 4.184, t1 = 295.15, t2 = 302.05, n = 0.05 gives qSolution = 2,886.96, 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.
2. from = calorimetry, m = 0.05321, c = 4.184, t1 = 298.05, t2 = 293.45, n = 0.0401 gives qReaction = 1.024101, dH = 25.538677. 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.
3. from = formation, species = {"side":"p","n":2,"hf":-207.4} or {"side":"p","n":1,"hf":90.25} gives 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.

## FAQ

### What is enthalpy change?

ΔH is the heat a reaction gives off or takes in at constant pressure. A negative ΔH means the reaction is exothermic (it gives off heat); a positive ΔH means it is endothermic (it takes heat in).

### How do I find ΔH from a calorimeter?

The solution’s heat is q = m × c × ΔT. The reaction’s heat is the opposite, q_rxn = −q, and ΔH = q_rxn ÷ moles reacted. 100 g of solution at 4.184 J/(g·°C) warming 6.9 °C takes in 2,887 J, so 0.0500 mol of reaction has ΔH = −57.7 kJ/mol.

### How do I use enthalpies of formation?

ΔH° = Σ n × ΔH°f(products) − Σ n × ΔH°f(reactants), with each n the coefficient in the balanced equation. Look up ΔH°f values in a table such as OpenStax Appendix G.

### Why is the ΔH°f of oxygen gas zero?

An element in its standard state (O₂ gas, solid carbon as graphite, H₂ gas) is the starting point for formation enthalpies, so its ΔH°f is 0 by definition.

### Why does the sign flip between the solution and the reaction?

Heat the reaction gives off goes into the solution. If the solution warms (q positive), the reaction lost that heat, so q_rxn is negative.

### What units does the answer use?

kJ per mole of reaction as written. With formation data, a ΔH of −138.32 kJ/mol means 138.32 kJ given off when the equation’s amounts react, for example 3 mol of NO₂ with 1 mol of water.

## 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