Enthalpy Calculator

Enthalpy $H$ is the heat content of a system at constant pressure. Only changes in it are measurable, and at constant pressure the enthalpy change equals the heat exchanged:

$\Delta H = q_p$

The sign convention is the system's point of view: $\Delta H < 0$ is exothermic (heat leaves the system), $\Delta H > 0$ is endothermic.

Heating without a reaction. When a substance simply warms or cools,

$q = m c \Delta T$

• $m$ — mass in g, $c$ — specific heat capacity in J g⁻¹ °C⁻¹ (4.184 for liquid water), $\Delta T = T_{\text{final}} - T_{\text{initial}}$ in °C or K — the size of a degree is the same on both scales, so no conversion is needed for a difference.

Reaction enthalpy from formation data. With tabulated standard enthalpies of formation $\Delta H_f^{\circ}$,

$\Delta H^{\circ}_{\text{rxn}} = \sum \nu\,\Delta H_f^{\circ}(\text{products}) - \sum \nu\,\Delta H_f^{\circ}(\text{reactants})$

where $\nu$ are the balanced coefficients. Standard state means 1 bar with each substance in its normal form at the stated temperature, usually 298.15 K, and $\Delta H_f^{\circ}$ of an element in its standard state is exactly zero. Physical states matter: liquid and gaseous water differ by about 44 kJ/mol.

1. Heat from a temperature change

Multiply mass, specific heat and $\Delta T$. Keep the sign of $\Delta T$: a negative value means heat was released. If a heat capacity $C$ for a whole object is given instead of a specific heat, use $q = C\Delta T$ with no mass.

2. Molar enthalpy from calorimetry data

A calorimetry experiment reports how much a known mass of solution changed temperature. Compute the heat absorbed by that solution, flip the sign to get the heat released by the reaction, then divide by the moles of the limiting reactant:

$\Delta H = \frac{-q_{\text{solution}}}{n}$

3. Reaction enthalpy from tables or Hess's law

Sum the formation enthalpies of the products, subtract those of the reactants, and weight each by its coefficient. Hess's law is the same principle stated generally: because enthalpy is a state function, the total change is the same whatever route is taken, so known reactions can be reversed (flip the sign) and scaled (multiply the value) and then added.

Units and significant figures

Answers usually convert from J to kJ, and reaction enthalpies are per mole of reaction as written. The measured mass or temperature change normally sets the significant figures; 4.184 is quoted to four.

• Dropping the sign. Exothermic reactions have negative $\Delta H$. Reporting $+890$ kJ/mol for a combustion reverses the physics.
• Reversing $\Delta T$. It is final minus initial. Getting it backwards flips the sign of $q$.
• Mixing J and kJ. $q = mc\Delta T$ with $c$ in J g⁻¹ °C⁻¹ gives joules; formation enthalpies are tabulated in kJ/mol.
• Forgetting to divide by moles. $q$ from a calorimeter is for the whole sample; $\Delta H$ in kJ/mol needs division by the moles of limiting reactant.
• Ignoring physical states. $\Delta H_f^{\circ}$ for $\mathrm{H_2O}(l)$ and $\mathrm{H_2O}(g)$ differ, and the products' states change the answer.
• Forgetting to scale a Hess's law step. Doubling a reaction doubles its $\Delta H$; reversing it changes the sign.
• Assuming $\Delta H_f^{\circ}$ of any element is zero. Only the standard form counts: $\mathrm{O_2}(g)$ is zero, ozone is not.