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Thermochemistry Calculator

What this calculator solves

Two thermochemistry workhorses share this widget.

Heat transfer: q = m × c × ΔT. Four variables, three given, one unknown — the calculator solves for the missing one. The relation assumes c is constant over the temperature range and that no phase changes occur (those need separate latent heat terms).

Reaction enthalpy via Hess’s law:

ΔH_rxn = Σ ν · ΔH_f(products) − Σ ν · ΔH_f(reactants)

where ν is the stoichiometric coefficient. This works because enthalpy is a state function — the path does not matter, only the start and end. Element standard states (O₂(g), C(graphite), H₂(g)) have ΔH_f = 0 by definition, so they fall out of the sum.

How to use it

For heat transfer, enter any three of {q, m, c, ΔT} and the fourth comes out. Pick a substance from the preset list (water, aluminum, iron, copper, ethanol) or type a custom c. The temperature-difference field accepts T_initial and T_final separately.

For enthalpy, enter the balanced equation’s coefficients and the ΔH_f values for each species (kJ/mol). The calculator multiplies, sums products, sums reactants, subtracts, and reports ΔH_rxn for the reaction as written.

Common specific heat values

Substancec (J/(g·K))
Water (liquid)4.184
Ice2.09
Steam2.01
Aluminum0.897
Iron0.449
Copper0.385
Gold0.129
Ethanol2.44

Water’s value is anomalously high. That single fact explains a startling amount of climate, biology, and engineering.

Worked examples

Heating water. Heat needed to bring 250 g of water from 20.0 °C to 80.0 °C. ΔT = 60.0 K. q = 250 × 4.184 × 60.0 = 62,760 J = 62.8 kJ.

Identifying a metal. A 50.0 g sample absorbs 1,500 J and rises from 25.0 to 95.0 °C. ΔT = 70.0 K. c = q/(m·ΔT) = 1500/(50.0 × 70.0) = 0.429 J/(g·K) — close to iron at 0.449.

Bomb-style calorimetry. Burning 1.00 g of fuel raises 200.0 g of water from 22.0 to 35.5 °C. q_water = 200.0 × 4.184 × 13.5 = 11,297 J. The fuel released −11.3 kJ per gram, with the negative sign reflecting heat leaving the system.

Hess’s law: methane combustion. CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l). ΔH_f values: CH₄ = −74.8, O₂ = 0, CO₂ = −393.5, H₂O(l) = −285.8 kJ/mol. ΔH = [(−393.5) + 2(−285.8)] − [(−74.8) + 2(0)] = −965.1 + 74.8 = −890.3 kJ/mol. Strongly exothermic, which is why methane is a fuel.

The sign convention trap

Heat released by a reaction has a negative sign from the system’s perspective and a positive sign from the surroundings’. In a calorimetry problem, the water gets warmer (q_water > 0), but the reaction itself has q_reaction < 0 of equal magnitude. Mixing up which side of the energy ledger you are on is the most common stumbling block in introductory thermochemistry.

Frequently Asked Questions

What is the heat transfer formula?
q = m × c × ΔT, where q is heat in joules, m is mass in grams, c is specific heat capacity in J/(g·K), and ΔT is the temperature change. ΔT works the same in °C or K because the size of the degree is identical between the two scales — only the zero point differs. The equation assumes c is constant over the temperature range, which holds well across modest ΔT but breaks for phase transitions.
What is specific heat capacity?
Specific heat capacity (c) is the energy required to raise 1 gram of a substance by 1 K. Water sits at 4.184 J/(g·K), which is unusually high — most metals are below 1 J/(g·K). That high value is why oceans moderate climate, why water is the universal coolant, and why coastal temperatures swing less than inland temperatures. Each substance has its own characteristic c.
What does a negative q value mean?
Sign follows the system. Negative q means the system is releasing heat (exothermic) — combustion, neutralization, condensation. Positive q means absorbing heat (endothermic) — melting, evaporation, dissolution of ammonium nitrate. The convention is mirror-symmetric: q for the system and q for the surroundings always have opposite signs and equal magnitudes (assuming no losses).
What is enthalpy of reaction?
ΔH_rxn is the heat absorbed or released at constant pressure for a reaction as written. Hess's law lets you compute it from tabulated standard enthalpies of formation: ΔH_rxn = Σ ΔH_f(products) − Σ ΔH_f(reactants), each weighted by its stoichiometric coefficient. Elements in their standard states have ΔH_f = 0 by definition, which is why O2(g) drops out of the sum.
How does calorimetry work?
A calorimeter measures heat by tracking the temperature change of a known mass of water (or solution). Heat lost by the reaction equals heat gained by the water, assuming the calorimeter is insulated: q_reaction = −m_water × 4.184 × ΔT. Coffee-cup calorimeters work at constant pressure (giving ΔH directly); bomb calorimeters work at constant volume (giving ΔU, which needs a small correction to convert to ΔH for gas-producing reactions).