formula.expert

Thermochemistry and spontaneity

Hess's lawenthalpy of reactionGibbs free energydelta G delta H delta Sheat of reaction

Hess's law both ways, the heat a reaction actually releases, and the Gibbs criterion that decides whether it runs at all.

Hess's Law (Three-Step Sum)

ΔHrxn=ΔH1+ΔH2+ΔH3\Delta H_{\text{rxn}} = \Delta H_1 + \Delta H_2 + \Delta H_3

Hess's law: the enthalpy change of a target reaction is the sum of the enthalpy changes of the steps you route it through.

Standard Enthalpy of Reaction from Formation Enthalpies

ΔHrxn∘=∑ΔHf,prod∘−∑ΔHf,react∘\Delta H^{\circ}_{\text{rxn}} = \sum \Delta H^{\circ}_{f,\text{prod}} - \sum \Delta H^{\circ}_{f,\text{react}}

The tabulated form of Hess's law: standard enthalpy of reaction equals the summed formation enthalpies of the products minus those of the reactants.

Heat of Reaction

q=nΔHq = n \Delta H

Scales a reaction's molar enthalpy change by the amount reacted to give the total heat released or absorbed.

Gibbs Free Energy Change (ΔG = ΔH − TΔS)

ΔG=ΔH−T ΔS\Delta G = \Delta H - T\,\Delta S

Combines a reaction's enthalpy and entropy changes at a given temperature to decide whether it can happen spontaneously.

Gibbs Free Energy and the Equilibrium Constant

ΔG∘=−RTln⁡K\Delta G^{\circ} = -RT\ln K

Converts between a reaction's standard free energy change and its equilibrium constant, the bridge joining thermodynamics to equilibrium tables.

How they fit together

Enthalpy is a state function, which is the whole content of Hess's law: the heat of a reaction depends only on where it starts and ends, never on the route. That lets you build the enthalpy of a reaction nobody can measure directly by summing steps that can be measured, or by subtracting formation enthalpies — reactants from products, in that order. Elements in their standard states have ΔHf = 0 by definition, which is why they simply drop out of the sum.

Use the step-sum form when you are handed a set of reactions to combine, remembering to reverse the sign of any step you flip and to scale ΔH by the same factor you scale the equation. Use the formation-enthalpy form when you have a table. Then keep enthalpy and free energy separate in your head: ΔH tells you whether heat comes out, ΔG tells you whether the reaction goes, and they routinely disagree. An exothermic reaction with a large entropy penalty can be non-spontaneous, and an endothermic one can be spontaneous if TΔS carries it — ice melting above 0 °C is exactly that. Watch the units: ΔH is usually tabulated in kJ/mol and ΔS in J/(mol·K), and the factor-of-1000 mismatch is the most common arithmetic error in the whole subject.