Gibbs Free Energy Calculator

Enthalpy wins when cold and entropy when hot — divide one by the other and the melting point falls out.

ΔG-0.0007 kJ/mol-6.01 − 273.15 × -0.022

Spontaneous?at equilibrium — ΔG is essentially zerospontaneous means thermodynamically favoured, and says NOTHING about the rate. Diamond turning to graphite is spontaneous and takes geological time

Enthalpy term-6.01 kJ/molexothermic — favours the reaction

Entropy term at this temperature6.0093 kJ/mol−TΔS. It scales with temperature, which is why the balance shifts as things heat up

CROSSOVER TEMPERATURE273.18 K (0.03 °C)ΔH ÷ ΔS — where the two terms exactly balance and ΔG is zero. For a phase change this IS the transition temperature, and it falls straight out of the arithmetic

Which term winsenthalpy, below the crossoverthe entropy term carries a T, so it grows with temperature while the enthalpy term does not

Water melting, as a check6.01 kJ/mol ÷ 22.0 J/(mol·K) = 273.2 Kwhich is 0.05 °C. The melting point is not put into the calculation — it comes out of it

At -50 °C-1.101 kJ/molspontaneous

At 25 °C0.549 kJ/molnot spontaneous

At 100 °C2.199 kJ/molnot spontaneous

The formula

ΔG = ΔH − TΔS; the crossover is at T = ΔH ÷ ΔS

Two terms in competition

Enthalpy is the heat of the reaction and entropy is the change in disorder. ΔG = ΔH − TΔS weighs one against the other.

The entropy term carries a temperature, so it grows as things heat up while the enthalpy term does not. Everything about when a reaction turns around is contained in that asymmetry.

The melting point falls out of the arithmetic

Water's fusion has ΔH = 6.01 kJ/mol and ΔS = 22.0 J/(mol·K). Divide and you get 273.2 K.

That is 0.05 °C, and it was never put into the calculation. The transition temperature is simply where the two terms balance, which is what an equilibrium is.

Spontaneous does not mean fast

A negative ΔG says a reaction is thermodynamically downhill. It says nothing whatever about how long it takes.

Diamond converting to graphite is spontaneous at room temperature and proceeds over geological time. Thermodynamics tells you where the system is going; kinetics tells you whether you will live to see it.

Ideal behaviour is an approximation

The colligative and gas relations here assume dilute solutions and ideal gases, which real systems approach and do not reach.

At high concentration or high pressure the deviations become large, and the corrections are substance-specific. These figures are right where the assumptions hold and approximate where they do not.