Thermodynamics

Gibbs free energy - formula in LaTeX

The sign of the result tells you whether a process is spontaneous at constant pressure and temperature: negative means spontaneous. Mind the units, because enthalpy is usually given in kJ/mol and entropy in J/(mol·K), and a factor of a thousand is easy to lose.

\Delta G = \Delta H - T\Delta S

LaTeX code

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$$
\Delta G = \Delta H - T\Delta S
$$

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What the symbols mean

$\Delta G$: change in Gibbs free energy
$\Delta H$: change in enthalpy
$T$: absolute temperature (K)
$\Delta S$: change in entropy

A thermodynamics formula - useful for gas processes, heat balances and physical chemistry.

Worked example

Ammonia synthesis N₂ + 3H₂ → 2NH₃ at 298 K: ΔH = −92.2 kJ/mol, ΔS = −198.7 J/(mol·K), or −0.1987 kJ/(mol·K) once converted to kilojoules. A negative ΔG means the reaction is spontaneous. Type the minus as an ordinary hyphen; in math mode LaTeX sets it as a proper minus sign.

\Delta G = -92.2\,\mathrm{kJ/mol} - 298\,\mathrm{K} \cdot (-0.1987\,\mathrm{kJ/(mol\,K)}) \approx -33.0\,\mathrm{kJ/mol}

LaTeX commands in this formula

\Delta: capital Greek letter Delta

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