Change in G Formula Chemistry: Free Energy Shift

This calculator works out the change in Gibbs free energy (ΔG) for a chemical reaction using the standard formula ΔG = ΔH − TΔS. You enter the enthalpy change (ΔH), the temperature (T) in kelvin, and the entropy change (ΔS), and it returns the Gibbs free energy change in kilojoules per mole, along with the entropy term (TΔS) so you can see which factor dominates.

Formula

The Gibbs free energy change is given by:

ΔG = ΔH − TΔS

• ΔG – change in Gibbs free energy (kJ/mol). If negative, the reaction is spontaneous; if positive, non-spontaneous; if zero, at equilibrium.
• ΔH – change in enthalpy (kJ/mol). Heat absorbed (positive) or released (negative) at constant pressure.
• T – absolute temperature (kelvin, K). Use K = °C + 273.15.
• ΔS – change in entropy (J/(mol·K)). Disorder increase (positive) or decrease (negative).

Because ΔS is usually given in joules, you must divide by 1000 to convert to kilojoules before multiplying by T, as done in the calculator.

Worked Example

Using the default values: ΔH = −100 kJ/mol, T = 298 K, ΔS = −200 J/(mol·K).

1. Convert ΔS to kJ/(mol·K): −200 / 1000 = −0.200 kJ/(mol·K).
2. Calculate TΔS: 298 × (−0.200) = −59.6 kJ/mol.
3. Apply the formula: ΔG = (−100) − (−59.6) = −100 + 59.6 = −40.4 kJ/mol.

The calculator gives ΔG = −40.40 kJ/mol, matching the step-by-step result. The negative ΔG indicates a spontaneous reaction at 298 K.

What the Sign and Magnitude Tell You

The sign of ΔG predicts spontaneity under constant temperature and pressure:

• ΔG < 0 – reaction is spontaneous (exergonic). It can proceed without external energy.
• ΔG > 0 – non-spontaneous (endergonic). It requires energy input to proceed.
• ΔG = 0 – the system is at equilibrium; no net change occurs.

The magnitude indicates how far from equilibrium the reaction is. A large negative ΔG (e.g., −100 kJ/mol) means the reaction strongly favors products; a small negative value (e.g., −1 kJ/mol) means it is near equilibrium and easily reversed. The entropy term TΔS becomes more significant at higher temperatures, which is why some reactions switch spontaneity with temperature.

How to Choose the Right Values

To use the formula correctly, you need accurate thermodynamic data:

• ΔH – usually from tables of standard enthalpies of formation. For a reaction, ΔH = ΣΔH_f(products) − ΣΔH_f(reactants).
• ΔS – from standard molar entropies (S°). ΔS = ΣS°(products) − ΣS°(reactants).
• T – the temperature at which the reaction occurs, always in kelvin. If you have °C, add 273.15.

Ensure ΔH and ΔS are for the same reaction and same physical states. If you mix kJ and J, you will get a wrong ΔG by a factor of 1000. The calculator handles the conversion for ΔS, but you must enter ΔH in kJ/mol.

Common Mistakes and Misconceptions

• Unit mismatch – Forgetting to convert J to kJ for ΔS is the most frequent error. Always divide ΔS by 1000 before multiplying by T.
• Temperature in Celsius – Using °C directly gives a wrong result because the formula requires absolute temperature. Convert to kelvin first.
• Confusing ΔG with ΔG° – The standard Gibbs free energy change (ΔG°) is for standard conditions (1 bar, 1 M, often 25°C). The formula here gives ΔG at any temperature, but it assumes ΔH and ΔS are constant with temperature, which is an approximation.
• Spontaneity ≠ speed – A negative ΔG means the reaction is thermodynamically favorable, but it may still be extremely slow without a catalyst (e.g., diamond converting to graphite).

Limitations of the Formula

The formula ΔG = ΔH − TΔS is exact only at constant temperature and pressure. It assumes ΔH and ΔS do not change with temperature, which is a good approximation over small temperature ranges but fails over large ones. For precise work, heat capacities must be integrated. Also, the formula applies to a closed system; if the reaction involves gases, partial pressures affect ΔG, and you would need the reaction quotient Q: ΔG = ΔG° + RT ln Q.

For biological reactions, the formula still works, but “standard� conditions differ (pH 7, etc.), so ΔG°′ is used. This calculator gives the raw thermodynamic value, not the biological standard.

Frequently Asked Questions

What is the difference between ΔG and ΔG°?

ΔG° is the standard Gibbs free energy change under standard conditions (1 bar pressure, 1 M concentration, usually 25°C). ΔG is the actual free energy change under any conditions. They are related by ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. At equilibrium, ΔG = 0 and Q = K (equilibrium constant), so ΔG° = −RT ln K.

Can ΔG be positive and the reaction still occur?

Yes, if the reaction is coupled to another reaction with a more negative ΔG, the overall process can be spontaneous. For example, ATP hydrolysis (ΔG ≈ −30 kJ/mol) drives many endergonic reactions in cells. Also, a positive ΔG means non-spontaneous under the given conditions, but changing temperature or concentrations can make it negative.

Why is temperature in kelvin, not Celsius?

Because the formula involves absolute temperature, which is proportional to the average kinetic energy of particles. The kelvin scale starts at absolute zero, where entropy is zero for a perfect crystal. Using Celsius would shift the zero point and give incorrect results, especially when multiplying by ΔS.

How do I find ΔH and ΔS values?

They are typically found in standard thermodynamic tables in textbooks or online databases. For a reaction, calculate ΔH using standard enthalpies of formation and ΔS using standard molar entropies. Ensure you account for stoichiometric coefficients. Many chemistry textbooks include these tables in appendices.

Does ΔG predict reaction rate?

No. ΔG tells you whether a reaction is thermodynamically favorable, but not how fast it proceeds. A reaction can have a very negative ΔG yet be extremely slow due to a high activation energy. Catalysts lower the activation energy without changing ΔG.

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in dH | Enthalpy change (ΔH) | kJ/mol | -100 | 0
in T | Temperature | K | 298 | 0
in dS | Entropy change (ΔS) | J/(mol·K) | -200 | 0
out dG | Gibbs free energy change (ΔG) | kJ/mol | dH - (T * dS / 1000) | 2
out TS | Entropy term (TΔS) | kJ/mol | T * dS / 1000 | 2