Standard Free Energy: Formula and Calculation

Standard free energy change is calculated as ΔG° = ΔH° − TΔS°; for a reaction under standard-state conditions, it can also be calculated as ΔG° = −RT ln K. Enter the standard enthalpy and entropy changes and the temperature to calculate ΔG° from the first formula; the result is in joules per mole.

Formula

The standard Gibbs free energy change is:

ΔG° = ΔH° − TΔS°

• ΔG° is the standard Gibbs free energy change, in kJ/mol.
• ΔH° is the standard enthalpy change, in kJ/mol.
• T is the absolute temperature, in kelvin (K).
• ΔS° is the standard entropy change, in J/(mol·K).

The calculator converts entropy from joules to kilojoules by dividing T × ΔS° by 1000. This is necessary because enthalpy is entered in kJ/mol. If all quantities are instead expressed in SI units, the equivalent form is ΔG° (J/mol) = ΔH° (J/mol) − T (K) × ΔS° (J/(mol·K)).

Worked Example

Using the calculator’s defaults, ΔH° = −100 kJ/mol, ΔS° = −200 J/(mol·K), and T = 298.15 K:

1. Calculate TΔS°: 298.15 × (−200) = −59630 J/mol.
2. Convert to kilojoules: −59630 / 1000 = −59.630 kJ/mol.
3. Substitute into the formula: ΔG° = −100 − (−59.630) = −40.370 kJ/mol.

Rounded to the calculator’s three decimal places, the standard free energy change is −40.370 kJ/mol.

Assumptions

• The entered enthalpy and entropy changes refer to the same balanced reaction and standard-state convention.
• The temperature is absolute temperature in kelvin; the calculator does not convert Celsius.
• ΔH° and ΔS° are treated as constant at the selected temperature. This approximation may be unsuitable across a wide temperature range if heat-capacity effects are significant.
• This is a study and lab-planning calculation. Where bench work is involved, follow your lab method, the safety data sheet (SDS) and your supervisor.

What “Standard” Means

The symbol ° indicates a standard-state quantity, not necessarily a measurement taken at 25 °C. Temperature must be specified separately. Standard states conventionally refer to substances in defined reference states, commonly a pure solid or liquid and a gas at a specified standard pressure; solutions use a specified standard concentration or activity convention. The precise conventions matter when comparing tabulated values.

For a reaction, ΔH° and ΔS° are changes for the reaction as written, with stoichiometric coefficients included. Reversing the reaction reverses the sign of both changes. Multiplying every coefficient by a factor multiplies ΔG°, ΔH°, and ΔS° by that factor too. A tabulated standard molar Gibbs energy of formation, ΔG°_f, is a different kind of entry: reaction ΔG° is obtained by summing formation values for products minus those for reactants, each multiplied by its coefficient.

How to Interpret the Result

A negative ΔG° means the forward reaction is thermodynamically favored at equilibrium under the standard-state conditions used. A positive value favors the reverse direction, while ΔG° = 0 corresponds to equilibrium for the standard-state reaction as written. These statements describe thermodynamic direction, not how quickly a reaction happens. A reaction with negative ΔG° can still be slow because of a kinetic barrier.

Standard free energy is also not the free energy change in every real mixture. For nonstandard conditions, the reaction quotient Q adjusts the result:

ΔG = ΔG° + RT ln Q

Here, ΔG is the actual reaction free energy, R is the gas constant, T is temperature in kelvin, and Q is the dimensionless reaction quotient built from activities. Concentrations or partial pressures are often used as practical approximations to activities, but that approximation can be poor for non-ideal systems.

Connection to the Equilibrium Constant

At equilibrium, ΔG = 0 and Q = K, which gives:

ΔG° = −RT ln K

In this equation R = 8.31446261815324 J/(mol·K), T is in kelvin, and K is the dimensionless thermodynamic equilibrium constant. Because R is in joules, the result is in J/mol; divide by 1000 for kJ/mol. If K is greater than 1, ΔG° is negative; if K is less than 1, ΔG° is positive. This relationship is especially useful when an equilibrium constant is known, but K must correspond to the same balanced reaction and temperature.

The enthalpy–entropy formula and the equilibrium-constant formula are consistent ways to obtain the same ΔG° when their data and standard-state definitions match. A mismatch can arise from using values measured at different temperatures or from mixing standard-state conventions.

Common Errors and Limits

• Mixing units: Do not subtract TΔS in J/mol from ΔH in kJ/mol without converting. This calculator divides the entropy product by 1000.
• Using Celsius: The formula requires kelvin. Convert a Celsius temperature with K = °C + 273.15 before entering it.
• Dropping the minus sign: A negative entropy change makes TΔS negative, so subtracting TΔS adds a positive contribution to ΔG°.
• Comparing different reactions: Check the balanced equation, direction, stoichiometric scaling, temperature, and standard-state definitions.
• Assuming ΔG° is the actual ΔG: Nonstandard concentrations or pressures can change the reaction’s actual driving force through RT ln Q.

The calculator uses supplied ΔH° and ΔS° values; it does not retrieve or verify thermodynamic data. Its constant-property calculation can be inaccurate when these quantities vary substantially with temperature. For a high-accuracy result over a broad temperature interval, temperature-dependent thermodynamic data and an appropriate model are needed.

Frequently Asked Questions

What is the standard free energy formula?
For Gibbs free energy, ΔG° = ΔH° − TΔS°. If the equilibrium constant is known, the equivalent relation is ΔG° = −RT ln K.

What units should I use?
Use consistent units: this calculator takes ΔH° in kJ/mol, ΔS° in J/(mol·K), and T in K, then returns ΔG° in kJ/mol.

Does a negative ΔG° mean the reaction is fast?
No. A negative value indicates thermodynamic favorability in the forward direction under standard-state conditions. It does not specify the reaction rate.

Is standard free energy always measured at 25 °C?
No. The standard-state symbol does not set the temperature. Use the temperature associated with the thermodynamic data; 298.15 K is common, but not universal.

What is the difference between ΔG° and ΔG?
ΔG° refers to standard states. Actual ΔG also depends on the current composition, through ΔG = ΔG° + RT ln Q.

Related

• Moles to Grams Calculator: Mass of a Compound From Moles
• Molecules to Moles Calculator: Divide by the Avogadro Constant
• Mass to Mole Calculator: Grams to Moles From the Molar Mass

in dh | Standard enthalpy change ΔH° | kJ/mol | -100 | -
in ds | Standard entropy change ΔS° | J/(mol·K) | -200 | -
in t | Temperature T | K | 298.15 | 0
out dg | Standard free energy change ΔG° | kJ/mol | dh - t * ds / 1000 | 3