Prodigy Free Energy Calculator: What It Can and Can’t Do

A Prodigy free energy calculator estimates a thermodynamic quantity called Gibbs free-energy change, ΔG, from the values and assumptions you provide. This general-purpose calculator uses ΔG = ΔH − TΔS: enter enthalpy change, entropy change, and temperature to get ΔG in joules per mole and kilojoules per mole.

Formula

The formula is ΔG = ΔH − TΔS. In this calculator, temperature is entered in degrees Celsius and converted to kelvin by adding 273.15; entropy is entered in joules per mole per kelvin and converted to kilojoules per mole per kelvin by dividing by 1,000. Thus the displayed calculation is ΔG (kJ/mol) = ΔH (kJ/mol) − [(t + 273.15) × ΔS (J/(mol·K)) ÷ 1,000].

ΔG is the Gibbs free-energy change, reported in kJ/mol or J/mol.
ΔH is the enthalpy change, in kJ/mol.
T is absolute temperature, in kelvin (K).
ΔS is the entropy change, in J/(mol·K).
t is the entered temperature in degrees Celsius (°C); the conversion is T = t + 273.15 K.

The calculator treats the entered values as applying to the reaction or process of interest at the specified temperature. The formula is a standard thermodynamic relationship, not a prediction engine that supplies missing chemical data. Obtain ΔH and ΔS from appropriate measurements, tables, or a defined thermodynamic model.

Worked Example

Using the block’s defaults—ΔH = −10 kJ/mol, ΔS = 50 J/(mol·K), and t = 25 °C—first convert the temperature: T = 25 + 273.15 = 298.15 K.

Convert the entropy term to kJ/mol: TΔS = 298.15 × 50 ÷ 1,000 = 14.9075 kJ/mol.

Then calculate ΔG: −10 − 14.9075 = −24.9075 kJ/mol, which rounds to −24.908 kJ/mol at three decimal places. In joules per mole, −24.9075 × 1,000 = −24907.5 J/mol, displayed as −24908 J/mol to the nearest joule.

Assumptions

The supplied enthalpy and entropy changes describe the same reaction, direction, and standard-state convention.
The entered values are treated as constant at the selected temperature. This is an approximation when heat capacities cause ΔH or ΔS to vary significantly with temperature.
The calculation uses absolute temperature, converting Celsius with +273.15, and consistent energy units.
The result is a thermodynamic change per mole of reaction as written, not a rate, yield, or concentration.

How to Interpret the Result

At constant temperature and pressure, a negative ΔG indicates that a process is thermodynamically favorable in the forward direction under the conditions represented by the inputs. A positive ΔG means the forward direction is unfavorable under those conditions, while a value of zero corresponds to equilibrium. These statements concern thermodynamic direction, not speed: a favorable reaction may proceed very slowly if it faces a large activation-energy barrier.

ΔG also does not say how much product will form. Actual composition depends on the reaction’s equilibrium constant and current activities or concentrations, and the system may not have reached equilibrium. A negative result is not a guarantee of a complete reaction or a practical process.

For a reaction written in reverse, ΔH, ΔS, and ΔG change sign. If the balanced equation is multiplied by a factor, these extensive changes scale by that factor too. For example, doubling every coefficient doubles the free-energy change for the reaction as written; it does not change ΔG per mole of a particular substance unless the reaction basis is changed accordingly.

What “Prodigy Free Energy Calculator” May Refer To

The phrase can mean a calculator sought by someone named Prodigy, or it may be a mistaken or shorthand search for a free-energy calculator. “Free energy” itself is not one uniquely defined quantity in every context: chemistry commonly means Gibbs free energy, while other settings may discuss Helmholtz free energy. This page calculates Gibbs free-energy change using enthalpy, entropy, and temperature; it is not tied to a particular product or service called Prodigy.

Some users instead need the change in Gibbs free energy from a standard value and reaction quotient. For that use, the relevant relationship is ΔG = ΔG° + RT ln Q, where R is the gas constant, T is in kelvin, and Q is the dimensionless reaction quotient defined with appropriate activities. That is a different input route from ΔH − TΔS. Do not substitute concentrations directly for Q without considering the standard-state convention and reaction stoichiometry.

Common Input Errors and Limits

Mixing units: Entropy is often listed in J/(mol·K), whereas enthalpy tables may use kJ/mol. This calculator performs the required division by 1,000 for the entropy term. If your entropy is already in kJ/(mol·K), convert it to J/(mol·K) before entering it.
Using Celsius directly: The TΔS term requires kelvin. The calculator adds 273.15 automatically; do not convert your temperature to kelvin first and then enter that number as Celsius.
Ignoring reaction direction: Values must match the balanced reaction direction and normalization used. Reversing the reaction reverses the signs.
Assuming values never change with temperature: The simple equation can be inaccurate over a wide temperature range if ΔH and ΔS vary appreciably. A more complete calculation may require heat-capacity data or temperature-specific thermodynamic values.
Overinterpreting rounding: The display rounds its result; that does not make the source data more precise. Report no more significant precision than the inputs justify.

The equation is useful for checking units, exploring how temperature affects a calculated value, and interpreting thermodynamic data. It cannot identify a compound’s enthalpy or entropy from its name, infer missing experimental conditions, account automatically for non-ideal mixtures, or establish reaction kinetics. Where bench work is implied, follow your lab method, the safety data sheet (SDS), and your supervisor.

Frequently Asked Questions

Is the Prodigy free energy calculator actually free?
This page provides the calculation without a charge. “Prodigy” may refer to a separate tool or search term; this calculator is not presented as an official product of any particular organization.

What does a negative ΔG mean?
For the specified conditions and forward reaction, a negative Gibbs free-energy change indicates thermodynamic favorability at constant temperature and pressure. It does not mean the reaction is fast, complete, or guaranteed to occur in practice.

Can I enter entropy in kJ/(mol·K)?
The input expects J/(mol·K). Multiply an entropy value in kJ/(mol·K) by 1,000 before entering it, so its units match the calculator’s conversion.

Why does the calculator convert Celsius to kelvin?
Thermodynamic equations use absolute temperature. Kelvin is obtained from Celsius by adding exactly 273.15, so a temperature of 25 °C is 298.15 K.

Is Gibbs free energy the same as reaction spontaneity?
A negative ΔG indicates a favorable direction under the stated conditions, but spontaneity does not imply a fast process. Activation barriers affect rate, and conditions such as concentrations can change the actual ΔG.

Formula used

in dh | Enthalpy change | kJ/mol | -10 | -
in ds | Entropy change | J/(mol·K) | 50 | -
in t | Temperature | °C | 25 | -273.15
out dg | Gibbs free-energy change | kJ/mol | dh - ((t + 273.15) * ds / 1000) | 3
out dj | Gibbs free-energy change | J/mol | dg * 1000 | 1

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.