Gibbs Free Energy Change (ΔG°rxn) Calculator | Calculate the δg rxn

Gibbs Free Energy Change (ΔG°rxn) Calculator

This calculator helps you determine the standard Gibbs Free Energy change (ΔG°rxn, sometimes written as δg rxn) of a chemical reaction using the standard enthalpy change (ΔH°rxn), temperature (T), and standard entropy change (ΔS°rxn). Understanding ΔG°rxn is crucial for predicting reaction spontaneity.

Calculate ΔG°rxn

Standard Enthalpy Change (ΔH°rxn):

Enter the standard enthalpy change of the reaction in kJ/mol.

Temperature (T):

Enter the temperature in Kelvin (K). 298.15 K is standard temperature (25°C).

Standard Entropy Change (ΔS°rxn):

Enter the standard entropy change of the reaction in J/(mol·K). Note the units.

Energy Contributions

Chart visualizing the contributions of ΔH°rxn and -TΔS°rxn to ΔG°rxn.

What is ΔG°rxn (Gibbs Free Energy Change)?

The Gibbs Free Energy change (ΔG°rxn or δg rxn) is a thermodynamic quantity that represents the maximum amount of non-expansion work that can be extracted from a closed system at constant temperature and pressure. More practically, it indicates the spontaneity of a chemical reaction under standard conditions (298.15 K and 1 atm pressure, with 1M concentrations for solutions or 1 bar partial pressures for gases). The term “calculate the δg rxn” refers to finding this value.

If ΔG°rxn is negative, the reaction is spontaneous (exergonic) in the forward direction.
If ΔG°rxn is positive, the reaction is non-spontaneous (endergonic) in the forward direction but spontaneous in the reverse.
If ΔG°rxn is zero, the reaction is at equilibrium.

Chemists, chemical engineers, and material scientists frequently calculate the δg rxn to predict whether a reaction will proceed without external energy input and to determine the conditions under which it might become favorable.

Common misconceptions include thinking that a spontaneous reaction is always fast (ΔG°rxn says nothing about reaction rate, only feasibility) or that standard conditions are always room temperature (standard is 25°C or 298.15K).

ΔG°rxn Formula and Mathematical Explanation

The most common way to calculate the δg rxn when standard enthalpy and entropy changes are known is using the equation:

ΔG°rxn = ΔH°rxn – TΔS°rxn

Where:

ΔG°rxn is the standard Gibbs Free Energy change of the reaction.
ΔH°rxn is the standard enthalpy change of the reaction (heat absorbed or released at constant pressure).
T is the absolute temperature in Kelvin.
ΔS°rxn is the standard entropy change of the reaction (change in disorder or randomness).

To use this formula correctly, ensure ΔH°rxn and TΔS°rxn are in the same energy units (usually kJ/mol). Since ΔS°rxn is often given in J/(mol·K), it needs to be divided by 1000 to convert to kJ/(mol·K) before multiplying by T.

Variables Used to Calculate the δg rxn
Variable	Meaning	Unit	Typical Range
ΔG°rxn	Standard Gibbs Free Energy Change	kJ/mol or J/mol	-1000 to +1000 kJ/mol
ΔH°rxn	Standard Enthalpy Change	kJ/mol or J/mol	-1000 to +1000 kJ/mol
T	Absolute Temperature	K (Kelvin)	> 0 K (often 298.15 K)
ΔS°rxn	Standard Entropy Change	J/(mol·K)	-300 to +300 J/(mol·K)

Practical Examples (Real-World Use Cases)

Let’s see how to calculate the δg rxn with some examples.

Example 1: Synthesis of Ammonia (Haber Process)

The reaction is N₂(g) + 3H₂(g) ⇌ 2NH₃(g).

ΔH°rxn = -92.2 kJ/mol
ΔS°rxn = -198.7 J/(mol·K)
T = 298.15 K (25°C)

ΔG°rxn = -92.2 kJ/mol – (298.15 K * (-198.7 J/(mol·K)) / 1000 J/kJ)

ΔG°rxn = -92.2 kJ/mol – (-59.25 kJ/mol) ≈ -32.95 kJ/mol

Since ΔG°rxn is negative, the reaction is spontaneous under standard conditions at 298.15 K.

Example 2: Decomposition of Calcium Carbonate

The reaction is CaCO₃(s) ⇌ CaO(s) + CO₂(g).

ΔH°rxn = +178.3 kJ/mol
ΔS°rxn = +160.5 J/(mol·K)
T = 298.15 K (25°C)

ΔG°rxn = +178.3 kJ/mol – (298.15 K * (160.5 J/(mol·K)) / 1000 J/kJ)

ΔG°rxn = +178.3 kJ/mol – (47.85 kJ/mol) ≈ +130.45 kJ/mol

At 298.15 K, ΔG°rxn is positive, so the decomposition is non-spontaneous. However, at higher temperatures, the TΔS°rxn term becomes larger, and ΔG°rxn can become negative, making the reaction spontaneous. This is why limestone decomposes when heated strongly. Let’s calculate the δg rxn at 1200 K:

ΔG°rxn (1200 K) = +178.3 – (1200 * 160.5 / 1000) = 178.3 – 192.6 = -14.3 kJ/mol. Spontaneous at 1200K.

How to Use This ΔG°rxn Calculator

Enter ΔH°rxn: Input the standard enthalpy change of the reaction in kJ/mol.
Enter Temperature (T): Input the temperature in Kelvin at which you want to calculate ΔG°rxn. Use 298.15 K for standard conditions if not otherwise specified.
Enter ΔS°rxn: Input the standard entropy change in J/(mol·K). The calculator will convert it to kJ/(mol·K).
Calculate: Click the “Calculate ΔG°rxn” button or simply change any input value.
Read Results: The calculator will display ΔG°rxn in kJ/mol, along with the intermediate TΔS°rxn term and the spontaneity of the reaction at the given temperature.
Visualize: The chart below the calculator shows the relative contributions of ΔH°rxn and -TΔS°rxn to the final ΔG°rxn.
Reset: Use the “Reset” button to return to default example values.
Copy: Use “Copy Results” to copy the calculated values and inputs.

Understanding the sign of the calculated ΔG°rxn is key: negative means spontaneous, positive means non-spontaneous, and zero means equilibrium.

Key Factors That Affect ΔG°rxn Results

Enthalpy Change (ΔH°rxn): A highly negative (exothermic) ΔH°rxn strongly favors a negative ΔG°rxn, making the reaction more likely to be spontaneous.
Entropy Change (ΔS°rxn): A positive ΔS°rxn (increase in disorder) contributes negatively to ΔG°rxn (-TΔS°rxn term), favoring spontaneity, especially at high temperatures. A negative ΔS°rxn disfavors spontaneity.
Temperature (T): Temperature directly scales the entropy contribution (TΔS°rxn). For reactions with positive ΔS°rxn, increasing temperature makes ΔG°rxn more negative (more spontaneous). For reactions with negative ΔS°rxn, increasing temperature makes ΔG°rxn more positive (less spontaneous or non-spontaneous).
State of Reactants and Products: The physical states (gas, liquid, solid, aqueous) significantly impact ΔH°f and S° values of substances, thus affecting ΔH°rxn and ΔS°rxn, and consequently the result of any attempt to calculate the δg rxn.
Pressure and Concentration: While this calculator uses standard conditions (ΔG°rxn), the actual Gibbs Free Energy change (ΔG) also depends on the actual pressures and concentrations of reactants and products (ΔG = ΔG° + RTlnQ, where Q is the reaction quotient).
Accuracy of Input Data: The calculated ΔG°rxn is only as accurate as the input ΔH°rxn and ΔS°rxn values, which are usually obtained from thermodynamic databases or experimental measurements.

Frequently Asked Questions (FAQ)

Q1: What does “spontaneous” mean in thermodynamics?
A1: A spontaneous reaction is one that can proceed in the forward direction without continuous external energy input, given enough time. It does not imply the reaction is fast. If ΔG°rxn < 0, it's spontaneous.

Q2: How does temperature affect ΔG°rxn?
A2: Temperature multiplies the entropy term (TΔS°rxn). If ΔS°rxn is positive, increasing T makes ΔG°rxn more negative. If ΔS°rxn is negative, increasing T makes ΔG°rxn more positive. When you calculate the δg rxn, temperature is a crucial input.

Q3: Can ΔG°rxn be zero?
A3: Yes, if ΔG°rxn = 0, the system is at equilibrium under standard conditions.

Q4: Why do we use Kelvin for temperature?
A4: The formula ΔG°rxn = ΔH°rxn – TΔS°rxn is derived based on absolute temperature scales, where 0 K represents the lowest possible temperature. Kelvin is an absolute scale.

Q5: What are “standard conditions”?
A5: Standard conditions usually refer to 298.15 K (25°C) and 1 atm pressure (or 1 bar), with solutions at 1 M concentration. ΔG°rxn is calculated for these conditions.

Q6: How can I find ΔH°rxn and ΔS°rxn values?
A6: These values are often found in thermodynamic data tables in chemistry textbooks or online databases (e.g., NIST WebBook). They can also be calculated from standard enthalpies and entropies of formation of reactants and products.

Q7: What is the difference between ΔG and ΔG°?
A7: ΔG° is the Gibbs free energy change under standard conditions. ΔG is the Gibbs free energy change under non-standard conditions (different temperatures, pressures, or concentrations) and is related by ΔG = ΔG° + RTlnQ. Our tool helps you calculate the δg rxn at standard state or other specified temperatures, assuming standard pressures/concentrations for ΔG°.

Q8: Does a negative ΔG°rxn mean the reaction will happen quickly?
A8: No. ΔG°rxn only indicates thermodynamic feasibility (spontaneity), not the rate of the reaction. Kinetics (activation energy) determines the reaction speed.

Related Tools and Internal Resources

Equilibrium Constant (K) Calculator: Calculate K from ΔG°rxn and vice versa, which is related when you calculate the δg rxn.
Enthalpy Change Calculator: Calculate ΔH°rxn from standard enthalpies of formation.
Entropy Change Calculator: Calculate ΔS°rxn from standard entropies.
Thermodynamics Basics: Learn more about the fundamental concepts of thermodynamics and how to calculate the δg rxn.
Reaction Rate Calculator: Explore factors affecting the speed of chemical reactions.
Ideal Gas Law Calculator: Useful for calculations involving gases in reactions.

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