Standard Gibbs Free Energy Calculator (ΔG° at 298 K)
Determine the spontaneity of a chemical reaction by calculating the standard Gibbs free energy change (ΔG°) using enthalpy and entropy values.
Enter the heat of reaction in kilojoules per mole (kJ/mol).
Enter the change in disorder in joules per mole Kelvin (J/mol·K).
Standard Gibbs Free Energy Change (ΔG°)
| ΔG° Value | Reaction Spontaneity | Description |
|---|---|---|
| ΔG° < 0 (Negative) | Spontaneous | The reaction favors the formation of products under standard conditions. |
| ΔG° > 0 (Positive) | Non-Spontaneous | The reaction does not favor the formation of products; the reverse reaction is spontaneous. |
| ΔG° = 0 | At Equilibrium | The forward and reverse reactions occur at equal rates; there is no net change. |
What is Standard Gibbs Free Energy (ΔG°)?
The standard Gibbs free energy change (ΔG°) is a thermodynamic quantity that represents the maximum amount of reversible work that can be performed by a system at a constant temperature and pressure. It is the most reliable indicator for predicting the spontaneity of a chemical reaction under standard conditions (298 K and 1 atm pressure). If the value of ΔG° is negative, the reaction is spontaneous in the forward direction. If it’s positive, the reaction is non-spontaneous. A value of zero indicates the reaction is at equilibrium.
The Formula to calculate δrg at 298 k using the following information
The calculation is based on a fundamental equation in thermodynamics that relates Gibbs free energy (G) to enthalpy (H) and entropy (S):
ΔG° = ΔH° – TΔS°
This formula is crucial for anyone needing to calculate δrg at 298 k using the following information. It shows how the change in heat (enthalpy) and the change in disorder (entropy) combine to determine if a reaction will proceed on its own.
| Variable | Meaning | Typical Unit | Role in Calculation |
|---|---|---|---|
| ΔG° | Standard Gibbs Free Energy Change | kJ/mol | The final result; determines spontaneity. |
| ΔH° | Standard Enthalpy Change | kJ/mol | The heat absorbed or released by the reaction. A negative value (exothermic) favors spontaneity. |
| T | Absolute Temperature | Kelvin (K) | Fixed at 298 K for standard calculations. It amplifies the effect of the entropy change. |
| ΔS° | Standard Entropy Change | J/mol·K | The change in the system’s disorder. A positive value (increased disorder) favors spontaneity. |
Practical Examples
Example 1: Spontaneous Reaction (Haber Process)
Let’s consider the synthesis of ammonia (NH₃) from nitrogen (N₂) and hydrogen (H₂), a classic industrial process.
- Inputs:
- ΔH° = -92.2 kJ/mol (Exothermic, releases heat)
- ΔS° = -198.7 J/mol·K (Becomes more ordered)
- Calculation Steps:
- Convert ΔS° to kJ: -198.7 J/mol·K / 1000 = -0.1987 kJ/mol·K
- Calculate TΔS°: 298 K * (-0.1987 kJ/mol·K) = -59.21 kJ/mol
- Calculate ΔG°: -92.2 kJ/mol – (-59.21 kJ/mol) = -32.99 kJ/mol
- Result: ΔG° is approximately -33.0 kJ/mol. Since the value is negative, the reaction is spontaneous at 298 K.
Example 2: Non-Spontaneous Reaction (Decomposition of Water)
Consider the decomposition of liquid water into hydrogen and oxygen gas.
- Inputs:
- ΔH° = +286 kJ/mol (Endothermic, absorbs heat)
- ΔS° = +163 J/mol·K (Becomes more disordered)
- Calculation Steps:
- Convert ΔS° to kJ: 163 J/mol·K / 1000 = 0.163 kJ/mol·K
- Calculate TΔS°: 298 K * (0.163 kJ/mol·K) = +48.57 kJ/mol
- Calculate ΔG°: +286 kJ/mol – (+48.57 kJ/mol) = +237.43 kJ/mol
- Result: ΔG° is approximately +237.4 kJ/mol. The large positive value indicates the reaction is highly non-spontaneous at room temperature.
How to Use This Calculator
Follow these steps to accurately calculate δrg at 298 k using the following information:
- Enter Standard Enthalpy Change (ΔH°): Input the known value for the reaction’s enthalpy change in the first field. Ensure the unit is kJ/mol.
- Enter Standard Entropy Change (ΔS°): Input the known value for the reaction’s entropy change in the second field. Note that this calculator expects the unit to be J/mol·K and will handle the conversion automatically.
- Review the Results: The calculator instantly provides the final ΔG° value. A negative number means the reaction is spontaneous, while a positive number means it is non-spontaneous.
- Analyze Intermediate Values: The results section also shows the temperature (fixed at 298 K), the converted entropy value in kJ, and the total TΔS° term, helping you understand how each component contributes to the final result. For more information, you might explore our guide on thermodynamics basics.
Key Factors That Affect Gibbs Free Energy
- Enthalpy (ΔH°): Exothermic reactions (negative ΔH°) release heat and are more likely to be spontaneous. Endothermic reactions (positive ΔH°) require energy and are less likely to be spontaneous.
- Entropy (ΔS°): Reactions that increase disorder (positive ΔS°), such as a solid turning into a gas, are more likely to be spontaneous.
- Temperature (T): Temperature acts as a weighting factor for entropy. At high temperatures, the TΔS° term becomes more significant and can make an endothermic reaction with a positive ΔS° spontaneous.
- Physical State: The state of reactants and products (solid, liquid, gas) heavily influences entropy. A reaction producing gas from a liquid will have a large positive ΔS°. A helpful tool is our Phase Change Energy Calculator.
- Concentration and Pressure: While this calculator uses standard conditions (1 M concentration, 1 atm pressure), changes in these variables affect the actual Gibbs free energy (ΔG), not the standard value (ΔG°).
- Catalysts: A catalyst speeds up the rate at which a reaction reaches equilibrium but does NOT change the value of ΔH°, ΔS°, or ΔG°. It cannot make a non-spontaneous reaction spontaneous. Learn more with our Activation Energy Calculator.
Frequently Asked Questions (FAQ)
A negative ΔG° indicates that the reaction is spontaneous under standard conditions. This means the products are thermodynamically favored over the reactants, and the reaction can proceed without a continuous input of external energy.
A positive ΔG° means the reaction is non-spontaneous. The energy of the reactants is lower than the energy of the products, so the reaction will not proceed on its own. Instead, the reverse reaction would be spontaneous.
298 K (which is 25°C or 77°F) is defined as standard temperature in thermodynamics for reporting data. This calculator is specifically designed to calculate δrg at 298 k to provide results based on this universal standard.
The most common mistake is failing to convert the entropy change (ΔS°) from Joules (J) to kilojoules (kJ). Enthalpy (ΔH°) is almost always given in kJ, so ΔS° must be divided by 1000 to match before using the formula. This calculator does this for you automatically.
Yes. If the increase in entropy (positive ΔS°) is large enough, the TΔS° term can overcome the positive ΔH°, resulting in a negative ΔG°. This typically happens at higher temperatures. You can investigate this relationship with an Enthalpy of Reaction Calculator.
Standard enthalpy (ΔH°f) and entropy (S°) values for most compounds are available in chemistry textbooks, scientific handbooks, and online databases like the NIST Chemistry WebBook.
In thermodynamics, “spontaneous” (or feasible) doesn’t mean fast. It only means a reaction can happen without external energy input. A spontaneous reaction could take seconds or millions of years, as its rate depends on the activation energy, not ΔG°. To analyze reaction rates, consider our Reaction Rate Calculator.
Yes, ‘δrg’ or ‘ΔrG°’ are common notations for the ‘change (Δ) in Gibbs free energy (G) for a reaction (r) under standard (°) conditions’.