Free Energy Change (ΔG°) Calculator from Keq

Determine a reaction’s spontaneity by calculating the standard Gibbs free energy change (ΔG°) from its equilibrium constant (Keq) and temperature.

Dynamic Analysis

ΔG° vs. Keq at 298.15 K

Keq	ln(Keq)	ΔG° (kJ/mol)	Spontaneity

What is Free Energy Change from Keq?

The standard Gibbs free energy change (ΔG°) is a critical thermodynamic value that indicates whether a chemical reaction will be spontaneous under standard conditions (1 atm pressure, 1 M concentration, and a specified temperature). Calculating the free energy change using the equilibrium constant (Keq) provides a direct link between the position of equilibrium and the reaction’s spontaneity.

Essentially, Keq tells us the ratio of products to reactants when a reaction has reached equilibrium. A large Keq (>1) means the reaction favors the products, while a small Keq (<1) means it favors the reactants. The ΔG° calculation quantifies the driving force behind this preference. This calculation is vital for chemists, biochemists, and engineers who need to predict the feasibility of reactions without performing them.

The Formula to Calculate Free Energy Change using Keq

The relationship between the standard free energy change (ΔG°), temperature (T), and the equilibrium constant (Keq) is defined by a fundamental thermodynamic equation:

ΔG° = -R × T × ln(Keq)

This equation elegantly connects a reaction’s equilibrium state to its energetic favorability. A link to the basics of thermodynamics can provide more context.

Variable Explanations

Variable	Meaning	Unit (Auto-Inferred)	Typical Range
ΔG°	Standard Gibbs Free Energy Change	kJ/mol or J/mol	-∞ to +∞
R	Ideal Gas Constant	8.314 J/(mol·K)	Constant
T	Absolute Temperature	Kelvin (K)	> 0 K
Keq	Equilibrium Constant	Unitless	> 0
ln(Keq)	Natural Logarithm of Keq	Unitless	-∞ to +∞

Practical Examples

Example 1: A Spontaneous Reaction

Consider a reaction at 25°C (298.15 K) with a large equilibrium constant, indicating it strongly favors the products.

• Input Keq: 1,500
• Input Temperature: 298.15 K
• Calculation: ΔG° = -8.314 J/(mol·K) * 298.15 K * ln(1500)
• Result: ΔG° ≈ -18.1 kJ/mol

The negative ΔG° confirms the reaction is spontaneous under standard conditions. Explore more spontaneous reactions in our detailed guide.

Example 2: A Non-Spontaneous Reaction

Now, consider a reaction at the same temperature but with an equilibrium constant much less than 1, indicating it favors the reactants.

• Input Keq: 0.005
• Input Temperature: 298.15 K
• Calculation: ΔG° = -8.314 J/(mol·K) * 298.15 K * ln(0.005)
• Result: ΔG° ≈ +13.1 kJ/mol

The positive ΔG° indicates the reaction is non-spontaneous in the forward direction; instead, the reverse reaction is favored.

How to Use This Calculator

1. Enter Keq: Input the equilibrium constant for your reaction. This must be a positive, unitless number.
2. Enter Temperature: Input the temperature and select the correct unit (°C, K, or °F). The calculator automatically converts it to Kelvin for the formula.
3. Analyze Results: The primary result shows ΔG° in kJ/mol. A negative value means the reaction is spontaneous (product-favored), a positive value means it’s non-spontaneous (reactant-favored), and a value of zero means it’s at equilibrium.
4. Review Breakdown: Check the intermediate values to understand how the result was derived.
5. Consult Visuals: Use the table and chart to see how ΔG° changes with Keq at the specified temperature. For further analysis, check out our guide on interpreting thermodynamic data.

Key Factors That Affect Free Energy Change

• Equilibrium Constant (Keq): The most direct factor. As Keq increases, ln(Keq) becomes more positive, making ΔG° more negative (more spontaneous).
• Temperature (T): Temperature directly scales the `ln(Keq)` term. For reactions with Keq > 1, increasing temperature makes ΔG° more negative. For reactions with Keq < 1, increasing temperature makes ΔG° more positive. This is a crucial concept explored in temperature effects on equilibrium.
• Concentration of Reactants/Products: While not a direct input in this calculator, concentrations determine the Reaction Quotient (Q). The relationship between Q and Keq dictates the direction a reaction must shift to reach equilibrium, which is fundamentally linked to free energy.
• Pressure (for gases): Pressure changes can shift the equilibrium position for reactions involving gases, thereby altering Keq and influencing ΔG°.
• Enthalpy (ΔH°): Though not directly in the `ΔG° = -RTln(Keq)` equation, enthalpy is a core component of free energy via `ΔG° = ΔH° – TΔS°`. It represents the heat change of the reaction.
• Entropy (ΔS°): Entropy, the measure of disorder, is the other major component. The balance between enthalpy and entropy ultimately determines the sign of ΔG° and the value of Keq.

Frequently Asked Questions

1. What does a negative ΔG° mean?
A negative ΔG° signifies that a reaction is spontaneous under standard conditions, meaning it will proceed in the forward direction to form products without external energy input.

2. What does a positive ΔG° mean?
A positive ΔG° indicates a reaction is non-spontaneous. The forward reaction will not occur on its own; instead, the reverse reaction is spontaneous.

3. What if ΔG° is zero?
If ΔG° is zero, the reaction is at equilibrium under standard state conditions. This occurs when Keq is exactly 1.

4. Why is Keq unitless?
Keq is technically calculated using the ‘activities’ of reactants and products, which are unitless ratios. This is why you can take the logarithm of Keq, as logarithmic functions are only defined for dimensionless numbers.

5. What is the standard temperature used in these calculations?
The standard temperature for thermodynamic calculations is typically 298.15 K (25 °C or 77 °F). However, this calculator allows you to compute ΔG° at any temperature. You can learn more about standard state conditions here.

6. How does this relate to ΔG = ΔH° – TΔS°?
Both equations describe Gibbs Free Energy. The two are related by the equation `ΔG° = -RTln(Keq)`. By combining them, you get `ΔH° – TΔS° = -RTln(Keq)`, which shows how enthalpy and entropy changes determine the equilibrium constant.

7. Can I use this calculator for non-standard conditions?
This calculator specifically finds the *standard* free energy change (ΔG°). To find the free energy change under non-standard conditions (ΔG), you would use the equation `ΔG = ΔG° + RTln(Q)`, where Q is the reaction quotient.

8. What units should my final answer be in?
Gibbs free energy is typically expressed in kilojoules per mole (kJ/mol) or joules per mole (J/mol). This calculator provides both.