Equilibrium Constant (K) Calculator
Calculate the equilibrium constant (K) by providing the standard Gibbs free energy change (ΔG°) and temperature.
Thermodynamic Calculator
Enter the value in kilojoules per mole (kJ/mol). A negative value indicates a spontaneous reaction.
Enter the temperature for the reaction.
K vs. Temperature (at constant ΔG°)
What is the Equilibrium Constant (K)?
The equilibrium constant, denoted as K, is a value that expresses the relationship between the concentrations of products and reactants of a chemical reaction at equilibrium. In simple terms, it tells you the extent to which a reaction will proceed to completion. A large K value (K > 1) indicates that the reaction mixture at equilibrium will contain mostly products, favoring the forward reaction. Conversely, a small K value (K < 1) indicates that the reaction will have mostly reactants at equilibrium, favoring the reverse reaction.
This calculator specifically focuses on calculating the equilibrium constant using the inverse log relationship derived from thermodynamics, particularly from the standard Gibbs free energy change (ΔG°).
The Formula for Calculating Equilibrium Constant from ΔG°
The relationship between the standard Gibbs free energy change (ΔG°), a measure of a reaction’s spontaneity under standard conditions, and the equilibrium constant (K) is one of the cornerstones of chemical thermodynamics. The equation is:
ΔG° = -RT ln(K)
To use this for calculating the equilibrium constant, we rearrange the formula. The user prompt mentions “inverse log”, and this is where it comes in. The inverse of the natural logarithm (ln) is the exponential function (ex).
K = e(-ΔG° / RT)
This formula is what our calculator uses. It shows that K is calculated via an exponential function, which is the inverse of the natural logarithm.
Variables Explained
| Variable | Meaning | Unit (in this calculator) | Typical Range |
|---|---|---|---|
| K | Equilibrium Constant | Unitless | 0 to ∞ |
| ΔG° | Standard Gibbs Free Energy Change | kJ/mol | -200 to +200 kJ/mol |
| R | Ideal Gas Constant | 8.314 J/(mol·K) | Constant |
| T | Absolute Temperature | Kelvin (K) | > 0 K |
Practical Examples
Example 1: A Spontaneous Reaction
Consider the synthesis of ammonia (Haber process) at 400 K, which has a negative ΔG° under certain conditions.
- Input ΔG°: -16.4 kJ/mol
- Input Temperature: 400 K
- Calculation:
- -ΔG°/RT = -(-16400 J/mol) / (8.314 J/(mol·K) * 400 K) ≈ 4.93
- K = e4.93 ≈ 138
- Result: A K value of approximately 138 indicates that at equilibrium, the products (ammonia) are significantly favored over the reactants.
Example 2: A Non-Spontaneous Reaction
Let’s look at the decomposition of calcium carbonate (limestone) at room temperature (298.15 K).
- Input ΔG°: +130.4 kJ/mol
- Input Temperature: 25 °C (298.15 K)
- Calculation:
- -ΔG°/RT = -(130400 J/mol) / (8.314 J/(mol·K) * 298.15 K) ≈ -52.6
- K = e-52.6 ≈ 1.4 x 10-23
- Result: An extremely small K value shows that at room temperature, the reaction barely proceeds, and the equilibrium mixture is almost entirely reactants (calcium carbonate). For more on this, check our Gibbs free energy calculator.
How to Use This Equilibrium Constant Calculator
- Enter Gibbs Free Energy (ΔG°): Input the standard Gibbs free energy change for your reaction in kJ/mol. Remember to use a negative sign for spontaneous reactions.
- Enter Temperature: Input the temperature at which the reaction occurs.
- Select Temperature Unit: Choose whether you are entering the temperature in Celsius (°C) or Kelvin (K). The calculator will automatically convert to Kelvin for the formula.
- Interpret the Results: The calculator instantly provides the unitless equilibrium constant (K). It also shows key intermediate values like the temperature in Kelvin, the value of the RT term, and the exponent used in the calculation to provide full transparency.
Key Factors That Affect the Equilibrium Constant
The value of K is not always constant; it is primarily affected by temperature. Understanding these factors is key to predicting how a reaction will behave under different conditions.
- Temperature: This is the most significant factor. For an exothermic reaction (releases heat, negative ΔH°), K decreases as temperature increases. For an endothermic reaction (absorbs heat, positive ΔH°), K increases as temperature increases. This is explained by Le Châtelier’s Principle.
- Nature of Reactants and Products: The inherent stability of the substances involved (reflected in ΔH° and ΔS°) determines the baseline ΔG° and thus the value of K.
- Stoichiometry of the Reaction: If you reverse a reaction, the new equilibrium constant is 1/K. If you multiply the coefficients of a reaction by a factor ‘n’, the new constant is Kn.
- Pressure (for gases): While changing pressure doesn’t change K, it can shift the equilibrium position if the number of moles of gas on the reactant and product sides are different.
- Solvent (for solutions): The solvent can affect the stability of dissolved species, thus influencing the equilibrium.
- Ionic Strength: In solutions containing ions, the activity of the ions can differ from their concentration, slightly altering the effective equilibrium constant.
For more details on thermodynamics, see our article what is thermodynamics.
Frequently Asked Questions (FAQ)
What is the difference between K > 1, K < 1, and K = 1?
If K > 1, products are favored at equilibrium. If K < 1, reactants are favored. If K = 1, there are appreciable amounts of both reactants and products, and ΔG° is zero.
Why is K unitless?
Strictly, the equilibrium constant is defined in terms of ‘activities’ rather than concentrations or pressures. Activities are dimensionless ratios, which makes K a unitless quantity.
How is “inverse log” related to this calculation?
The term “inverse log” can be confusing. In this context, it refers to the inverse of the natural logarithm (ln), which is the exponential function (ex). The formula K = e(-ΔG°/RT) is the mathematical execution of this concept.
Does a catalyst change the equilibrium constant?
No. A catalyst increases the rate of both the forward and reverse reactions equally. It helps the system reach equilibrium faster but does not change the final position of the equilibrium (the value of K).
What is the difference between Kp and Kc?
Kc is the equilibrium constant expressed in terms of molar concentrations, while Kp is expressed in terms of partial pressures for gaseous reactions. You can explore this with a chemical equilibrium formula tool.
Why must temperature be in Kelvin?
Thermodynamic formulas like this one are based on an absolute temperature scale, where zero represents the true absence of thermal energy. Kelvin is an absolute scale, whereas Celsius is relative. Using Celsius would lead to incorrect results, including division by zero or negative values.
What does a positive ΔG° mean?
A positive standard Gibbs free energy change means the reaction is non-spontaneous under standard conditions. This leads to a K value less than 1, indicating that reactants are favored at equilibrium.
Can I use this calculator for non-standard conditions?
This calculator computes K from the *standard* free energy change (ΔG°). The resulting K is valid for the specified temperature, but the relationship ΔG = -RTlnK is for standard conditions. For non-standard conditions, you would use the related equation: ΔG = ΔG° + RTlnQ, where Q is the reaction quotient. See our reaction quotient calculator for more.