How to use the gibbs free energy and equilibrium constant calculator
- Choose what you know: dH and dS, the free energy dG, or the equilibrium constant K.
- Choose the temperature unit and enter the temperature.
- Enter dH in kJ/mol and dS in J/(mol K), or dG in kJ/mol, or K, depending on your choice.
- Read dG, K, ln K, the temperature used, whether the products are favored and the temperature where dG is zero.
Formula
dG = dH - T x dS, with dS converted to kJ/(mol K)
dG = -R x T x ln K, with R = 8.314462618 J/(mol K)
K = exp(-dG / (R x T))
Temperature where dG = 0 is T = dH / dS, when dH and dS have the same sign
The two relations link thermodynamics to equilibrium. A negative dG gives a K above 1 and favors products, and a positive dG gives a K below 1 and favors reactants.
Ammonia synthesis at 298.15 K
With dH = -92.2 kJ/mol and dS = -198.7 J/(mol K), dG = -92.2 - 298.15 x (-0.1987) = -32.9576 kJ/mol. Then ln K = 32957.6 / (8.314462618 x 298.15) = 13.2949, so K = 594184, and the products are favored.
The temperature where dG is zero is -92.2 / -0.1987 = 464.02 K. Above that, dG becomes positive because the entropy term wins. A dG of -10 kJ/mol at 298.15 K gives K = 56.48, and a K of 1000 gives dG = -17.12 kJ/mol.
Spontaneous does not mean fast
A negative dG says the reaction can proceed toward products and that the equilibrium lies on the product side. It says nothing about the rate. Some strongly favored reactions are very slow without a catalyst or enough energy to start them.
Once you have K, an ICE table gives the amounts at equilibrium. See the ICE table equilibrium calculator, and for a weak acid in water the pH and weak acid calculator.
Assuming dH and dS are constant
The formula assumes that dH and dS do not change with temperature. That is reasonable over a modest range but not over several hundred kelvin, when heat capacities matter. The temperature where dG is zero is therefore a good estimate and not an exact value.
Standard state values refer to defined conditions, and the equilibrium constant here is the thermodynamic one. For gas quantities see the ideal gas law calculator.
Assumptions and limits
- The enthalpy and entropy changes are constant over the temperature range.
- dH and dG are in kJ/mol and dS is in J/(mol K).
- K is the thermodynamic equilibrium constant for the reaction as written.
- Temperature must be above absolute zero.
Frequently asked questions
How do I get K from dG?
Use K = exp(-dG / (R T)), with dG in joules per mole. The page converts from kJ/mol for you.
What does a positive dG mean?
The reaction does not favor products under standard conditions, and K is below 1. It may still proceed if conditions change or if it is coupled to another reaction.
Why does the page give a temperature where dG is zero?
It is the crossover point where the entropy term balances the enthalpy term. The preferred direction changes there.
Can I use Celsius?
Yes. Choose Celsius and the page converts it to kelvin, because the equations need absolute temperature.