ΔG = ΔH − TΔS — fill in every field except the one you want; the empty field is solved for.
Example:
J/(mol·K)
Gibbs energy change (ΔG) = -32.958 kJ/mol
- Convert T: 25 °C =
298.15 K - Rearrange:
ΔG = ΔH − T × ΔS ÷ 1000 - Substitute:
(-92.2 kJ/mol) − (298.15 K) × (-198.7 J/(mol·K)) ÷ 1000=-32.958 kJ/mol
How it works
ΔH is entered in kJ/mol and ΔS in J/(mol·K), the units data tables use, so the calculator divides TΔS by 1000 before combining them. Temperatures must be absolute, so °C and °F are converted to kelvin. Leave ΔG as 0 and solve for T to find the temperature at which a reaction switches between spontaneous and non-spontaneous.
In the second mode, R = 8.3145 J/(mol·K). A negative ΔG° gives K greater than 1 (products favoured); a positive ΔG° gives K less than 1. Treating ΔH and ΔS as constant with temperature is an approximation, reasonable over moderate ranges.
Frequently asked questions
- How do I know if a reaction is spontaneous?
- Calculate ΔG = ΔH − TΔS. If ΔG is negative, the reaction is thermodynamically favourable at that temperature; if positive, it is not; if zero, the system is at equilibrium.
- At what temperature does CaCO₃ start to decompose?
- With ΔH ≈ +178 kJ/mol and ΔS ≈ +161 J/(mol·K), ΔG becomes zero at T = 178,000 ÷ 161 ≈ 1106 K (about 830 °C). Above that, decomposition is favourable — which is why lime kilns run hot.
- How are ΔG° and K related?
- ΔG° = −RT ln K. At 25 °C, every 5.7 kJ/mol more negative ΔG° multiplies K by ten.
- Does a negative ΔG mean the reaction is fast?
- No. ΔG says whether a reaction can happen, not how fast. Diamond turning into graphite is favourable but immeasurably slow at room temperature.
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