Spontaneity and ΔG HL Only
Quick Notes:
- A process is spontaneous at constant pressure if ΔG < 0.
- ΔG = ΔH − TΔS accounts for:
- Entropy change of the system (ΔS)
- Entropy change of the surroundings (via ΔH)
- ΔG links:
- ΔH (enthalpy change of system)
- ΔS (entropy change of system)
- T (temperature in Kelvin)
- To find the temperature at which a reaction becomes spontaneous:
T = ΔH / ΔS (set ΔG = 0).
Full Notes:
The background theory to Gibbs Free Energy Change (ΔG) is outlined full detail in R1.4.2 here.
ΔG and Spontaneity
The sign of ΔG tells us whether a process is thermodynamically favorable (spontaneous) under constant pressure and temperature:
- ΔG < 0 → Spontaneous
- ΔG > 0 → Non-spontaneous
- ΔG = 0 → At equilibrium
By spontaneous, we mean the reaction can happen without any overall external energy input. The terms 'spontaneous' and feasible' are often used interchangably.
The Full Interpretation of ΔG
The expression ΔG = ΔH − TΔS accounts for:
- ΔS of the system:
disorder change from the reaction or process itself. - Enthalpy Change, ΔH:
reflects the heat exchange, which indirectly affects entropy of the surroundings:- Exothermic (ΔH < 0): increases entropy of surroundings.
- Endothermic (ΔH > 0): decreases entropy of surroundings.
So ΔG effectively measures the total entropy change (system + surroundings).
Finding Temperature for Feasibility
You can rearrange the Gibbs equation to find the minimum temperature at which a reaction becomes feasible:
To find the minimum temperature (T) where a reaction is feasible, we can set ΔG = 0:
(If ΔG has to be zero or lower for a reaction to be feasible, then the temperature when ΔG is zero is the minimum that it can be!)
This now gives:
T = ΔH / ΔS
- If T is high, the reaction is only feasible at high temperatures.
- If T is low, the reaction is feasible at lower temperatures.
A reaction has ΔH = +50 kJ mol⁻¹ and ΔS = +100 J K⁻¹ mol⁻¹. Find the minimum temperature, T, at which the reaction is feasible.
- Convert ΔS: +100 J K⁻¹ mol⁻¹ = +0.100 kJ K⁻¹ mol⁻¹
- Use ΔG = ΔH − TΔS and set ΔG = 0
- T = ΔH / ΔS = 50 / 0.100 = 500 K
The reaction becomes feasible at T ≥ 500 K.
Summary Table
We can predict whether a reaction will be spontaneous based on the signs of enthalpy change (ΔH) and entropy change (ΔS).
| ΔH | ΔS | Spontaneity |
|---|---|---|
| − | + | Always spontaneous |
| + | − | Never spontaneous |
| − | − | Spontaneous only at low temperatures |
| + | + | Spontaneous only at high temperatures |
Why Some Feasible Reactions Don’t Happen
Just because a reaction can happen (ΔG is negative) and is feasible doesn’t mean that it will happen — a high activation energy barrier may prevent a feasible reaction from occurring. The rate of reaction may be so slow that the reaction doesn’t happen fast enough to observe.
Example Diamond vs Graphite
The conversion of diamond into graphite has a negative ΔG, meaning it is thermodynamically feasible. In theory, this process should happen spontaneously.
However, in reality, the transformation does not occur noticeably because it has a very high activation energy (Ea). This large energy barrier prevents the reaction from proceeding at a measurable rate under standard conditions.
This is the difference between thermodynamic feasibility (ΔG < 0) and kinetic feasibility (reaction rate fast enough to observe).
Summary
- A process is spontaneous at constant pressure if ΔG < 0.
- ΔG = ΔH − TΔS accounts for entropy changes of both system and surroundings.
- Temperature determines feasibility when ΔH and ΔS have the same sign.
- Some thermodynamically feasible reactions do not occur due to high activation energy barriers.
Linked Course Questions
How can electrochemical data also be used to predict the spontaneity of a reaction?
Electrochemical data, specifically standard electrode potentials (E°), can be used to predict whether a redox reaction is spontaneous. If the overall cell potential (E°cell = E°cathode − E°anode) is positive, the reaction is thermodynamically spontaneous under standard conditions.