Q.State whether following reactions are spontaneous or not. Further state whether they are exothermic or endothermic. a. ΔH = -110 kJ and ΔS = +40 JK−1 at 400 K b. ΔH = +50 kJ and ΔS = -130 JK−1 at 250 K
Concept understanding — Gibbs Free Energy
Gibbs Free Energy: The "Why" Behind Spontaneous Reactions
Imagine you're pushing a boulder downhill. It's going to happen naturally — you don't need to keep pushing. But if you want to roll it uphill, you have to work against gravity the whole way. Chemistry works the same way: some reactions happen on their own (spontaneous), and others need a constant push of energy.
The question is: what decides which is which? That's exactly what Gibbs Free Energy answers.
The Two Competing Forces
Two things drive every chemical change:
-
Enthalpy (H) — the total heat content. Nature tends to move toward lower energy. A fire releases heat; that's enthalpy driving the reaction forward. Reactions that release heat (exothermic, ΔH<0) are favoured.
-
Entropy (S) — the measure of disorder. Nature also tends toward more chaos. A messy room doesn't tidy itself; a gas spreads to fill its container. Reactions that increase disorder (positive ΔS) are favoured.
But here's the catch: these two can pull in opposite directions. An endothermic reaction (absorbs heat, ΔH>0) might still happen if it creates enough disorder. Ice melting is a perfect example — it absorbs heat, but the liquid water is far more disordered than the crystal.
The Resolution: Gibbs Free Energy
Josiah Willard Gibbs combined these two forces into one number that tells you the net direction:
ΔG=ΔH−TΔS
Where:
- ΔG = change in Gibbs free energy (kJ/mol)
- ΔH = change in enthalpy (kJ/mol)
- T = absolute temperature (Kelvin)
- ΔS = change in entropy (J/K·mol — careful with units!)
The sign of ΔG is the final verdict:
| ΔG sign | What it means |
|---|---|
| Negative (ΔG<0) | Spontaneous — reaction happens on its own |
| Positive (ΔG>0) | Non-spontaneous — needs constant energy input |
| Zero (ΔG=0) | Equilibrium — no net change |
Why Temperature Matters
Notice the T in front of ΔS. Temperature decides which force wins. At low temperatures, the enthalpy term (ΔH) dominates. At high temperatures, the entropy term (TΔS) takes over.
This explains everyday observations:
- Ice melts spontaneously above 0°C (entropy wins at higher T)
- Water freezes spontaneously below 0°C (enthalpy wins at lower T)
- At exactly 0°C, ΔG=0 — ice and water coexist in equilibrium
The Precise Statement
Gibbs Free Energy is the maximum useful work obtainable from a closed system at constant temperature and pressure. When a reaction proceeds, the system loses free energy (ΔG<0), and that energy is available to do work — like running a muscle or powering a battery.
Spontaneity does NOT mean speed. A reaction can have ΔG<0 but take millions of years (diamond turning to graphite). Gibbs Free Energy tells you if something can happen, not how fast.
Quick Reference: The Four Cases
| ΔH | ΔS | Temperature effect | Example |
|---|---|---|---|
| Negative (exothermic) | Positive (more disorder) | Spontaneous at all T | Burning paper |
| Positive (endothermic) | Negative (less disorder) | Non-spontaneous at all T | Water splitting into H₂ and O₂ |
| Negative (exothermic) | Negative (less disorder) | Spontaneous only below a certain T | Water freezing |
| Positive (endothermic) | Positive (more disorder) | Spontaneous only above a certain T | Ice melting |
The Bottom Line
Think of ΔG as nature's accountant. It subtracts the "disorder benefit" (TΔS) from the "energy cost" (ΔH). If the result is negative, the reaction pays for itself. If positive, you need to keep investing energy to make it happen.
Students searching for "Gibbs Free Energy: Definition, Formula & Real-World Examples" or "Gibbs Free Energy 11 chemistry" will find this explanation directly aligned with the Class 11 Chemistry curriculum prescribed under NCERT/CBSE. It is also a recurring theme in JEE Main, NEET and state CET Chemistry papers, so working through it carefully pays off well beyond board exams.
Compute ΔG=ΔH−TΔS for each case (converting ΔS to kJ K−1); the sign of ΔG decides spontaneity and the sign of ΔH decides exo/endothermic.
a. ΔG=−126 kJ: spontaneous and exothermic. b. ΔG=+82.5 kJ: nonspontaneous and endothermic -- digit-for-digit the textbook's printed final.
a. −110−400×0.040=−126 kJ (spontaneous, exothermic); b. +50−250×(−0.130)=+82.5 kJ (nonspontaneous, endothermic).
Step 1 (a). TΔS=400 K×(+40×10−3 kJ K−1)=+16 kJ.
Step 2 (a). ΔG=ΔH−TΔS=−110 kJ−16 kJ=−126 kJ. ΔG<0: spontaneous; ΔH<0: exothermic.
Step 3 (b). TΔS=250 K×(−130×10−3 kJ K−1)=−32.5 kJ.
Step 4 (b). ΔG=+50−(−32.5)=50+32.5=+82.5 kJ. ΔG>0: nonspontaneous; ΔH>0: endothermic.
a. ΔG=−110−16=−126 kJ -- spontaneous, exothermic. b. ΔG=50+32.5=+82.5 kJ -- nonspontaneous, endothermic. Both digit-for-digit the textbook's printed final.
Convert each DeltaS from J K-1 to kJ K-1, evaluate DeltaG = DeltaH - T DeltaS at the stated temperature, and read spontaneity from DeltaG's sign and exo/endothermic from DeltaH's sign.
- Leaving DeltaS in J K-1 while DeltaH is in kJ, making the T-DeltaS term a thousand times too large.
- Sign slip in part (b): subtracting a negative T-DeltaS ADDS 32.5 kJ.
- Confusing the two verdicts: spontaneity follows DeltaG, exo/endothermic follows DeltaH.
- CBSE 2026Set ANNUAL1 markQ.The value of change in Gibbs energy (ΔG) for the spontaneous process is always ______.
›Reveal solutionSolution
For any spontaneous process at constant T and P, ΔG < 0 (negative).
Gibbs free energy is defined as G = H - TS. Its change during a process, ΔG = ΔH - TΔS, combines the enthalpy and entropy changes into a single criterion for spontaneity at constant temperature and pressure: if ΔG < 0, the process is spontaneous (proceeds on its own in the forward direction); if ΔG > 0, the process is non-spontaneous (won't proceed as written; the reverse process is spontaneous); if ΔG = 0, the system is at equilibrium.
✓Final answerΔG is always negative for a spontaneous process.
- CBSE 2026Set ANNUAL1 markMCQQ.The change in internal energy (ΔU) for an isolated system when there is no transfer of energy as heat or as work will be equal to(a) a) q(b) b) w(c) c) 0(d) d) 1
›Reveal solutionSolution
[!TLDR]
c) 0
Why
First law: ΔU = q + w. With no heat (q=0) and no work (w=0) exchanged, ΔU = 0 (true of an isolated system).
[!ANSWER]
c) 0
- CBSE 2023Set ANNUAL1 markMCQQ.Which of the following statements is true ?(a) ΔG may be lesser or greater or equal to ΔH.(b) ΔG is always proportional to ΔH.(c) ΔG is always greater than ΔH.(d) ΔG is always less than ΔH.
›Reveal solutionSolution
dG can be lesser, greater or equal to dH.
The Gibbs-Helmholtz relation is dG = dH - TdS. The relationship between dG and dH therefore depends entirely on the term TdS:
- If dS > 0, then TdS > 0 and dG < dH.
- If dS < 0, then TdS < 0 and dG > dH.
- If dS = 0, then dG = dH. So no fixed proportionality or inequality holds in general; dG may be lesser than, greater than or equal to dH.
Gibbs free energy is a central concept in the NCERT Class 11 Chemistry Thermodynamics chapter.
✓Final answer(a) dG may be lesser or greater or equal to dH.
- CBSE 2022Set ANNUAL1 markQ.Write the Gibbs equation.
›Reveal solutionSolution
The Gibbs equation is delta-G = delta-H - T(delta-S).
Gibbs free energy (G) combines enthalpy (H) and entropy (S) into a single quantity that predicts the spontaneity of a process at constant temperature and pressure: delta-G = delta-H - T x delta-S, where delta-H is the enthalpy change, T is the absolute temperature, and delta-S is the entropy change of the system. A process is spontaneous when delta-G is negative, non-spontaneous when delta-G is positive, and at equilibrium when delta-G = 0.
✓Final answerdelta-G = delta-H - T(delta-S).
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