Step 1 — What is ΔSsurr?
The surroundings act like a giant heat reservoir at constant temperature T and pressure P. At constant P, heat exchanged by the system is qsys=ΔHsys.
Why this step? At constant pressure, the heat term equals the enthalpy change — that's literally the definition of enthalpy (qP=ΔH).
The surroundings absorb the opposite heat: qsurr=−ΔHsys.
Step 2 — Entropy of surroundings.
For a reservoir absorbing heat reversibly:
ΔSsurr=Tqsurr=T−ΔHsys
Why this step? The reservoir is so large its temperature never changes, so the heat flow is effectively reversible for it — meaning ΔS=qrev/T applies exactly.
Step 3 — Substitute back.ΔSuniv=ΔSsys−TΔHsys
Step 4 — Multiply by −T (a positive number, so flip the inequality).−TΔSuniv=ΔHsys−TΔSsys
We define the right-hand side as the Gibbs free energy change:
Step 5 — Read off the spontaneity criterion.
Since T>0: ΔSuniv>0⟺ΔG<0.
What thermodynamic quantity determines spontaneity at constant T and P?
The Gibbs free energy change ΔG; spontaneous if ΔG<0.
Derive the sign relationship between ΔG and ΔS_univ.
ΔG=−TΔSuniv, so ΔG<0⟺ΔSuniv>0.
Why does entropy of surroundings equal −ΔH/T?
Surroundings absorb −ΔH of heat reversibly at temperature T, so ΔSsurr=qsurr/T=−ΔH/T.
For ΔH<0, ΔS>0, when is the reaction spontaneous?
Always (at all temperatures), since ΔG is always negative.
For ΔH>0, ΔS>0, when spontaneous?
Only at high temperature, when TΔS>ΔH.
At what temperature does an exothermic, entropy-decreasing reaction stop being spontaneous?
When T>ΔH/ΔS (both negative), i.e. above T=ΔH/ΔS.
Does ΔG<0 tell you the reaction is fast?
No — it tells you it's feasible, not the rate; rate depends on activation energy.
Relationship between ΔG° and K?
ΔG∘=−RTlnK.
What is ΔG at equilibrium?
Exactly zero.
Full form of ΔG under non-standard conditions?
ΔG=ΔG∘+RTlnQ.
Recall Feynman: explain to a 12-year-old
Nature has two "wants": it likes things to be low energy (like a ball rolling downhill — that's ΔH) and it likes things to be messy/spread out (that's ΔS). Gibbs energy is a single scoreboard that adds both wants together, with temperature deciding how much "messiness" counts. If the score ΔG goes down, the change happens by itself. Hot conditions make messiness count a lot; cold conditions make energy count more. That's the whole story.
Dekho, Gibbs free energy ka pura funda ek hi line mein hai: ΔG=ΔH−TΔS. Yeh actually second law ka hi ek smart repackaging hai. Second law kehta hai ki reaction tabhi khud-ba-khud hoti hai jab universe ki total entropy badhe (ΔSuniv>0). Lekin surroundings ko measure karna mushkil hai, isliye humne surroundings wala part (−ΔH/T) ko system ke terms mein chhupa diya. Result: sirf beaker dekh kar prediction — agar ΔG negative hai to reaction spontaneous hai.
Ismein do "forces" ka tug of war hai. Nature ko low energy pasand hai (enthalpy, ΔH) aur disorder/messiness bhi pasand hai (entropy, ΔS). Temperature T decide karta hai ki disorder ko kitna weightage milega. Low temperature pe enthalpy jeetega, high temperature pe entropy jeetega. Isiliye kuch reactions sirf garam karne pe hi chalti hain aur kuch sirf thanda hone pe.
Char cases yaad rakho: ΔH<0,ΔS>0 → hamesha spontaneous; ΔH>0,ΔS<0 → kabhi nahi; baaki do temperature pe depend karte hain, aur crossover temperature T=ΔH/ΔS pe milta hai (jaise ice ka melting point 273 K).
Ek important warning: ΔG<0 ka matlab reaction "possible" hai, "fast" nahi. Diamond se graphite banna spontaneous hai par crore saal lagte hain — kyunki wo kinetics (activation energy) ka mamla hai, thermodynamics ka nahi. Aur units ka dhyan rakho — ΔS J mein hota hai, ΔH kJ mein, subtract karne se pehle same unit mein lao warna answer ulta aa jayega.
