Gibbs free energy ΔG = ΔH − TΔS; spontaneity criteria

2.5.14 · Chemistry › Thermodynamics (Chemical)

1. ΔG ko Second Law se Derive Karna (scratch se)

Step 1 — $Δ S_{s u r r}$ kya hai? Surroundings ek giant heat reservoir ki tarah kaam karte hain jo constant temperature $T$ aur pressure $P$ par hota hai. Constant $P$ par, system dwara exchange ki gayi heat $q_{sy s} = Δ H_{sy s}$ hoti hai.

Ye step kyun? Constant pressure par, heat term enthalpy change ke barabar hoti hai — yahi enthalpy ki definition hai ( $q_{P} = Δ H$ ).

Surroundings opposite heat absorb karte hain: $q_{s u r r} = - Δ H_{sy s}$ .

Step 2 — Surroundings ki entropy. Ek reservoir ke liye jo reversibly heat absorb karta hai: $Δ S_{s u r r} = \frac{q _{s u r r}}{T} = \frac{- Δ H _{sy s}}{T}$

Ye step kyun? Reservoir itna bada hota hai ki uska temperature kabhi nahi badalta, isliye uske liye heat flow effectively reversible hai — matlab $Δ S = q_{r e v} / T$ exactly apply hota hai.

Step 3 — Wapas substitute karo. $Δ S_{u ni v} = Δ S_{sy s} - \frac{Δ H _{sy s}}{T}$

Step 4 — $- T$ se multiply karo (ek positive number, isliye inequality flip ho jaati hai). $- T Δ S_{u ni v} = Δ H_{sy s} - T Δ S_{sy s}$

Hum right-hand side ko Gibbs free energy change ke roop mein define karte hain:

Step 5 — Spontaneity criterion padho. Kyunki $T > 0$ : $Δ S_{u ni v} > 0 ⟺ Δ G < 0$ .

2. Chaar sign combinations (80/20 core table)

Behaviour signs of $Δ H$ aur $Δ S$ par depend karta hai, aur kabhi kabhi $T$ par bhi.

$Δ H$	$Δ S$	$Δ G = Δ H - T Δ S$	Spontaneous?
− (exo)	+	hamesha −	Hamesha spontaneous
+ (endo)	−	hamesha +	Kabhi bhi spontaneous nahi
− (exo)	−	− low $T$ par	Sirf low $T$ par spontaneous
+ (endo)	+	− high $T$ par	Sirf high $T$ par spontaneous

Figure — Gibbs free energy ΔG = ΔH − TΔS; spontaneity criteria

3. Worked examples

4. Common mistakes (Steel-man + fix)

5. Flashcards

Constant T aur P par spontaneity kaun sa thermodynamic quantity determine karta hai?

Gibbs free energy change

Δ G

; spontaneous if

Δ G < 0

ΔG aur ΔS_univ ke beech sign relationship derive karo.

Δ G = - T Δ S_{u ni v}

, isliye

Δ G < 0 ⟺ Δ S_{u ni v} > 0

Surroundings ki entropy −ΔH/T kyun hoti hai?

Surroundings temperature

T

par reversibly

- Δ H

heat absorb karte hain, isliye

Δ S_{s u r r} = q_{s u r r} / T = - Δ H / T

ΔH<0, ΔS>0 ke liye, reaction kab spontaneous hai?

Hamesha (sabhi temperatures par), kyunki

Δ G

hamesha negative hota hai.

ΔH>0, ΔS>0 ke liye, kab spontaneous?

Sirf high temperature par, jab

T Δ S > Δ H

Ek exothermic, entropy-decreasing reaction kis temperature par spontaneous rehna band kar deti hai?

Jab

T > Δ H /Δ S

(dono negative), yaani

T = Δ H /Δ S

ke upar.

Kya ΔG<0 batata hai ki reaction fast hai?

Nahi — yeh batata hai ki feasible hai, rate nahi; rate activation energy par depend karta hai.

ΔG° aur K ke beech relationship?

Δ G^{\circ} = - R T ln K

Equilibrium par ΔG kya hota hai?

Exactly zero.

Non-standard conditions mein ΔG ki full form?

Δ G = Δ G^{\circ} + R T ln Q

Recall Feynman: 12-saal ke bacche ko explain karo

Nature ki do "wants" hain: usse cheezein low energy mein pasand hain (jaise ball downhill roll karna — woh $Δ H$ hai) aur usse cheezein messy/spread out honi pasand hain (woh $Δ S$ hai). Gibbs energy ek single scoreboard hai jo dono wants ko saath add karta hai, aur temperature decide karta hai ki "messiness" kitna count karti hai. Agar score $Δ G$ neeche jaata hai, toh change apne aap hota hai. Hot conditions mein messiness zyada count hoti hai; cold conditions mein energy zyada count hoti hai. Puri kahani yahi hai.

Connections

Second Law of Thermodynamics — parent principle $Δ S_{u ni v} > 0$ .
Enthalpy and ΔH — energy term provide karta hai.
Entropy and ΔS — disorder term provide karta hai.
Chemical Equilibrium and K — $Δ G^{\circ} = - R T ln K$ ke zariye.
Phase Transitions — melting/boiling jahan $Δ G = 0$ .
Electrochemistry ΔG = −nFE — cell potential se free energy.

1. ΔG ko Second Law se Derive Karna (scratch se)

2. Chaar sign combinations (80/20 core table)

3. Worked examples

4. Common mistakes (Steel-man + fix)

5. Flashcards

Connections

Concept Map