Ostwald's dilution law (weak acid) - α = √(Ka - C)

2.6.12 · Chemistry › Equilibrium

Ostwald's Dilution Law Kya Hai?

KYUN yeh matter karta hai? Weak acids (acetic acid, HF, carbonic acid) fully ionize nahi hote. Unka behavior dono par depend karta hai — Ka (intrinsic strength) aur C (concentration). Ostwald's law hume pH, buffer capacity, aur titration curves predict karne deta hai.

First Principles Se Derivation

Ek weak monoprotic acid HA consider karo: $HA ⇌ H^{+} + A^{-}$

Step 1: Equilibrium table set up karo

	HA	H⁺	A⁻
Initial	C	0	0
Change	-Cα	+Cα	+Cα
Equilibrium	C(1-α)	Cα	Cα

KYUN Cα? Agar C moles/L se start karo, aur fraction α dissociate hota hai, toh Cα moles/L dissociate hote hain.

Step 2: Ka expression likho

Step 3: Weak acid approximation apply karo

Weak acids ke liye, α << 1, isliye (1 - α) ≈ 1. Yeh simplification tab valid hai jab α < 0.05 (5% ionization).

KYUN yeh kaam karta hai? Agar α = 0.01 hai, toh 1 - 0.01 = 0.99 ≈ 1 (error < 1%). Basically hum yeh keh rahe hain ki "itna kam dissociate hota hai ki denominator ~C hi rehta hai."

$K_{a} \approx C α^{2}$

Step 4: α ke liye solve karo

Figure — Ostwald's dilution law (weak acid) - α = √(Ka - C)

Step 5: [H⁺] aur pH derive karo

Kyunki [H⁺] = Cα: $[[H^{+}] = C α = C \cdot \frac{K _{a}}{C} = K_{a} \cdot C$

$pH = - lo g [H^{+}] = - \frac{1}{2} lo g (K_{a} \cdot C) = \frac{1}{2} (pK_{a} - lo g C)$

KYUN ½ factor? α mein jo square root hai woh log lete waqt ½ ban jaata hai.

Worked Examples

Common Mistakes aur Unhe Kaise Fix Karein

Active Recall Flashcards

#flashcards/chemistry

Degree of ionization α kya hai?

Weak electrolyte molecules ka woh fraction jo equilibrium par ions mein dissociate hota hai: α = moles dissociated / total moles initially.

Weak acid ke liye Ostwald's dilution law batao

α = √(Ka/C), jahan α degree of ionization hai, Ka acid dissociation constant hai, C initial concentration hai.

Dilution ke saath α qualitatively kaise change hota hai?

α dilution ke saath badhta hai kyunki α ∝ 1/√C. Kam concentration equilibrium ko ions ki taraf shift karta hai.

Weak acid ke liye dilution se [H⁺] kaise change hoti hai?

[H⁺] = √(KaC) dilution se ghatti hai kyunki yeh √C ke proportional hai, C ke nahi.

Approximation (1-α) ≈ 1 kab valid hai?

Jab α < 0.05 (5% ionization). Zyada α ke liye, full quadratic Ka = Cα²/(1-α) use karni padegi.

Ostwald's law se weak acid ke liye [H⁺] derive karo

[H⁺] = Cα = C√(Ka/C) = √(KaC). pH = ½(pKa - log C).

Ka constant kyun rehta hai jabki α dilution ke saath change hota hai?

Ka ek thermodynamic constant hai (sirf temperature par depend karta hai). α adjust hota hai taaki Ka = Cα²/(1-α) maintain rahe jab C change hota hai.

0.1 M acetic acid (Ka=1.8×10⁻⁵) ke liye α estimate karo

α = √(1.8×10⁻⁵/0.1) = √(1.8×10⁻⁴) ≈ 0.013 ya 1.3%.

Deep Understanding

Recall Feynman Explanation (ek 12-saal ke bachche ko)

Socho tumhare paas 100 "acid robots" ka ek jar hai. Yeh robots shy hain — sirf kuch hi dare karke H⁺ bots aur A⁻ bots mein split hote hain. Bheed wale jar mein (high concentration), sirf 1 ya 2 split hote hain kyunki jagah nahi hoti.

Ab robots ko zyada paani wale bade jar mein daalo (dilution). Achanak jagah ho gayi! Shayad 4 robots split hone ki himmat karenge. Percentage jo split hue (α) woh badh gayi. Lekin trick yeh hai: poore jar mein phir bhi total split robots kam hain, kyunki wohi 100 se shuru kiya tha lekin unhe zyada jagah mein failaa diya.

Ostwald's law woh math hai jo exactly predict karta hai kitne split honge: yeh √(himmat ÷ bheed) jaisa hai. Zyada bheed (C) → kam splits. Zyada himmat (Ka) → zyada splits. √ isliye aata hai kyunki jab ek robot split hota hai, toh woh do pieces banata hai, isliye math mein square hota hai.

Connections:

Le Chatelier's Principle: dilution equilibrium ko ions ki taraf shift karta hai (zyada particles)
Henderson-Hasselbalch Equation: half-neutralization par, pH = pKa (jab α → 0.5 region, buffer action shuru hoti hai)
Common Ion Effect: A⁻ add karne se equilibrium left shift ho jaata hai aur α suppress hota hai
Polyprotic Acids: successive Ka values ghatti hain, isliye Ostwald's law har step par apply hota hai
Conductivity of Solutions: conductance ∝ Cα, isliye weak acids ki conductance vs C non-linear hoti hai
Buffer Capacity: α par depend karta hai; α ≈ 0.5 par optimal hota hai (HA aur A⁻ equal amounts mein)
pH Calculation Methods: Ostwald approximate [H⁺] = √(KaC) shortcut deta hai

Summary: Ostwald's dilution law reveal karta hai ki weak acids ek balancing act hain Ka (intrinsic strength) aur C (concentration) ke beech. √(Ka/C) relationship quadratic equilibrium expression se nikalta hai jab ionization chhoti hoti hai. Dilution % ionization badhata hai lekin total [H⁺] ghata deta hai — yeh ek subtle distinction hai jo bahut se students ko confuse karta hai. Ise master karo, aur tum buffer behavior, titration curves, aur pura weak electrolyte landscape samajh jaoge.