Concentration cells

2.7.7 · Chemistry › Redox & Electrochemistry (Intro)

Concentration Cell Kya Hota Hai?

YEH KAAM KYUN KARTA HAI?

• Ek typical galvanic cell mein (jaise Zn|Cu), driving force $E°$ values ka farq hoti hai. Zinc copper se zyada electrons dena chahta hai.
• Concentration cell mein, $E{°}_{\text{anode}}=E{°}_{\text{cathode}}$ hota hai kyunki same metal hai. Toh standard cell potential $E{°}_{\text{cell}}=0$ V hota hai.
• Lekin real cells non-standard conditions mein kaam karti hain. Nernst equation batata hai ki potential concentrations par depend karta hai.
• Nernst equation ek potential difference create karta hai jab concentrations alag hoti hain, chahe electrodes identical hi kyun na hon.

YEH KAAM KAISE KARTA HAI?

1. Do half-cells setup karo same metal electrode ke saath (maano, copper).
2. Ek beaker mein high $[{\text{Cu}}^{2+}]$ hai (concentrated), doosre mein low $[{\text{Cu}}^{2+}]$ hai (dilute).
3. Unhe salt bridge aur wire se connect karo.
4. Dilute side par (anode): $\text{Cu}(s)\to {\text{Cu}}^{2+}(aq)+2e^{-}$ (oxidation se dilute concentration badhti hai)
5. Concentrated side par (cathode): ${\text{Cu}}^{2+}(aq)+2e^{-}\to \text{Cu}(s)$ (reduction se concentrated solution kam hoti hai)
6. Net result: Electrons dilute → concentrated ki taraf flow karte hain, aur concentrations equal ho jaati hain.

Cell Potential Derive Karna

Shuru karo Nernst equation se ek half-cell ke liye: $E=E°-\frac{0.0592}{n}\log \frac{[\text{reduced form}]}{[\text{oxidized form}]}$

${\text{Cu}}^{2+}$ solution mein ek copper electrode ke liye (${\text{Cu}}^{2+}+2e^{-}\to \text{Cu}$): $E=E{°}_{{\text{Cu}}^{2+}/\text{Cu}}-\frac{0.0592}{2}\log \frac{1}{[{\text{Cu}}^{2+}]}$

(Pure solids ke liye convention se $[\text{Cu}(s)]=1$ hota hai.)

Ab concentration cell setup karo:

• Cathode (reduction, concentrated): $[{\text{Cu}}^{2+}]=C_{\text{high}}$
• Anode (oxidation, dilute): $[{\text{Cu}}^{2+}]=C_{\text{low}}$

Concentrated side cathode KYUN hai? Kyunki Nernst equation zyada positive potential deta hai jab concentration zyada hoti hai: $E_{\text{cathode}}=E°-\frac{0.0592}{2}\log \frac{1}{C_{\text{high}}}$ $E_{\text{anode}}=E°-\frac{0.0592}{2}\log \frac{1}{C_{\text{low}}}$

Cell potential: $E_{\text{cell}}=E_{\text{cathode}}-E_{\text{anode}}$

Step-by-step derivation:

$E_{\text{cell}}=\left(E°-\frac{0.0592}{2}\log \frac{1}{C_{\text{high}}}\right)-\left(E°-\frac{0.0592}{2}\log \frac{1}{C_{\text{low}}}\right)$

$E°$ terms cancel ho jaate hain:

$E_{\text{cell}}=-\frac{0.0592}{2}\log \frac{1}{C_{\text{high}}}+\frac{0.0592}{2}\log \frac{1}{C_{\text{low}}}$

$E_{\text{cell}}=\frac{0.0592}{2}\left(\log \frac{1}{C_{\text{low}}}-\log \frac{1}{C_{\text{high}}}\right)$

$\log a-\log b=\log (a/b)$ use karke:

$E_{\text{cell}}=\frac{0.0592}{2}\log \frac{C_{\text{high}}}{C_{\text{low}}}$

YEH STEP KYUN? Kyunki $\log (1/C_{\text{low}})-\log (1/C_{\text{high}})=\log (C_{\text{high}}/C_{\text{low}})$ log properties se.

Worked Examples

Common Mistakes

Memory Aids

Connections

• Nernst equation — mathematical foundation; concentration cells ek special case hain jahan $E{°}_{\text{cell}}=0$
• Galvanic cells — concentration cells ek type ke galvanic cells hain jisme unusual symmetry hoti hai
• Le Chatelier's principle — concentration changes equilibrium shift karti hain; cell balance restore karne ke liye operate karta hai
• Entropy and free energy — concentration cells entropy increase (mixing) se drive hoti hain, enthalpy se nahi
• Membrane potentials — biological concentration cells (cell membranes par ion gradients nerve signals generate karte hain)
• pH meters — H⁺ gradients ke saath concentration cell principle use karte hain
• Electrochemical series — samajhne mein help karta hai ki kuch metals doosron se better kyun kaam karte hain, haalaanki concentration cells same metal use karte hain

Practice Problems

#flashcards/chemistry

Concentration cell kya hota hai? :: Ek electrochemical cell jisme dono electrodes ek hi material ke bane hote hain, lekin same ion ki alag-alag concentrations wale solutions mein daale jaate hain. Potential purely concentration ke farq se aata hai.

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