Batteries — primary (dry cell), secondary (lead-acid, Li-ion)

2.7.8 · Chemistry › Redox & Electrochemistry (Intro)

Core Concepts

[!definition] Primary vs Secondary Batteries

==Primary batteries== single-use hote hain (non-rechargeable). Jab chemical reactants khatam ho jaate hain, redox reaction ruk jaati hai aur battery dead ho jaati hai. Ye reactions essentially irreversible hoti hain normal conditions mein.
==Secondary batteries== rechargeable hote hain. Redox reactions reversible hoti hain—external voltage lagane se reaction ulti direction mein chalta hai, reactants regenerate ho jaate hain. Inhe hundreds se thousands of times cycle kar sakte ho.

Yeh distinction kyun matter karta hai: Primary batteries ki chemistry simpler hoti hai (sasti, zyada stable shelf life), lekin waste create karta hai. Secondary batteries mein zyada sophisticated electrode materials chahiye jo repeated redox cycling ke through apni structure maintain karein.

1. Primary Battery: Dry Cell (Leclanché Cell)

Structure & Components

Figure — Batteries — primary (dry cell), secondary (lead-acid, Li-ion)

Ek dry cell ek paste electrolyte use karta hai (liquid nahi), jisse yeh leak-resistant aur portable ban jaata hai.

Components:

Anode (−): Zinc metal can (outer casing) — oxidize hota hai
Cathode (+): Graphite rod jo MnO₂ (manganese dioxide) se ghira hota hai, carbon powder ke saath mila hua
Electrolyte: NH₄Cl (ammonium chloride) aur ZnCl₂ ka paste, kabhi kabhi starch thickener ke taur pe
Separator: Porous paper electrolyte mein soaked, electrodes ke beech direct contact rokti hai

Chemistry — First Principles se Derive Karte Hain

Anode pe (oxidation): Zinc metal electrons khota hai: $Zn (s) \to Zn^{2 +} (a q) + 2 e^{-} E_{ox}^{\circ} = + 0.76 V$

Zn oxidize kyun karna chahta hai? Zinc activity series mein upar hota hai—yeh stable Zn²⁺ ions banane ke liye aasaani se electrons khota hai. Zn²⁺/Zn ka standard reduction potential −0.76 V hai, isliye oxidation +0.76 V deta hai.

Cathode pe (reduction): Yahan interesting ho jaata hai. Cathode reaction complex hai aur multiple steps involve karta hai:

Primary reduction: MnO₂ external circuit se electrons lekar reduce hota hai: $2 MnO_{2} (s) + 2 H^{+} (a q) + 2 e^{-} \to Mn_{2} O_{3} (s) + H_{2} O (l)$
H⁺ kyun? Ammonium chloride electrolyte hydrolysis ke through protons provide karta hai: $NH_{4}^{+} (a q) ⇌ NH_{3} (a q) + H^{+} (a q)$
Secondary reaction: Anode se zinc ions ammonia aur chloride ke saath react karte hain: $Zn^{2 +} (a q) + 2 NH_{3} (a q) + 2 Cl^{-} (a q) \to [Zn (NH_{3})_{2}] Cl_{2} (s)$

Isse ek complex salt banta hai jo precipitate ho jaata hai, Zn²⁺ buildup rokta hai (jo Le Chatelier's principle ke via reaction slow kar deta).

Overall approximate reaction: $Zn (s) + 2 MnO_{2} (s) + 2 NH_{4}^{+} (a q) \to Zn^{2 +} (a q) + Mn_{2} O_{3} (s) + 2 NH_{3} (a q) + H_{2} O (l)$

Cell voltage: Shuru mein ~1.5 V, reactants khatam hone pe ~0.9 V tak gir jaata hai.

[!example] Worked Example: Flashlight mein Electron Flow

Setup: Ek flashlight do 1.5 V dry cells series mein use karta hai (total 3.0 V) ek 0.3 A bulb jalane ke liye.

Step 1 — Electrons per second calculate karo: Current I = 0.3 A = 0.3 coulombs/second. Ek electron $e = 1.6 \times 1 0^{- 19}$ C carry karta hai. $Number of electrons/s = \frac{0.3}{1.6 \times 1 0 ^{- 19}} = 1.875 \times 1 0^{18} e^{-} / s$

Yeh step kyun? Current defined hai charge per time ke roop mein. Hum fundamental charge carriers mein convert kar rahe hain.

Step 2 — Ek ghante mein kitna Zn consume hota hai? Har Zn atom 2 electrons release karta hai: $Zn \to Zn^{2 +} + 2 e^{-}$ $Zn atoms consumed/s = \frac{1.875 \times 1 0 ^{18}}{2} = 9.375 \times 1 0^{17} atoms/s$

Moles per second: $\frac{9.375 \times 1 0 ^{17}}{6.022 \times 1 0 ^{23}} = 1.557 \times 1 0^{- 6} mol/s$

Per hour: $1.557 \times 1 0^{- 6} \times 3600 = 5.6 \times 1 0^{- 3} mol = 0.0056 mol$

Zn ki mass (M = 65.4 g/mol): $0.0056 \times 65.4 = 0.366 g$

Yeh kyun matter karta hai: Ek typical AA dry cell mein ~4 g Zn hota hai, toh theoretically flashlight ~11 ghante chal sakti hai, lekin voltage drop aur incomplete reaction ki wajah se practice mein ~8 ghante milte hain.

2. Secondary Battery: Lead-Acid

Lead-acid battery (1859 mein invented, aaj bhi cars mein!) lead compounds ke beech reversible redox use karta hai.

Structure

Anode (−): Spongy lead (Pb) plates
Cathode (+): Lead dioxide (PbO₂) plates
Electrolyte: Concentrated sulfuric acid (H₂SO₄), ~4.5 M

Chemistry — Discharge (power provide karna)

Anode pe (oxidation): $Pb (s) + SO_{4}^{2 -} (a q) \to PbSO_{4} (s) + 2 e^{-} E^{\circ} = + 0.36 V$

Lead PbSO₄ kyun banata hai? Electrolyte mein sulfate ions abundant hain. Lead(II) sulfate sparingly soluble hai—yeh electrode surface pe precipitate ho jaata hai, electrical contact maintain karta hai.

Cathode pe (reduction): $PbO_{2} (s) + 4 H^{+} (a q) + SO_{4}^{2 -} (a q) + 2 e^{-} \to PbSO_{4} (s) + 2 H_{2} O (l) E^{\circ} = + 1.69 V$

Yeh direction kyun? PbO₂ mein lead +4 oxidation state mein hai—yeh ek strong oxidizer hai (electrons chahta hai). Acidic solution mein, yeh electrons aur protons grab karta hai, Pb²⁺ tak reduce hota hai jo PbSO₄ ke roop mein precipitate ho jaata hai.

Overall discharge reaction: $Pb (s) + PbO_{2} (s) + 2 H_{2} SO_{4} (a q) \to 2 PbSO_{4} (s) + 2 H_{2} O (l)$

Discharge ke dauran key observations:

Dono electrodes PbSO₄ banate hain (white coating)
Sulfuric acid consume hoti hai — concentration ghatti hai
Paani banta hai — electrolyte zyada dilute ho jaata hai
EMF: $E_{cell} = 1.69 - 0.36 = 2.0 V$ per cell (car batteries mein 6 cells hote hain = 12 V)

Chemistry — Charging (reaction reverse karna)

Har cell pe >2.0 V ka external voltage lagao. Har reaction ulta chalta hai:

Charging ke dauran cathode pe (ab oxidation): $PbSO_{4} (s) + 2 H_{2} O (l) \to PbO_{2} (s) + 4 H^{+} (a q) + SO_{4}^{2 -} (a q) + 2 e^{-}$

Charging ke dauran anode pe (ab reduction): $PbSO_{4} (s) + 2 e^{-} \to Pb (s) + SO_{4}^{2 -} (a q)$

Result:

PbSO₄ wapas Pb aur PbO₂ mein convert ho jaata hai
H₂SO₄ concentration badhti hai
Paani consume hota hai

[!example] Worked Example: Car Start Karna

Problem: Ek car starter motor 3 seconds ke liye 200 A draw karta hai. Cathode pe kitna PbO₂ consume hota hai?

Step 1 — Total charge calculate karo: $Q = I \cdot t = 200 A \times 3 s = 600 C$

Yeh step kyun? Charge = current × time by definition. Ek mole electrons = 96,485 C (Faraday's constant).

Step 2 — Electrons ke moles: $n_{e^{-}} = \frac{600}{96 , 485} = 0.00622 mol$

Step 3 — Cathode reaction ki stoichiometry: $PbO_{2} + 4 H^{+} + SO_{4}^{2 -} + 2 e^{-} \to PbSO_{4} + 2 H_{2} O$ Har PbO₂ 2 electrons consume karta hai, isliye: $n_{PbO_{2}} = \frac{0.00622}{2} = 0.00311 mol$

2 se divide kyun? Balanced equation 2 e⁻ per PbO₂ dikhata hai. Stoichiometry ko respect karna padega.

Step 4 — PbO₂ ki mass: PbO₂ ki molar mass = 207.2 + 2(16) = 239.2 g/mol $m = 0.00311 \times 239.2 = 0.744 g$

Interpretation: Ek car battery mein har cell mein ~1kg PbO₂ hota hai, toh yeh 3-second draw ek cell ki material ka <0.1% consume karta hai—easily sustainable.

3. Secondary Battery: Lithium-Ion

Lithium-ion battery (1991, portable electronics mein revolution laya) intercalation chemistry use karta hai—Li⁺ ions layered materials ke beech shuttle karte hain crystal structure ko destroy kiye bina.

Structure (LiCoO₂ cathode variant)

Anode (−): Graphite layers jo Li atoms ko planes ke beech host kar sakti hain
Cathode (+): Lithium cobalt oxide (LiCoO₂) — layered oxide
Electrolyte: Organic solvent (e.g., ethylene carbonate) LiPF₆ salt ke saath — Li⁺ conduct karta hai, electrons nahi
Separator: Porous polymer film (short circuit rokti hai lekin ions pass karne deti hai)

Chemistry — Discharge

Anode pe (oxidation): Lithium atoms graphite se deintercalate (nikalte) hain: $Li_{x} C_{6} \to x Li^{+} + x e^{-} + C_{6}$ Typically $x \approx 1$ , fully charged hone par $LiC_{6}$ banta hai.

Graphite kyun? Iske layered structure mein van der Waals gaps hain jo Li atoms ko reversibly accommodate karte hain. Carbon planes electrons conduct karte hain jabki Li⁺ unke beech baithta hai.

Cathode pe (reduction): Li⁺ ions LiCoO₂ lattice mein intercalate (insert) hote hain: $Li_{1 - x} CoO_{2} + x Li^{+} + x e^{-} \to LiCoO_{2}$

CoO₂ kyun? Cobalt Co³⁺ aur Co⁴⁺ oxidation states ke beech cycle karta hai, Li⁺ insert hone pe electrons accept karta hai. Layered structure Co-O planes ko cycling ke dauran intact rakhti hai.

Overall discharge: $LiC_{6} + Li_{1 - x} CoO_{2} \to C_{6} + LiCoO_{2}$

Voltage: ~3.7 V per cell (lead-acid ke 2V se kaafi zyada energy density!)

High voltage kyun? Lithium (bahut electropositive, electrons khona chahta hai) aur cobalt(IV) oxide (strong oxidizer, electrons chahta hai) ke beech chemical potential mein bada farq hai.

Charging

Har step reverse karo:

Li⁺ ions LiCoO₂ cathode se nikalte hain (ab oxidation): $LiCoO_{2} \to Li_{1 - x} CoO_{2} + x Li^{+} + x e^{-}$
Li⁺ ions graphite anode mein insert hote hain (ab reduction): $C_{6} + x Li^{+} + x e^{-} \to Li_{x} C_{6}$

[!example] Worked Example: Phone Battery Capacity

Specs: Ek phone battery 3.7 V pe 3000 mAh rated hai.

Step 1 — Stored energy calculate karo: $E = Q \times V = (3000 mAh) \times (3.7 V)$ mAh ko coulombs mein convert karo: $3000 mAh = 3 Ah = 3 \times 3600, C = 10, 800 C$ $E = 10, 800 C \times 3.7 V = 39, 960 J \approx 11.1 Wh$

Yeh step kyun? Energy = charge × voltage. Hum units convert karte hain watt-hours mein paane ke liye, jo battery energy ka standard hai.

Step 2 — Ek full cycle mein kitna lithium move hota hai? Total charge: 10,800 C Electrons ke moles: $n = \frac{10 , 800}{96 , 485} = 0.112 mol$

Har Li atom 1 electron provide karta hai, isliye 0.112 mol Li cycle karta hai. Mass: $0.112 mol \times 6.94 g/mol = 0.777 g$

Yeh kyun matters: 1 gram se bhi kam lithium cycling se itni energy store hoti hai ki tumhara phone poora din chal sake. Isko compare karo ~50 g Pb se jo car battery mein same energy ke liye consume hota hai—yahi hai high voltage + lightweight materials ki power.

Common Misconceptions

Common mistake "Batteries electrons store karti hain"

Yeh sahi kyun lagta hai: Electricity = electrons, toh batteries electron containers honi chahiye, hai na? Fix: Batteries chemical potential energy store karti hain, electrons nahi. Ek battery mein electrons ki sankhya constant rehti hai (atoms vanish nahi hote!). Jo change hota hai woh hai unka arrangement—high-energy (reduced) compounds anode pe, low-energy (oxidized) compounds cathode pe. Jab tum battery "use" karte ho, tum electrons ko high se low potential energy tak girne de rahe ho, jaise paani turbine se neeche girta hai.

Mistake ko steel-man karo: Confusion isliye hoti hai kyunki hum negative terminal se electrons nikaalte hain. Lekin woh electrons turant anode pe oxidation reaction ke electrons se replace ho jaate hain. Yeh ek flow hai, reservoir nahi.

Practice Problems

Recall Feynman Check: 12-saal ke bacche ko explain karo

"Okay, socho tumhare paas do alag sandboxes hain. Ek sandbox mein sand ka bada pile hai (bahut saare electrons jo jaana chahte hain—woh hai dry cell mein zinc). Doosre sandbox mein ek gaddha hai (electrons chahta hai—woh hai manganese dioxide). Tum unke beech ek slide banate ho, lekin trick yeh hai: slide tumhare toy car se guzarti hai. Jab tum sandboxes connect karte ho, sand grains pile se gaddhe ki taraf slide karte hain, aur raste mein unhe tumhari toy car ke wheels push karne padte hain. Woh 'wheels push karna' woh electrical energy hai jo tumhari flashlight run kar rahi hai!

Ek rechargeable battery ek aisi sandbox ki tarah hai jahan tum ek vacuum (charger) use karke sand wapas pile par chusa sakte ho. Kuch sandboxes yeh karne dete hain (secondary), dusre sand ko mud ya rocks mein badal dete hain, aur tum aasaani se undo nahi kar sakte (primary)."

Connections

2.7.01-Oxidation-numbers-and-redox-definition — Batteries practical galvanic cells hain; oxidation states changing identify karo
2.7.04-Galvanic-cells-and-cell-notation — Battery structure galvanic cell design follow karta hai (anode/cathode/electrolyte/separator)
2.7.05-Standard-electrode-potentials — EMF half-cell potentials se calculate hota hai; feasibility predict karta hai
2.7.06-Nernst-equation-and-concentration-effects — Battery voltage drop hoti hai jaise reactants deplete hote hain (Q badhta hai)
2.7.09-Corosion-and-prevention — Zinc casing corrode karta hai (intentional oxidation), unwanted corrosion se analogous
3.1.12-Gibs-free-energy-and-spontaneity — $Δ G = - n F E_{cell}$ battery voltage ko thermodynamic spontaneity se connect karta hai

#flashcards/chemistry

Primary battery kise define karta hai? :: Ek non-rechargeable battery jahan redox reaction essentially irreversible hoti hai normal conditions mein. Jab reactants khatam ho jaate hain, battery dead ho jaati hai (e.g., dry cell).

Secondary battery kise define karta hai?

Ek rechargeable battery jahan redox reactions reversible hoti hain. External voltage lagane se reactants regenerate hote hain, repeated charge/discharge cycles allow karte hain (e.g., lead-acid, lithium-ion).

Dry cell mein anode pe kya oxidize hota hai?

Zinc metal (Zn) Zn²⁺ mein oxidize hota hai:

Zn (s) \to Zn^{2 +} + 2 e^{-}

. Zinc can khud anode ka kaam karta hai.

Dry cell mein cathode material kya hai?

Manganese dioxide (MnO₂) carbon powder ke saath mixed, ek graphite rod ke around. MnO₂ discharge ke dauran reduce hota hai.

Leclanché dry cell mein electrolyte kya hai?

Ammonium chloride (NH₄Cl) aur zinc chloride (ZnCl₂) ka paste, aksar starch se thicken kiya hua. Paste ise "dry" (leak-resistant) banata hai.

Dry cell ~~1.5 V kyun produce karta hai? ::: Zn oxidation (~~+0.76 V) aur acidic medium mein MnO₂ reduction (~+1.2 V theoretical) ke beech potential difference ~2 V deta hai, lekin real overpotential losses 1.5 V practice mein dete hain.

Lead-acid battery ke liye overall discharge reaction likho :: $Pb (s) + PbO_{2} (s) + 2 H_{2} SO_{4} (a q) \to 2 PbSO_{4} (s) + 2 H_{2} O (l)$ . Dono electrodes lead sulfate banate hain.

Lead-acid discharge ke dauran sulfuric acid ka kya hota hai?

H₂SO₄ consume hoti hai (concentration ghatti hai). Paani banta hai, electrolyte dilute hota jaata hai. Density ~1.25 se ~1.15 g/cm³ tak giriti hai.

Discharge hoti lead-acid battery ke dono electrodes pe kya banta hai? :: Lead sulfate (PbSO₄), ek white precipitate. Yeh unusual hai—zyaadatar batteries har electrode pe alag compounds banati hain.

Ek lead-acid cell ka EMF kya hota hai?

~2.0 V per cell. Car batteries 6 cells series mein use karti hain 12 V produce karne ke liye.

Li-ion battery anode mein lithium kaise store hota hai?

Lithium atoms graphite layers ke beech intercalate (insert) hote hain LiC₆ banane ke liye. Layered structure mein van der Waals gaps hain jo Li reversibly accommodate karte hain.

Common lithium-ion batteries mein cathode material kya hai?

Lithium cobalt oxide (LiCoO₂) — ek layered oxide jahan Li⁺ ions intercalate/deintercalate karte hain jabki cobalt Co³⁺ aur Co⁴⁺ ke beech cycle karta hai.

Intercalation kya hai?

Ions (jaise Li⁺) ka ek layered host structure mein reversible insertion, crystal lattice destroy kiye bina. Host material kaafi cycles ke through apni integrity maintain karta hai.

Lithium-ion batteries mein lead-acid se zyada energy density kyun hai? :: Higher voltage per cell (~3.7 V vs. 2.0 V) aur hafka lithium (M = 6.94 g/mol) bhaari lead (M = 207.2 g/mol) ke muqable. Zyada energy per unit mass.

Capacity unit mAh kya hai, aur charge se iska kya relation hai?

Milliampere-hour: 1 mA current se 1 ghante mein deliver kiya gaya charge.

1 mAh = 3.6 C

. Ek 3000 mAh battery

3000 \times 3.6 = 10, 800 C

store karti hai.

Primary (dry cell) battery recharge kyun nahi kar sakte?

Reactions irreversible side products banati hain (complex salts, structural damage). Reverse current force karne se paani ka electrolysis hota hai (H₂ gas), pressure buildup, leakage, ya explosion hota hai.

Electrolyte ki kaun si property lead-acid state of charge indicate karti hai?

H₂SO₄ solution ki density (specific gravity). Charged: ~1.25 g/cm³ (concentrated acid). Discharged: ~1.15 g/cm³ (paani banne se diluted).

Lead-acid charging ke dauran positive plate pe kya hota hai?

PbSO₄ wapas PbO₂ mein oxidize ho jaata hai:

PbSO_{4} + 2 H_{2} O \to PbO_{2} + 4 H^{+} + SO_{4}^{2 -} + 2 e^{-}

. Sulfuric acid regenerate hoti hai.

Li-ion batteries mein anode ke roop mein graphite kyun use hota hai?

Iska layered structure van der Waals gaps ke saath reversible Li intercalation allow karta hai structural collapse ke bina. Graphite electrons bhi acche se conduct karta hai.

Lithium-ion battery mein electrolyte kya hota hai?

Ek organic solvent (e.g., ethylene carbonate, dimethyl carbonate) jisme lithium salt (LiPF₆) hota hai. Yeh Li⁺ ions conduct karta hai lekin electrons nahi (electronically insulating).