1.1.16
Intuition Ek-line ka ideaJab tum ek solution ko dilute karte ho (solvent, usually water, add karte ho), to tum same amount of solute ko ek bade volume mein spread kar dete ho. Moles of solute kabhi nahi badlte — sirf volume badhti hai, isliye concentration kam hoti hai. Yahi ek conservation fact IS the formula.
Dilution woh process hai jisme solution ki concentration kam ki jaati hai aur zyada solvent add karke , jabki solute ki amount (moles) constant rehti hai .
Definition Molarity (pehle yeh samjho)Molarity M M = V n ⇒ n = M ⋅ V n V in litres .
Poori cheez ek conserved quantity: moles of solute pe tiki hai.
Step 1 — Dilution se pehle moles count karo.
Pehle, hamare paas concentration M 1 V 1 n before = M 1 V 1 Yeh step kyun? Kyunki n = M V
Step 2 — Dilution ke baad moles count karo.
Water add karne ke baad, concentration M 2 V 2 n after = M 2 V 2 Yeh step kyun? Same definition — molarity times volume gives moles, chahe numbers kuch bhi hon.
Step 3 — Conservation apply karo.
Solvent add karne se koi solute molecules add nahi hote. Tumne koi solute create ya destroy nahi kiya — tumne sirf usse zyada paani se ghera. Isliye:
n before = n after Yeh step kyun? Yahi physical core hai: paani mein zero solute hota hai, isliye solute count frozen rehta hai.
Step 4 — Substitute karo.
M 1 V 1 = M 2 V 2
Worked example Example 1 — Final concentration dhundhoTum 50 mL 2 M 250 mL
Step 1: Identify karo: M 1 = 2 V 1 = 50 V 2 = 250 M 2 Kyun? Humein 4 mein se 3 quantities pata hain → 4th ke liye solve karo.
Step 2: Rearrange karo: M 2 = V 2 M 1 V 1 = 250 2 × 50 Kyun? Dono sides ko V 2
Step 3: M 2 = 250 100 = 0.4 M Yeh sahi kyun lagta hai? Volume 5× badh gaya, isliye concentration 5× kam honi chahiye (2/5 = 0.4
Worked example Example 2 — Kitna paani add karna hai yeh dhundho100 mL 6 M 1.5 M
Step 1: M 1 V 1 = M 2 V 2 ⇒ V 2 = M 2 M 1 V 1 = 1.5 6 × 100 = 400 mL Kyun? Yeh total final volume hai.
Step 2: Water added = V 2 − V 1 = 400 − 100 = 300 mL Yeh step kyun? Formula final total volume deta hai, paani nahi. Tumhe starting volume subtract karni padegi.
Worked example Example 3 — Stock banana (concentrate up? Nahi — yeh phir bhi dilution logic hai)500 mL 0.10 M 12 M
Step 1: V 1 V 1 = M 1 M 2 V 2 = 12 0.10 × 500 Kyun? Unknown stock volume ke liye solve karo.
Step 2: V 1 = 12 50 ≈ 4.17 mL 500 mL Yeh sahi kyun lagta hai? Bahut strong acid ka chhota volume → weak acid ka bada volume. ✔
Common mistake "Mujhe final volume ke liye subtract karna chahiye."Yeh sahi kyun lagta hai: Dilution mein "add karna" feel hota hai, isliye log V 1 + V water V 1 Fix: M 1 V 1 = M 2 V 2 V 2 water added pooche, pehle formula se V 2 V 2 − V 1
Common mistake "Volumes additive hain, toh main concentrations bhi add kar sakta hoon."Yeh sahi kyun lagta hai: Chemistry mein bahut cheezein additive hoti hain.
Fix: Concentration ek ratio hai (moles/volume), koi amount nahi. Tum moles conserve karte ho (M 1 V 1
V 1 V 2 Yeh sahi kyun lagta hai: Molarity "officially" litres maangti hai, isliye students ek convert kar lete hain aur doosra bhool jaate hain.
Fix: Kyunki V dono sides pe aata hai aur cancel ho jaata hai, sirf dono mein same unit use karo. Half-convert mat karo.
Common mistake Ise tab use karna jab chemical reaction ho rahi ho.Yeh sahi kyun lagta hai: Yeh ek "mixing" formula lagta hai.
Fix: M 1 V 1 = M 2 V 2 dilute ho raha hai, consumed nahi. Agar acid base se react kare (neutralisation), toh moles use ho jaate hain — wahan stoichiometry / N 1 V 1 = N 2 V 2
Recall Feynman: 12-saal ke bacche ko samjhaoSocho tumhare paas ek glass bahut meetha juice hai — maano 10 sugar cubes waala. Ab tum use ek bade jug mein daalte ho aur paani se bhar dete ho. Tumne koi sugar nahi hataya — abhi bhi 10 cubes hain! Lekin kyunki zyada liquid hai, har ghooont thoda kam meetha lagta hai. "Meethaas per ghooont" kam ho gayi, lekin "total sugar" same raha. Formula M 1 V 1 = M 2 V 2 (meethaas₁)×(size₁) = total sugar = (meethaas₂)×(size₂) . Dono sides pe same sugar.
"Money In = Money Out." M M oney, V V olume. Tumne same cash ek bade wallet mein shift kiya — total money (M V 1 = pehle, 2 = baad mein (time mein upar count karo).
Dilution mein kaunsi single physical quantity conserved hoti hai?
M 1 V 1 = M 2 V 2 V 2 Yahan litres ki jagah mL kyun use kar sakte hain?
Dilution ke dauran kaunsi quantity conserved hoti hai? Moles of solute (solvent add karne se koi solute add nahi hota).
Dilution formula batao. M 1 V 1 = M 2 V 2
M 1 V 1 = M 2 V 2 n = M V = M 1 V 1 = M 2 V 2 M 1 V 1 = M 2 V 2
M 1 V 1 = M 2 V 2 V 2 Total FINAL volume, na ki add kiye gaye paani ki amount.
Add kiye gaye paani ka volume kaise dhundhte hain? Formula se V 2 V 2 − V 1
Litres ki jagah dono sides mein mL use karna theek kyun hai? Volume dono sides pe aata hai aur cancel ho jaata hai, isliye koi bhi consistent unit kaam karti hai.
50 mL of 2 M HCl ko 250 mL tak dilute kiya → final molarity? M 2 = ( 2 ) ( 50 ) /250 = 0.4
M 1 V 1 = M 2 V 2 Jab solute chemically consumed ho jaaye (jaise neutralisation) — tab stoichiometry use karo.
Agar volume 5× badhe, toh concentration kya karta hai? 5× kam hoti hai (inverse proportion, kyunki M V
Stock volume V 1 V 1 = M 2 V 2 / M 1
Molarity and concentration units — definition M = n / V The Mole concept — n Normality and N1V1 = N2V2 — equivalents ke liye same logic.Titration and neutralisation — jahan yeh formula blindly use NAHI karna chahiye (reaction hoti hai).ppm and parts-per notation — dilution logic kisi bhi amount/volume unit tak extend hoti hai.
Units must match, they cancel
