Dalton's law of partial pressures — Hinglish notes

2.4.3 · Chemistry › States of Matter (Quantitative)

KIYA hai partial pressure?

YEH sach kyun hai? (Derivation scratch se)

Ideal gas ki core assumption: molecules ka volume negligible hota hai aur unke beech interaction forces bhi negligible hoti hain. Isliye gas A ke molecules gas B ke molecules ko feel nahi karte — har gas aise behave karti hai jaise baaki gases wahan hain hi nahi.

Ideal gas law ko har component par alag-alag apply karo, shared volume $V$ aur shared $T$ par:

$p_{1} = \frac{n _{1} R T}{V}, p_{2} = \frac{n _{2} R T}{V}, \dots$

Ab inhe add karo:

$p_{1} + p_{2} + \dots = \frac{n _{1} R T}{V} + \frac{n _{2} R T}{V} + \dots = \frac{( n _{1} + n _{2} + \dots ) R T}{V} = \frac{n _{total} R T}{V}$

Mole fraction se partial pressure KAISE nikaalein

Mole fraction $x_{i} = \frac{n _{i}}{n _{total}}$ define karo.

Single-gas equation ko total equation se divide karo:

$\frac{p _{i}}{P _{total}} = \frac{n _{i} R T / V}{n _{total} R T / V} = \frac{n _{i}}{n _{total}} = x_{i}$

Figure — Dalton's law of partial pressures

Paani ke upar collect ki gayi gas

Jab gas ko paani ke displacement se collect kiya jaata hai, toh woh water vapour se saturated hokar aati hai. Measured pressure gas plus water vapour ka hota hai:

$P_{total} = p_{dry gas} + p_{water vapour}$

$p_{dry gas} = P_{atm} - p_{water}$

jahan $p_{water}$ = aqueous tension hai (us $T$ par paani ka saturated vapour pressure, ek fixed value jo tum table se dekhte ho).

Worked Examples

Common mistake Common mistakes ko steel-man karke dekho

Mistake A: "Pressures ko us volume se add karo jo mixing se pehle har gas ne occupy kiya tha." Kyun sahi lagta hai: volumes bhi additive lagte hain. Fix: partial pressure final shared volume $V$ par define hota hai, mixing se pehle ke volume par nahi. Agar gases alag containers se aayi hain, toh pehle nayi $V$ se $p_{i} = n_{i} R T / V$ recalculate karo.

Mistake B: "Mole fraction ki jagah galat quantity (mass fraction) use karna." Kyun sahi lagta hai: saare fractions ek jaese lagte hain. Fix: Dalton mole fraction use karta hai. Pehle mass ko moles mein convert karo ( $n = m / M$ ).

Mistake C: "Aqueous tension subtract karna bhool jaana." Kyun sahi lagta hai: barometer total pressure read karta hai, lagta hai wahi gas ka pressure hai. Fix: paani ke upar measured pressure mein water vapour bhi shamil hota hai; dry gas paane ke liye aqueous tension subtract karo.

Mistake D: "Reacting gases par Dalton's law apply karna." Kyun sahi lagta hai: woh phir bhi gases hain. Fix: agar gases react karti hain, toh $n_{i}$ change hota hai; yeh law sirf non-reacting mixtures par equilibrium composition pe laagu hota hai.

Recall Feynman: ek 12-saal ke baache ko samjhao

Ek box mein laal bouncy balls aur neele bouncy balls rakh do. Har colour walls se takrake apni alag "push" banata hai. Laal balls ko pata hi nahi ki neele balls exist karte hain aur neele balls ko laal balls ki khabar nahi. Isliye wall par total push bas laal ki push plus neele ki push hai. Agar laal balls saare balls ka ek-paanchwa hissaa hain, toh woh total push ka ek-paanchwa hi cause karte hain. Bas itna hi!

Active-Recall Flashcards

#flashcards/chemistry

Kisi mixture mein gas ka partial pressure kya hota hai?

Woh pressure jo woh gas akele exert karti agar same volume mein same temperature par hoti.

Dalton's law of partial pressures state karo.

P_{total} = \sum_{i} p_{i}

non-reacting ideal gases ke liye fixed

V, T

par.

Partial pressure aur mole fraction ko jodne wala formula.

p_{i} = x_{i} P_{total}

, jahan

x_{i} = n_{i} / n_{total}

Partial pressures add kyun hote hain?

Ideal-gas molecules interact nahi karte, isliye har gas ke collisions (aur pressure) independent aur additive hote hain.

Paani ke upar collect ki gayi gas ke liye dry gas pressure kaise nikaalte hain?

p_{dry} = P_{atm} - p_{water}

(aqueous tension subtract karo).

Aqueous tension kya hoti hai?

Di gayi temperature par paani ka saturated vapour pressure.

Kya Dalton's law reacting gases par laagu hoti hai?

Nahi — sirf non-reacting mixtures par (moles fixed rehne chahiye).

Saare mole fractions ka sum kitna hota hai?

1, jo guarantee karta hai ki

\sum p_{i} = P_{total}

Connections

Ideal Gas Equation — Dalton's law seedha $P V = n R T$ se derive hoti hai.
Mole Fraction and Concentration Terms — $x_{i}$ provide karta hai.
Kinetic Theory of Gases — explain karta hai KI pressures additive kyun hain (independent collisions).
Real Gases and van der Waals Equation — jahan Dalton's law toot ti hai intermolecular forces ki wajah se.
Vapour Pressure — aqueous tension ka background.