Liquid state — vapour pressure, viscosity, surface tension

2.4.11 · Chemistry › States of Matter (Quantitative)

1. Vapour Pressure

KYA ho raha hai (Feynman-level): Ek closed vessel mein, fast surface molecules escape karte hain (evaporate hote hain). Jaise-jaise vapour build hota hai, kuch molecules vapas crash karte hain (condense hote hain). Jab rate of evaporation = rate of condensation ho jaata hai, vapour pressure change karna band kar deta hai — wahi steady value vapour pressure hai.

KYUN ye temperature par depend karta hai? Kitne fraction molecules mein escape ke liye kaafi energy hai, ye Boltzmann distribution se set hota hai. Jo molecules escape barrier beat kar sakte hain, unki sankhya $T$ ke saath exponentially badhti hai. Isko derive karte hain:

Liquid⇌vapour equilibrium mein $\Delta G=0$ hai, isliye vapour pressure $p$ Clausius–Clapeyron relation follow karta hai. Clapeyron se shuru karte hain: $\frac{dp}{dT}=\frac{\Delta H_{vap}}{T\Delta V}$

Ye step kyun? Phase equilibrium mein dono phases ki molar Gibbs energies coexistence line ke saath equal rehti hain, aur unke changes ko equate karne se ye slope milta hai.

Maano vapour ideal hai aur $V_{gas}\gg V_{liq}$, isliye $\Delta V\approx V_{gas}=RT/p$: $\frac{dp}{dT}=\frac{\Delta H_{vap}p}{R{T}^2}\Rightarrow \frac{d\ln p}{dT}=\frac{\Delta H_{vap}}{R{T}^2}$

Ye step kyun? $\Delta V$ substitute karne aur $p$ se divide karne par LHS $d\ln p/dT$ ban jaata hai — ek clean, integrable form.

Integrate karte hain ($\Delta H_{vap}$ constant maanke):

Trends: Zyada IMF ⇒ kam vapour pressure ⇒ zyada boiling point. Zyada volatile liquid = zyada vapour pressure.

2. Surface Tension

DO definitions ek hi kyun hain (derivation): Length $\ell$ ki wire ko surface ke against distance $dx$ slide karo, kaam karte hue $dW=Fdx$. Isse new area banta hai $dA=\ell dx$ (ya do faces wali film ke liye $2\ell dx$). Energy per area: $\gamma =\frac{dW}{dA}=\frac{Fdx}{\ell dx}=\frac{F}{\ell }$ Ye step kyun? Force-per-length aur energy-per-area literally same ratio hain — units confirm karte hain ($\text{N/m}={\text{J/m}}^2$).

Capillary rise (force balance se derivation): Raised column ka weight = circumference ke around surface tension ka upward pull. $\underset{\text{weight}}{\underbrace{\rho gh\pi r^2}}=\underset{\text{upward force}}{\underbrace{2\pi r\gamma \cos \theta }}$ $\boxed{h=\frac{2\gamma \cos \theta }{\rho gr}}$ Ye step kyun? Vertical surface-tension force wetted circumference ($2\pi r$) ke along act karta hai, contact angle $\theta$ se tilt hoke; ise liquid weight se balance karne par height milta hai.

Trends: ↑IMF ⇒ ↑surface tension. ↑Temperature ⇒ ↓surface tension (thermal motion inward pull ko weak karta hai).

3. Viscosity

HOW ye define hota hai (Newton's law of viscosity): Ek layer slide karne ki force uski area $A$ aur flow ke perpendicular velocity gradient $du/dz$ ke proportional hoti hai: $F=\eta A\frac{du}{dz}$ Ye step kyun? Experiment dikhata hai ki drag contact area aur layers ke beech speed change ki rate ke saath badhta hai; $\eta$ proportionality constant hai jo us resistance ko define karta hai.

Temperature dependence (Arrhenius-type — gases ke unlike!): $\eta =A{e}^{E_a/RT}$ Ye step kyun? Flow ke liye molecules ko energy barrier $E_a$ hop karna padta hai neighbours se slip karne ke liye. High $T$ par zyada molecules hop karne capable hote hain ⇒ viscosity kam hoti hai. + sign note karo: viscosity $T$ badhne par decrease karti hai (honey garam hone par better flow karta hai).

Trends: ↑IMF ⇒ ↑viscosity. ↑Molecular size / H-bonding (glycerol, glucose) ⇒ ↑viscosity. ↑Temperature ⇒ ↓viscosity.

Connections

• Intermolecular Forces — teeno properties ka common root cause
• Clausius-Clapeyron Equation — vapour pressure ka thermodynamic derivation
• Boiling Point and Phase Diagrams — boiling = vapour pressure meets external pressure
• Gibbs Free Energy — $\Delta G=0$ at phase equilibrium derivation ko underlie karta hai
• Boltzmann Distribution — kyun escaping/hopping fractions $T$ ke saath exponentially badhte hain
• Capillary Action and Contact Angle — surface tension ka application

Flashcards

Concept Map