CHM-06

Clausius–Clapeyron

ln(P2/P1) = −(ΔHvap/R)(1/T2 − 1/T1). Vapour pressure vs T.

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Phase changeClausius–Clapeyron

Governing equation

\ln\dfrac{P_2}{P_1}=-\dfrac{\Delta H_{\mathrm{vap}}}{R}\left(\dfrac1{T_2}-\dfrac1{T_1}\right)

$T_2 \in \left[200, 500\right]$

where

P_1: P at T1 (kPa)
T_1: T1 (K)
T_2: T2 (K)
\Delta H_{vap}: Enthalpy of vaporisation (kJ/mol)
P_2: P at T2 (kPa)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\ln\dfrac{P_2}{P_1}=-\dfrac{\Delta H_{\mathrm{vap}}}{R}\left(\dfrac1{T_2}-\dfrac1{T_1}\right)

$T_2 \in \left[200, 500\right]$

$T_2 = 200$ $P_2 = 0.001$

Along the curve

②

Domain of the variable — blue

T_2_{\min} = 200,\quad T_2_{\max} = 500

$T_2 \in \left[200, 500\right]$

$T_2 = 200$ $T_2 = 200$

Along the curve

③

Response curve — green

\ln\dfrac{P_2}{P_1}=-\dfrac{\Delta H_{\mathrm{vap}}}{R}\left(\dfrac1{T_2}-\dfrac1{T_1}\right)

$T_2 \in \left[200, 500\right]$

$T_2 = 200$ $P_2 = 0.001$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}P_2}{\mathrm{d}T_2}

$T_2 \in \left[200, 500\right]$

$T_2 = 201.9$ $P_2^{\prime} = 1.81\times 10^{-4}$

Along the curve

Lecture brief

Historical brief

Ideal-gas law, van ’t Hoff, Nernst, Michaelis–Menten and Clausius–Clapeyron are physical chemistry’s working equations of equilibrium and rate. The lab is pressure, potential and kinetics. This sheet (CHM-06 — Clausius–Clapeyron) is the form associated with Clausius–Clapeyron. Working symbols: $P_1$ , $T_1$ , $T_2$ , $\Delta H_{vap}$ $\rightarrow$ $P_2$ . Ideal vapour, neglected liquid volume, constant ΔHvap. The slope of ln P vs 1/T is −ΔHvap/R.

Purpose

Purpose: compute

P_2

from

P_1

T_1

T_2

\Delta H_{vap}

in Physical chemistry via

\ln\dfrac{P_2}{P_1}=-\dfrac{\Delta H_{\mathrm{vap}}}{R}\left(\dfrac1{T_2}-\dfrac1{T_1}\right)

ln(P2/P1) = −(ΔHvap/R)(1/T2 − 1/T1). Vapour pressure vs T. Use it when a real physical chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

P_1 = 101.300\,\mathrm{kPa}

T_1 = 373.000\,\mathrm{K}

T_2 = 353.000\,\mathrm{K}

\Delta H_{vap} = 40.700\,\mathrm{kJ/mol}

, the governing relation

\ln\dfrac{P_2}{P_1}=-\dfrac{\Delta H_{\mathrm{vap}}}{R}\left(\dfrac1{T_2}-\dfrac1{T_1}\right)

yields

P_2 = 48.161\,\mathrm{kPa}

. Two temperatures on the coexistence curve. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

P at T1 P_1101.3 kPaT1 T_1373 KT2 T_2353 KEnthalpy of vaporisation \Delta H_{vap}40.7 kJ/mol

Outputs

P at T2 P_248.161 kPa

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Narration of this film

Two temperatures on the coexistence curve.

Ideal vapour, neglected liquid volume, constant ΔHvap. The slope of ln P vs 1/T is −ΔHvap/R.

Reading speed

Watch on YouTube