CHM-29

Clausius–Clapeyron

Vapour vs T.

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Physical chemistryClausius–Clapeyron

Governing equation

\\ln(P_2/P_1)=-\\Delta H/R(1/T_2-1/T_1)

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

where

P_1: P1 (kPa)
T_1: T1 (K)
T_2: T2 (K)
\Delta H: ΔH (kJ/mol)
P_2: P2 (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(P_2/P_1)=-\\Delta H/R(1/T_2-1/T_1)

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

$T_2 = 200$ $P_2 = 0.001$

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(P_2/P_1)=-\\Delta H/R(1/T_2-1/T_1)

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

$T_2 = 200$ $P_2 = 0.001$

Along the curve

④

Rate of change — amber

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

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

$T_2 = 201.9$ $P_2^{\prime} = 2.14\times 10^{-4}$

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-29 — Clausius–Clapeyron) is the form associated with Clausius–Clapeyron. Working symbols: $P_1$ , $T_1$ , $T_2$ , $\Delta H$ $\rightarrow$ $P_2$ . Vapour vs T.

Purpose

Purpose: compute

P_2

from

P_1

T_1

T_2

\Delta H

in Physical chemistry via

\\ln(P_2/P_1)=-\\Delta H/R(1/T_2-1/T_1)

Vapour 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 = 101.000\,\mathrm{kPa}

T_1 = 373.000\,\mathrm{K}

T_2 = 353.000\,\mathrm{K}

\Delta H = 40.000\,\mathrm{kJ/mol}

, the governing relation

\\ln(P_2/P_1)=-\\Delta H/R(1/T_2-1/T_1)

yields

P_2 = 48.63\,\mathrm{kPa}

. Vapour vs T. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

P1 P_1101 kPaT1 T_1373 KT2 T_2353 KΔH \Delta H40 kJ/mol

Outputs

P2 P_248.63 kPa

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Narration of this film

Vapour vs T.

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