CHM-12

Kirchhoff ΔH(T)

ΔH(T2) = ΔH(T1) + ΔCp (T2 − T1). Enthalpy at a second temperature.

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ThermochemistryKirchhoff

Governing equation

\Delta H(T_2)=\Delta H(T_1)+\Delta C_p(T_2-T_1)

$T_2 \in \left[200, 1200\right]$

where

\Delta H_1: ΔH at T1 (kJ/mol)
\Delta C_p: ΔCp (J/(mol·K))
T_1: T1 (K)
T_2: T2 (K)
\Delta H_2: ΔH at T2 (kJ/mol)

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

\Delta H(T_2)=\Delta H(T_1)+\Delta C_p(T_2-T_1)

$T_2 \in \left[200, 1200\right]$

$T_2 = 200$ $\Delta H_2 = -88.08$

Along the curve

②

Domain of the variable — blue

T_2_{\min} = 200,\quad T_2_{\max} = 1200

$T_2 \in \left[200, 1200\right]$

$T_2 = 200$ $T_2 = 200$

Along the curve

③

Response curve — green

\Delta H(T_2)=\Delta H(T_1)+\Delta C_p(T_2-T_1)

$T_2 \in \left[200, 1200\right]$

$T_2 = 200$ $\Delta H_2 = -88.08$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta H_2}{\mathrm{d}T_2}

$T_2 \in \left[200, 1200\right]$

$T_2 = 206.3$ $\Delta H_2^{\prime} = -0.04$

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-12 — Kirchhoff ΔH(T)) is the form associated with Kirchhoff. Working symbols: $\Delta H_1$ , $\Delta C_p$ , $T_1$ , $T_2$ $\rightarrow$ $\Delta H_2$ . From dH = Cp dT applied to products minus reactants. Constant-ΔCp snapshot.

Purpose

Purpose: compute

\Delta H_2

from

\Delta H_1

\Delta C_p

T_1

T_2

in Physical chemistry via

\Delta H(T_2)=\Delta H(T_1)+\Delta C_p(T_2-T_1)

ΔH(T2) = ΔH(T1) + ΔCp (T2 − T1). Enthalpy at a second temperature. 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

\Delta H_1 = -92.000\,\mathrm{kJ/mol}

\Delta C_p = -40.000\,\mathrm{J/(mol·K)}

T_1 = 298.000\,\mathrm{K}

T_2 = 500.000\,\mathrm{K}

, the governing relation

\Delta H(T_2)=\Delta H(T_1)+\Delta C_p(T_2-T_1)

yields

\Delta H_2 = -100.080\,\mathrm{kJ/mol}

. Mean ΔCp between T1 and T2. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

ΔH at T1 \Delta H_1-92 kJ/molΔCp \Delta C_p-40 J/(mol·K)T1 T_1298 KT2 T_2500 K

Outputs

ΔH at T2 \Delta H_2-100.080 kJ/mol

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Narration of this film

Mean ΔCp between T1 and T2.

From dH = Cp dT applied to products minus reactants. Constant-ΔCp snapshot.

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