CHM-08

Gibbs free energy G = H − TS

G = H − T S. The isothermal–isobaric potential.

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ThermochemistryGibbs 1876

Governing equation

G=H-TS

$T \in \left[50, 2000\right]$

where

H: Enthalpy (kJ)
S: Entropy (kJ/K)
T: Temperature (K)
G: Gibbs energy (kJ)

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

G=H-TS

$T \in \left[50, 2000\right]$

$T = 50$ $G = 36$

Along the curve

②

Domain of the variable — blue

T_{\min} = 50,\quad T_{\max} = 2000

$T \in \left[50, 2000\right]$

$T = 50$ $T = 50$

Along the curve

③

Response curve — green

G=H-TS

$T \in \left[50, 2000\right]$

$T = 50$ $G = 36$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}G}{\mathrm{d}T}

$T \in \left[50, 2000\right]$

$T = 62.26$ $G^{\prime} = -0.08$

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-08 — Gibbs free energy G = H − TS) is the form associated with Gibbs 1876. Working symbols: $H$ , $S$ , $T$ $\rightarrow$ $G$ . dG = V dP − S dT + μ dN. At constant T, P a process is spontaneous if ΔG < 0.

Purpose

Purpose: compute

G

from

H

S

T

in Physical chemistry via

G=H-TS

G = H − T S. The isothermal–isobaric potential. 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

H = 40.000\,\mathrm{kJ}

S = 0.080\,\mathrm{kJ/K}

T = 298.000\,\mathrm{K}

, the governing relation

G=H-TS

yields

G = 16.160\,\mathrm{kJ}

. Closed system, given H, S, T. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Enthalpy H40 kJEntropy S0.08 kJ/KTemperature T298 K

Outputs

Gibbs energy G16.160 kJ

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Narration of this film

Closed system, given H, S, T.

dG = V dP − S dT + μ dN. At constant T, P a process is spontaneous if ΔG < 0.

Reading speed

Watch on YouTube