CHM-16

BET isotherm snapshot

n/nm = c x / ((1−x)(1−x+c x)), x = p/p0. Multilayer adsorption.

Reading speed

SurfacesBET 1938

Governing equation

\dfrac{n}{n_m}=\dfrac{c x}{(1-x)(1-x+cx)}

where

c: BET C (—)
x: p/p0 (—)
n_m: Monolayer amount (mmol/g)
n: Adsorbed amount (mmol/g)

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-16 — BET isotherm snapshot) is the form associated with BET 1938. Working symbols: $c$ , $x$ , $n_m$ $\rightarrow$ $n$ . Brunauer–Emmett–Teller stacks Langmuir layers. Surface area from nm.

Purpose

Purpose: compute

n

from

c

x

n_m

in Physical chemistry via

\dfrac{n}{n_m}=\dfrac{c x}{(1-x)(1-x+cx)}

n/nm = c x / ((1−x)(1−x+c x)), x = p/p0. Multilayer adsorption. 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

c = 50.000\,\mathrm{—}

x = 0.200\,\mathrm{—}

n_m = 2.000\,\mathrm{mmol/g}

, the governing relation

\dfrac{n}{n_m}=\dfrac{c x}{(1-x)(1-x+cx)}

yields

n = 2.3148\,\mathrm{mmol/g}

. Type-II isotherm, x < 1. Pedagogical c and x. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

BET C c50 —p/p0 x0.2 —Monolayer amount n_m2 mmol/g

Outputs

Adsorbed amount n2.3148 mmol/g

Reading speed

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Narration of this film

Type-II isotherm, x < 1. Pedagogical c and x.

Brunauer–Emmett–Teller stacks Langmuir layers. Surface area from nm.

Reading speed

Watch on YouTube