CHE-03

Arrhenius rate constant

k = A exp(−Ea/RT) for an elementary step.

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KineticsArrhenius 1889

Governing equation

k=A\exp(-E_a/RT)

where

A: Pre-exponential (1/s)
E_a: Activation energy (kJ/mol)
T: Temperature (K)
k: Rate constant (1/s)

Lecture brief

Historical brief

From CSTR/PFR mole balances and Arrhenius rates to McCabe–Thiele stages and NTU exchangers, chemical engineering is conservation plus equilibrium. The lab is that design arithmetic. This sheet (CHE-03 — Arrhenius rate constant) is the form associated with Arrhenius 1889. Working symbols: $A$ , $E_a$ , $T$ $\rightarrow$ $k$ . Collision or transition-state theory both produce an exponential barrier Ea/RT multiplying a weakly T-dependent prefactor A.

Purpose

Purpose: compute

k

from

A

E_a

T

in Chemical engineering via

k=A\exp(-E_a/RT)

k = A exp(−Ea/RT) for an elementary step. Use it when a real chemical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

A = 1.000e+10\,\mathrm{1/s}

E_a = 75.000\,\mathrm{kJ/mol}

T = 500.000\,\mathrm{K}

, the governing relation

k=A\exp(-E_a/RT)

yields

k = 146.0565\,\mathrm{1/s}

. Gas-phase elementary reaction, Ea in kJ/mol. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Pre-exponential A10000000000 1/sActivation energy E_a75 kJ/molTemperature T500 K

Outputs

Rate constant k146.0565 1/s

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Narration of this film

Gas-phase elementary reaction, Ea in kJ/mol.

Collision or transition-state theory both produce an exponential barrier Ea/RT multiplying a weakly T-dependent prefactor A.

Reading speed

Watch on YouTube