World Library  
Flag as Inappropriate
Email this Article

Arrhenius plot

Article Id: WHEBN0012674074
Reproduction Date:

Title: Arrhenius plot  
Author: World Heritage Encyclopedia
Language: English
Subject: Chemical kinetics, Q10 (temperature coefficient), Enthalpy–entropy compensation, Surface diffusion
Collection: Chemical Kinetics, Plots (Graphics)
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Arrhenius plot

An Arrhenius plot displays the logarithm of kinetic constants (\ln(k), ordinate axis) plotted against inverse temperature (1/T, abscissa). Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the activation energy and the pre-exponential factor can both be determined.
Example:
Nitrogen dioxide decay
2 NO2 → 2 NO + O2
Conventional plot:
k against T
Arrhenius plot: ln(k) against 1/T.

The Arrhenius equation can be given in the form:

k = A e^{-E_a/RT}

or alternatively

k = A e^{-E_a/k_B T}

The only difference is the energy units: the former form uses energy/mole, which is common in chemistry, while the latter form uses energy directly, which is common in physics. The different units are accounted for in using either the gas constant R or the Boltzmann constant k_B.

The former form can be written equivalently as:

\ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right)
Where:
k = Rate constant
A = Pre-exponential factor
E_a = Activation energy
R = Gas constant
T = Absolute temperature, K

When plotted in the manner described above, the value of the true y-intercept (at x = 1/T = 0) will correspond to \ln(A), and the slope of the line will be equal to -E_a/R. The values of y-intercept and slope can be determined from the experimental points using simple linear regression with a spreadsheet.

The pre-exponential factor, A, is an empirical constant of proportionality which has been estimated by various theories which take into account factors such as the frequency of collision between reacting particles, their relative orientation, and the entropy of activation.

The expression e^{-E_a/RT} represents the fraction of the molecules present in a gas which have energies equal to or in excess of activation energy at a particular temperature.

Worked Example

Based on the red "line of best fit" plotted in the graph given above:

Let y = ln(k[10-4 cm3 mol-1 s-1])
Let x = 1/T[K]

Points read from graph:

y = 4.1 at x = 0.0015
y = 2.2 at x = 0.00165

Slope of red line = (4.1 - 2.2) / (0.0015 - 0.00165) = -12,667

Intercept [y-value at x=0] of red line = 4.1 + (0.0015 x 12667) = 23.1

Inserting these values into the form above:

\ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right)

yields:

\ln(k) = 23.1 - 12,667 (1/T)
k = e^{23.1} \cdot e^{-12,667/T}
k = 1.08 \times 10^{10} \cdot e^{-12,667/T}

for:

k in 10-4 cm3 mol-1 s-1
T in K

Substituting for the quotient in the exponent of e:

-Ea / R = -12,667 K
approximate value for R = 8.31446 J K−1  mol−1

The activation energy of this reaction from these data is then:

Ea = R x 12,667 K = 105,300 J mol-1 = 105.3 kJ mol-1.

See also

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 



Copyright © World Library Foundation. All rights reserved. eBooks from World eBook Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.