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- Arrhenius plot - Wikipedia
- 6.2.3.4: The Arrhenius Law - Arrhenius Plots - Chemistry LibreTexts
- 6.2.3.1: Arrhenius Equation - Chemistry LibreTexts
- Arrhenius equation - Wikipedia
- Arrhenius Equation: Explanation, Graph, and Solved Examples
- 6.2.3.3: The Arrhenius Law - Activation Energies
- Arrhenius Equation - Expression, Explanation, Graph, Solved …
- Arrhenius Equation - Chemistry Steps
- Arrhenius Equation (Plot): Definition, Form, Variables, and …
- Temperature as Secondary X Axis in Arrhenius Plot
arrhenius plot
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In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, (
ln
(
k
)
{\displaystyle \ln(k)}
, ordinate axis) plotted against reciprocal of the temperature (
1
/
T
{\displaystyle 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.
The Arrhenius equation can be given in the form:
k
=
A
exp
(
−
E
a
R
T
)
=
A
exp
(
−
E
a
′
k
B
T
)
{\displaystyle k=A\exp \left({\frac {-E_{\text{a}}}{RT}}\right)=A\exp \left({\frac {-E_{\text{a}}'}{k_{\text{B}}T}}\right)}
where:
k
{\displaystyle k}
= rate constant
A
{\displaystyle A}
= pre-exponential factor
E
a
{\displaystyle E_{\text{a}}}
= (molar) activation energy
R
{\displaystyle R}
= gas constant, (
R
=
k
B
N
A
{\displaystyle R=k_{\text{B}}N_{\text{A}}}
, where
N
A
{\displaystyle N_{\text{A}}}
is the Avogadro constant).
E
a
′
{\displaystyle E_{\text{a}}'}
= activation energy (for a single reaction event)
k
B
{\displaystyle k_{\text{B}}}
= Boltzmann constant
T
{\displaystyle T}
= absolute temperature
The only difference between the two forms of the expression is the quantity used for the activation energy: the former would have the unit joule/mole, which is common in chemistry, while the latter would have the unit joule and would be for one molecular reaction event, which is common in physics. The different units are accounted for in using either the gas constant
R
{\displaystyle R}
or the Boltzmann constant
k
B
{\displaystyle k_{\text{B}}}
.
Taking the natural logarithm of the former equation gives:
ln
(
k
)
=
ln
(
A
)
−
E
a
R
(
1
T
)
{\displaystyle \ln(k)=\ln(A)-{\frac {E_{\text{a}}}{R}}\left({\frac {1}{T}}\right)}
When plotted in the manner described above, the value of the y-intercept (at
x
=
1
/
T
=
0
{\displaystyle x=1/T=0}
) will correspond to
ln
(
A
)
{\displaystyle \ln(A)}
, and the slope of the line will be equal to
−
E
a
/
R
{\displaystyle -E_{\text{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
{\displaystyle 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
exp
(
−
E
a
/
R
T
)
{\displaystyle \exp(-E_{\text{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. In almost all practical cases,
E
a
≫
R
T
{\displaystyle E_{\text{a}}\gg RT}
, so that this fraction is very small and increases rapidly with
T
{\displaystyle T}
. In consequence, the reaction rate constant
k
{\displaystyle k}
increases rapidly with temperature
T
{\displaystyle T}
, as shown in the direct plot of
k
{\displaystyle k}
against
T
{\displaystyle T}
. (Mathematically, at very high temperatures so that
E
a
≪
R
T
{\displaystyle E_{\text{a}}\ll RT}
,
k
{\displaystyle k}
would level off and approach
A
{\displaystyle A}
as a limit, but this case does not occur under practical conditions.)
Worked example
Considering as example the decomposition of nitrogen dioxide into nitrogen monoxide and molecular oxygen:
2 NO2 → 2 NO + O2
Based on the red "line of best fit" plotted in the graph given above:
Points read from graph:
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 × 12667) = 23.1
Inserting these values into the form above:
ln
(
k
)
=
ln
(
A
)
−
E
a
R
(
1
T
)
{\displaystyle \ln(k)=\ln(A)-{\frac {E_{a}}{R}}\left({\frac {1}{T}}\right)}
yields:
ln
(
k
)
=
23.1
−
12
,
667
(
1
/
T
)
{\displaystyle \ln(k)=23.1-12,667(1/T)}
k
=
e
23.1
⋅
e
−
12
,
667
/
T
{\displaystyle k=e^{23.1}\cdot e^{-12,667/T}}
as shown in the plot at the right.
k
=
1.08
×
10
10
⋅
e
−
12
,
667
/
T
{\displaystyle 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
{\displaystyle e}
:
E
a
/
R
=
−
12
667
K
{\displaystyle E_{a}/R=-12\,667\,\mathrm {K} }
where the approximate value for R is 8.31446 J K−1 mol−1
The activation energy of this reaction from these data is then:
See also
Arrhenius equation
Eyring equation
Polymer degradation
References
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arrhenius plot
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Arrhenius plot - Wikipedia
In chemical kinetics, an Arrhenius plot displays the logarithm of a reaction rate constant, ( (), ordinate axis) plotted against reciprocal of the temperature (/, abscissa). [1] Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions.
6.2.3.4: The Arrhenius Law - Arrhenius Plots - Chemistry LibreTexts
Feb 13, 2023 · The Arrhenius plot is obtained by plotting the logarithm of the rate constant, k, versus the inverse temperature, 1/T. The resulting negatively-sloped line is useful in finding the missing components of the Arrhenius equation.
6.2.3.1: Arrhenius Equation - Chemistry LibreTexts
Feb 14, 2024 · The exponential term in the Arrhenius equation implies that the rate constant of a reaction increases exponentially when the activation energy decreases. Because the rate of a reaction is directly proportional to the rate constant of a …
Arrhenius equation - Wikipedia
In physical chemistry, the Arrhenius equation is a formula for the temperature dependence of reaction rates. The equation was proposed by Svante Arrhenius in 1889, based on the work of Dutch chemist Jacobus Henricus van 't Hoff who had noted in 1884 that the Van 't Hoff equation for the temperature dependence of equilibrium constants suggests ...
Arrhenius Equation: Explanation, Graph, and Solved Examples
Apr 19, 2024 · What is the Arrhenius plot and its use? An Arrhenius plot graphs ln( k ) against 1/ T (inverse temperature). This plot is linear, and its slope and intercept are used to determine the activation energy and the pre-exponential factor, respectively .
6.2.3.3: The Arrhenius Law - Activation Energies
Feb 13, 2023 · Because radicals are extremely reactive, E a for a radical reaction is 0; an arrhenius plot of a radical reaction has no slope and is independent of temperature. The activation energy can also be calculated directly given two known temperatures and a …
Arrhenius Equation - Expression, Explanation, Graph, Solved …
The Arrhenius equation is an expression that provides a relationship between the rate constant (of a chemical reaction), the absolute temperature, and the A factor (also known as the pre-exponential factor; can be visualized as the frequency of correctly oriented collisions between reactant particles).
Arrhenius Equation - Chemistry Steps
Arrhenius Plots The Arrhenius equation can be expressed in a more applicable form by taking the natural logarithm of both sides which gives a form of a linear equation: This means a plot of ln k versus 1/ T gives a straight line with a slope (m) of – E a/ R and an intercept (b) of ln A.
Arrhenius Equation (Plot): Definition, Form, Variables, and …
What is Arrhenius equation or Arrhenius plot. What are the variables. How to determine the constants from its graph. Learn a few example problems.
Temperature as Secondary X Axis in Arrhenius Plot
Feb 4, 2015 · A linear regression on Arrhenius plot will solve intercept which corresponds to ln(A), and the slope which corresponds to -E a /R. Here we will show you how to make an Arrhenius plot from raw data, and add a linked secondary top axis as experimental temperature ( 0 C).