**Reactivity in Chemistry **

**R****eaction
Kinetics**

**MK1. Determination of Activation Parameters**

Intuitively, you know that a reaction goes faster as the temperature is raised, as more reactant molecules have the energy needed to overcome the activation barrier to the reaction. The Arrhenius equation relates reaction rate constants (k) and temperature. One of the forms of the Arrhenius equation is:

ln k = -Ea/RT + ln A

where Ea is the activation energy for the reaction, T is the absolute temperature (in Kelvin) at which a corresponding k is determined, R is the gas constant, and A is a pre-exponential factor. The activation energy may then be extracted from a plot of ln k vs. 1/T, which should be linear. This plot is called an "Arrhenius plot".

Problem MK1.1.

Recall that y = mx + b.

a) In a so-called “Arrhenius plot” plot, what is the slope?

b) What is the intercept?

Problem MK1.2.

Using the following data, construct an Arrhenius plot and determine the activation energy (in both kcal/mol and kJ/mol) and the pre-exponential factor.

1/T (K |
ln k (unitless) |

0.00152 | 3.7 |

0.00157 | 3.2 |

0.00160 | 2.9 |

0.00165 | 2.2 |

0.00170 | 1.6 |

Problem MK1.3.

Using the following data, construct an Arrhenius plot and determine the activation energy (in both kcal/mol and kJ/mol) and the pre-exponential factor.

T (°C) | k (mol L^{-1} s^{-1}) |

40 | 1.3 x 10^{-4} |

50 | 2.2 x 10^{-4} |

60 | 4.0 x 10^{-4} |

70 | 7.5 x 10^{-4} |

80 | 1.4 x 10^{-3} |

In practice, activation energies are not often cited in the current literature. Instead, a similar but more useful equation called the Eyring equation is used. The Eyring equation is:

ln (k/T) = -ΔH^{‡} /RT + ln (k_{B}/h) + ΔS^{‡} /R

where k, T and R are the same as in the Arrhenius equation, k_{B} is
Boltzmann’s constant, h is
Planck’s constant and ΔH^{‡} and ΔS^{‡} are the enthalpy
and entropy of activation, respectively.

Problem MK1.4.

a) What should be plotted to make an Eyring plot?

b) What is equal to the slope?

c) What is equal to the intercept?

Note that the activation parameters (ΔH^{‡} and ΔS^{‡} ) are not the same as the
entropy and enthalpy of the reaction, which can usually be calculated from
tables of values. Since they depend on how the reaction proceeds, not just the
initial and final states of the reaction, they must be determined
experimentally. Once that has been done, interpretation of the numerical values
provides insight into the mechanism of the reaction.

contribution from Brian Johnson, College of Saint Benedict / Saint John's University

This site is written and maintained by Chris P. Schaller, Ph.D., College of Saint Benedict / Saint John's University (with contributions from other authors as noted). It is freely available for educational use.

**
**
Structure & Reactivity in Organic, Biological and Inorganic Chemistry

Send corrections to cschaller@csbsju.edu

This material is based upon work supported by the National Science Foundation under Grant No. 1043566.

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