Lecture 28: Arrhenius Equation, Thermal Energy Distribution, and Collision Theory

The Effect of Temperature on Rate

Arrhenius Equation


T = Temperature, R = Gas constant \cdot 8.314 J/mol \cdot K

A = Frequency factor

Ea = Activation energy, the extra energy needed to start the molecules reaction

  • Rate of a reaction increases with Temperature
  • For any reaction, Activation Energy is needed. (Ea)

Activation Energy - The amount of energy needed to convert reactants into the activated complex

Activation Complex - Chemical species with partially broken and partially formed bonds (always very high in energy because of its partial bonds)

Isomerization of Methyl Isonitrile

CH3NCCH3CNCH_{3}-N\equiv C\rightarrow CH_{3}-C\equiv N

  • Methyl Isonitrile rearranges to acetonitrile
  • For this reaction to occur the H3_{3}C-N bond must break and a new H3_{3}C-C bond forms
  • As the reaction begins the C-N bond weakens enough for the C\equiv N group to start to rotate

The Exponential Factor (number between 0 and 1)

  • Fraction of reactant molecules with sufficient energy to cross over the energy barrier. The higher the energy barrier - fewer molecules overcome it.
  • Extra energy comes from Kinetic energy of motion
  • Increasing the temperature increases the average kinetic energy.
  • Increasing the temperature increases the number of molecules with sufficient energy to overcome the energy barrier
  • Increasing the temperature increases the reaction rate

Thermal Energy Distribution

  • When temperature increases, the fraction of molecules with enough energy to surmount the activation energy barrier also increases.

The Arrhenius Equation

ln(K)=EaR(1T)+ln(A)ln(K)=\frac{-Ea}{R}\left ( \frac{1}{T} \right )+ln(A)

(In the form of a line y=mx + b)

y=ln(K)y = ln(K)

x=x = (1T)(\frac {1} {T} )

Determine the activation energy and frequency factor of the reaction O3(g)O2(g)+O(g)O_{3(g)}\rightarrow O_{2(g)}+O_{(g)} given the following data.

y=1.12104x+26.8y = -1.12  ⋅ 10^{4} x + 26.8

Slope = 1.12104K1.12  ⋅ 10^{4} K y intercept = 26.8

Ea = (1.12 \cdot 104^{4}K) (8.314 J/mol \cdot K) = 9.31104J/mol9.31  ⋅ 10^{4}  J/mol

ln (K) = EaR\frac {-Ea}{R} (1T)(\frac {1}{T}) + ln(A)ln(A)

Ea = 93.1kJ/mol 93.1 kJ/mol

A = e26.8^{26.8} = 4.361011 4.36  ⋅ 10^ {11}  

A = 4.361011M1S14.36 \cdot 10^{11} M^{-1} \cdot S^{-1}

A = eyintercept^{y-intercept}

Collision Theory of Kinetics

  • Reaction to take place - reacting molecules must collide with each other
  • Once molecules collide they may react together or they may not, depending on 2 factors
  • Collision should have enough energy to "break the bonds holding reactant molecules together"
  • Reacting molecules collide in the proper orientation for new bonds to form

For a collision to lead to overcoming the energy barrier the reacting molecules much have sufficient kinetic energy so that when they collide the activated complex can form

Energetic Collision leads to product

Effective Collision - meeting the conditions of energy and orientation

The higher the frequency of effective collision, the faster the reaction rate.

Activated Complex - 2 molecules - Effective collision, a temporary, high energy (unstable) chemical species formed.

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