Unformatted text preview: M 0.38×10-4 3.30×10-4 6.50×10-4 12.3×10-4 [An]/M 0.22×10-4 0.22×10-4 0.22×10-4 0.22×10-4 τ-1/s-1 5.1×104 8.4×104 1.07×105 1.58×105 L Grondahl CHEM2056 L Grondahl CHEM2056 Experimental evidence Molecular Kinetics
The next two lectures will explore how we can explain the
temperature dependence of the rate constant. Sections 18.9, 18.15, 19.3 Experimental data has shown that the rate constant of most reactions (all elementary reactions) increases with increasing temperature (empirical relationship): k Ae E a / RT The Arrhenius Equation (1889).
Ea is called the activation energy (unit kJ mol‐1). A is called the pre‐
exponential factor (unit as rate constant).
Wide applicability: flashing of fire flies, rate of aging, rate of counting and forgetting L Grondahl CHEM2056 Theory of Chemical Kinetics
Early theory to account for this behaviour of chemical reactions: An energy barrier exists for chemical reactions and in order to react the colliding molecules must have a total potential energy greater than this barrier, or activation energy, Ea. For 1st order reactions the molecules must gain sufficient energy to overcome the activation barrier. How do they do this? Can they gain energy a different way? Van’t Hoff’s argument
Van’t Hoff Equation: Relationship between rate and equilibrium constants: d ln K H dT
RT 2 k1
k 1 ∆H is positive L Grondahl CHEM2056 Treatment of data L Grondahl CHEM2056 k Ae E a / RT
ln k ln A a RT Slope = -Ea /R Can be used to calculate Ea if k is known at two or more temperatures
Can be used to calculate k at a new temperature if Ea is known ln L Grondahl CHEM2056 ∆H is negative Example calculation
The body becomes hotter when ill.
The rate at which your antibodies react needs to increase twofold in
order to fight infection when you are ill. This rate increase is achieved
by raising the body’s temperature from 37 °C to 40 °C. What is the
activation energy of the reaction?
Use the equation: ln E 1 1
k2 a k1
R T1 T2 E 1 1
k2 a k1
R T1 T2 Try problem 3 on ‘Practice problem sheet week 6’.
L Grondahl CHEM2056 Arrhenius behaviour: The Arrhenius Equation k Ae E a / RT Reactions whose temperature dependence of the rate constant follows the Arrhenius equation (at least within a reasonable temperature range) are said to display Arrhenius behaviour. Two theories to explain the temperature dependence: k aT m e E a / RT ‐where m = 1, ½, ‐½. The activation energy is again temperature independent but the non‐exponential component now has a temperature dependence. Hard-Sphere Collision Theory for gas phase reactions k aT m e Ea / RT ; m 12 ; A aT 1/ 2 Some reactions do not follow this, i.e. a straight line plot is not obtained that either A or Ea (or both) are not temperature independent. Some theories predict an alternative relationship: k Ae E a / RT Activated Complex Theory k aT m e Ea / RT ; m 1 ; A aT In either case, the greater the value of Ea the greater is the temperature dependence on the rate.
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