Concept 05 / 06Chemical Kinetics
Effect of Temperature: Arrhenius Equation, Activation Energy and Catalysis
Why reaction rates increase with temperature, the Arrhenius equation k = A exp(-Ea/RT) and its logarithmic and two-temperature forms, graphical determination of activation energy, the energy profile with the activated complex, temperature coefficient, and how catalysts work.
For most chemical reactions, the rate constant nearly doubles for every rise in temperature (temperature coefficient to ).
Activation energy. Reactants must pass over an energy barrier to become products. At the top of the barrier lies the activated complex (transition state), an unstable arrangement in which old bonds are partly broken and new ones partly formed. The activation energy is the minimum extra energy (above the average energy of reactants) needed to reach it (see figure). .
Arrhenius equation (1889).
,
where is the pre-exponential (frequency) factor and is the fraction of molecules with energy at least .
Logarithmic form: ; a plot of against is a straight line with slope and intercept (or against with slope ).
Two temperatures: .
Higher temperature increases the fraction of molecules with enough energy, and this effect is exponential, so a modest temperature rise gives a large rate increase. Reactions with larger are more sensitive to temperature. As , .
Catalysts. A catalyst increases the rate without being consumed, by providing an alternative pathway with lower activation energy (see figure). Consequences:
it does not change or of the reaction;
it speeds up forward and backward reactions equally, so equilibrium is reached faster but is unchanged;
it cannot make a non-spontaneous reaction () occur;
a small amount is usually enough, and it is recovered unchanged at the end.
The intermediate complex theory: the catalyst combines with reactants to form a temporary unstable intermediate, which decomposes to products and regenerates the catalyst. Inhibitors (negative catalysts) slow reactions.
Key Takeaways:
- ; slope of vs is .
- .
- .
- Catalysts lower for both directions; they do not change , or .
- Pitfall: a catalyst does not change the position of equilibrium, only how fast it is reached.
Brain-Teaser 1: The rate constant of a reaction doubles when the temperature rises from to . Find .
Solution: , with . .
Brain-Teaser 2: For a reaction, and . What is for the reverse reaction? If a catalyst lowers the forward barrier by , what happens to the reverse barrier?
Solution: . The catalyst lowers the peak itself, so the reverse barrier also falls by , to ; stays .
Brain-Teaser 3: The rate constant of a first-order reaction is . Find , , and the temperature at which .
Solution: Comparing with : and , so . For : , so .
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