Concept 04 / 06Chemical Kinetics
Pseudo First Order Reactions, Gas-Phase Kinetics and Determining Order
Pseudo first order reactions such as acid hydrolysis of esters and inversion of cane sugar, first-order kinetics followed by total pressure in gas-phase decompositions, and methods of determining order: initial rates, integrated rate law (graphical) and half-life methods.
Pseudo first order reactions. A reaction that is really of higher order behaves as first order when one reactant is present in large excess, so its concentration hardly changes.
Acid hydrolysis of ethyl acetate: . Rate , but water is the solvent (about ) and effectively constant, so rate with . It is followed by titrating the acetic acid formed against NaOH.
Inversion of cane sugar: (glucose) (fructose); rate . It is followed with a polarimeter: dextrorotatory sucrose gives a laevorotatory mixture, hence "inversion".
First-order gas-phase reactions followed by pressure. For with initial pressure : if decomposes, and total , so and
.
For other stoichiometries, express each partial pressure through the extent of reaction: for , if the pressure of falls by , the total pressure is .
Determining the order.
Initial rate method: vary one concentration at a time (see previous concept).
Integrated rate law (graphical) method: plot , and against ; the straight line identifies zero, first or second order.
Substitution method: calculate from each data point using each integrated equation; the one that gives a constant is correct.
Half-life method: , so from two runs, . Successive half-lives are equal only for first order (see figure).
Ostwald's isolation method: use large excess of all reactants but one, so the order in that one can be measured (pseudo order).
Key Takeaways:
- Pseudo first order: one reactant in large excess (ester hydrolysis, sugar inversion).
- For : .
- Linear plots: (zero), (first), (second).
- Half-life method: .
- Pitfall: in pressure problems, use the partial pressure of the reactant, not the total pressure, in the rate equation.
Brain-Teaser 1: is first order. Starting at , the total pressure is after . Find .
Solution: . .
Brain-Teaser 2: For a reaction, the half-life is when the initial concentration is and when it is . Find the order.
Solution: Doubling halves : , so and (second order).
Brain-Teaser 3: Why is the acid-catalysed hydrolysis of an ester first order, though two molecules react?
Solution: The rate law is really , but water is present in huge excess (as solvent), so its concentration stays essentially constant and is absorbed into . The observed kinetics are first order in ester only (pseudo first order), while the molecularity of the key step is still two.
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