Penicillinase converts penicillin into inactive molecules. Rates: 1.0 x 10^-10 at 2.0 x 10^-6 M penicillin, 1.5 x 10^-10 at 3.0 x 10^-6 M, and 2.0 x 10^-10 mol/L/min at 4.0 x 10^-6 M. What is the order in penicillin?
ASecond order in penicillin
BZero order in penicillin
CFirst order in penicillin
DHalf order in penicillin
Answer & Solution
Correct answer: C. First order in penicillin
1. Compare how the rate responds as the penicillin concentration rises.
2. Doubling the concentration from 2.0 x 10^-6 to 4.0 x 10^-6 M doubles the rate from 1.0 x 10^-10 to 2.0 x 10^-10.
3. The middle trial fits the same pattern: 1.5 times the concentration gives 1.5 times the rate.
4. Rate rising in direct proportion to concentration is the signature of first order.
5. Second order would have quadrupled the rate on doubling, which these data rule out.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.4 Integrated Rate Laws_
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