Some bacteria are resistant to the antibiotic penicillin because they produce penicillinase, an enzyme with a molecular weight of \({\bf{3 \times 1}}{{\bf{0}}^{\bf{4}}}\)g/mole that converts penicillin into inactive molecules. Although the kinetics of enzyme-catalysed reactions can be complex, at low concentrations this reaction can be described by a rate equation that is first order in the catalyst (penicillinase) and that also involves the concentration of penicillin. From the following data: 1.0 L of a solution containing 0.15 ยตg (\({\bf{0}}{\bf{.15 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\)g) of penicillinase, determine the order of the reaction with respect to penicillin and the value of the rate constant.
(Penicillin) (M) | Rate (mole/L/min) |
\({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\) \(\) | \({\bf{1}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\) |
\({\bf{3}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\) | \({\bf{1}}{\bf{.5 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\) |
\({\bf{4}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 6}}}}\) | \({\bf{2}}{\bf{.0 \times 1}}{{\bf{0}}^{{\bf{ - 10}}}}\) |