Question 18.7: In acidic conditions, benzyl penicillin (BP) undergoes the f...
In acidic conditions, benzyl penicillin \left( BP \right) undergoes the following parallel reaction:In the molecular structures, R_{1} and R_{2} indicate alkyl substituents. Imagine swallowing penicillin while in your stomach PH is \sim 3. At this pH the rate constants for the processes at 22°C are k_{1}=7.0×10^{-4}s^{-1} ,k_{2}=4.1×10^{-3}s^{-1} , and k_{3}=5.7×10^{-3}s^{-1} . What is the yield for P_{1} formation?

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Using Equation (18.79),
\Phi_{i}=\frac{k_{i}}{\sum_{n}^{}k_{n}} (18.79)
\Phi_{P_{1}}=\frac{k_{1}}{k_{1}+k_{2}+k_{3}}=\frac{7.0×10^{-4}s^{-1}}{7.0×10^{-4}s^{-1}+4.1×10^{-3}s^{-1}+5.7×10^{-3}s^{-1}}
=0.067
Of the BP that undergoes acid-catalyzed dissociation, 6.7\% will result in the formation of P_{1}.
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