Question

Antibiotic-resistant bacteria have an enzyme, penicillinase, that catalyzes the decomposition of the antibiotic. The molecular mass of penicillinase is 31200 g/mol. The turnover number of the enzyme at 28 °C is 2.00 × 103 s–1. If 4.10 μg of penicillinase catalyzes the destruction of 2.83 mg of amoxicillin, an antibiotic with a molecular mass of 364 g/mol, in 29.6 seconds at 28 °C, how many active sites does the enzyme have? Assume that the enzyme is fully saturated under the conditions described above.

Answer 1

The number of active sites enzyme have is 1.

Step-by-step explanation:

Mass of penicillinase = 4.10 μg =
`4.10* 10^(-6) g`

1 g = 1000000 μg

The turnover number of the enzyme at 28 °C =
`2.00* 10^3 s^(-1)`

Moles of penicillinase =

`(4.10* 10^(-6) g)/(31200 g/mol)=1.31410* 10^(-10) mol`

Mass of antiboitic-amoxicillin =2.83 mg =
`2.83* 10^(-3) g`

Moles of amoxicillin =

`(2.83* 10^(-3) g)/(364 g/mol)=7.7747* 10^(-6) mol`

Moles of reactant which are converted into product per second:

`1.31410* 10^(-10) mol* 2.00* 10^3 s^(-1)`

=
`2.6282* 10^(-7) mol/s`

Moles of product converted in 29.6 seconds:

`2.6282* 10^(-7) mol/s* 29.6 s=7.779472* 10^(-6) mol`

Number of sites:

`=\frac{\text{moles of product}}{\text{moles of reactant}}`

`=(7.779472* 10^(-6) mol)/(7.7747* 10^(-6) mol)=1.00`