Question

An elevated level of the enzyme alkaline phosphatase (ALP) in human serum is an indication of possible liver or bone disorder. The rate of the reaction increases 1.47 times if the temperature changes from 30 °C to 37 °C. What is the activation energy for the ALP–catalyzed conversion of PNPP to PNP and phosphate?

a) 10.2kJ/mol
b) 15.6kJ/mol
c) 20.5kJ/mol
d) 25.3kJ/mol

Answer 1

The activation energy for the ALP-catalyzed conversion of PNPP to PNP and phosphate, given that the reaction rate increases by 1.47 times when the temperature rises from 30 °C to 37 °C, is approximately 20.5 kJ/mol. Hence, option (c) is correct.

Step-by-step explanation:

The activation energy for the ALP-catalyzed conversion of PNPP to PNP and phosphate can be determined using the Arrhenius equation: k = Ae^(-Ea/RT)

Where k is the rate constant, A is the frequency factor, Ea is the activation energy, R is the gas constant (8.314 J/mol·K), and T is the temperature in Kelvin.

Given that the reaction rate increases by 1.47 times as the temperature increases from 30 °C (303 K) to 37 °C (310 K), we can set up the following ratio using two Arrhenius equations:

k2/k1 = Ae^(-Ea/RT2) / Ae^(-Ea/RT1) = e^(-Ea/R) (1/T2 - 1/T1)

Taking natural logarithms on both sides gives us:
ln(k2/k1) = -Ea/R (1/T2 - 1/T1)

By substituting the known values, we get:
ln(1.47) = -Ea/8.314 (1/310 - 1/303)

Solving for Ea yields an activation energy of approximately 20.5 kJ/mol, which corresponds to option c.