Consider an in vitro enzyme reaction using the enzyme glucos

Consider an in vitro enzyme reaction using the enzyme glucose isomerase, which has been immobilized by covalently bonding to a non-porous support structure. Determine the surface concentration Ssof the substrate glucose at the surface of the support under steady state conditions, given the following known enzyme and mass transfer parameters:

· Michealis-Menten enzyme KM = 20 mg/L; VM = 0.5 mg glucose / cm2 support-min

· Mass transfer coefficient for the film region kL = 0.0035 cm/min

· Substrate concentration in the bulk solution phase Sb = 60 mg/L Show clearly your solution to this problem by either the analytical or graphical method. Also, calculate the Damkohler number for this instance. Based on that value, what process is limiting?

Solution

Damkohler number can be given as

Da= maximum rate of reaction/ maximum rate of diffusion

= Vm / k_L[S_b]

here, KL = 0.0035cm/min , Vm = 0.5 mg glucose / cm2 support minute, Sb = 60 mg/ litre

= 0.5/0.0035*60

= 2.38

Since the value of Da is more than 1

If Da>>1, then diffusion rate is limiting the observed rate .