I need help with these problems

Question

A series of reactions containing 20μΜ invertase with different sucrose concentrations in each are

performed and initial velocities are measured. Invertase has a k_cat of 1 x 10 4. K_M is measured to be

25mM.

1.) What is the efficiency of invertase? Pay attention to units!

2.) What is v₀ for this system if 12mM sucrose is present? include all units

3.) If invertase lowers the activation energy barrier for the reaction by 16 kcal/mol, what is the

acceleration of the reaction due to this enzyme?

Answer 1

To determine the efficiency of invertase, we can use the data provided, as follows:

efficiency = k_cat / K_m

k_cat = 1x10⁴ sec^-1 (although you didn't provide the units)

K_m = 25 mM = 2.5x10^-2 M

efficiency = 1x10⁴ / 2.5x10^-2

efficiency = 4x10⁵ M^-1 (units are M^-1 because k_cat is 1st order constant and K_m is 2nd order constant)

V_o = Vmax[S] / Km + [S]

First, we need to find Vmax, which is equal to kcat[E] and [E] = 20 uM as given in the question

Vmax = (1x10⁴ sec^-1)(20x10^-6 mol / L)

Vmax = 0.20 mol / L-sec = 0.20 M/sec

Now, plugging this back in to the V_o equation and solving for V_o

V_o = 0.20 M/sec (0.012 M / 0.025 M + 0.012 M) = 0.20 M/sec (0.012 M/0.037 M)

V_o = 0.065 M/sec or 0.065 moles/L-sec or 65 mmoles / L-sec

Please be sure to check all of the above math as I am prone to making math errors.