Problem 3: The enzyme glucose oxidase is used commercially to remove glucose fro

Question

Problem 3: The enzyme glucose oxidase is used commercially to remove glucose from dehydrated egg to improve color, flavor, and shelf life. The reaction is:

a. What minimum amount of glucose is required in the culture medium to produce 3 kg of gluconic acid?

b. If 1000 L of air at 20 C and 1 atm pressure is pumped into the fermenter, is there enough O2 to produce 3 kg of gluconic acid?

Molecular Weights:

Glucose= 180 g/gmol

O2= 32 g/gmol

gluconic acid = 196 g/gmol

Explanation / Answer

Ans. Stoichiometry of reaction: 1 mol glucose reacts with a mol each of O2 and H2O to produces 1 mol gluconic acid and 1 mol hydrogen peroxide.

Part A: Mass of gluconic acid = 3 kg

                                                = 3000 g                                  ; [1 kg = 1000 g]

            Moles of gluconic acid = mass / molar mass

                                                = 3000 g / (196 g mol-1)

= 15.31 mol

According to the stoichiometry of balanced reaction, 1 mol gluconic acid is produced by 1 mol glucose. So,

            Moles of glucose required = moles of gluconic acid to be produced

                                                            = 15.31 mol

Minimum mass of glucose required = Moles x molar mass

                                                            = 15.31 mol x (180 g mol-1)

                                                            = 2755.10 g

                                                            = 2.75510 g

Part B. Ideal gas Law:           PV = nRT        - equation 1

            Where, P = pressure in atm

            V = volume in L                     

            n = number of moles

            R = universal gas constant= 0.0821 atm L mol-1K-1

            T = absolute temperature (in K)

Given, P = 1 atm ; V = 1000 L ; T = 200C = (273.15 + 20) K = 293.15 K

Putting the values in equation 1-

            1 atm x 1000 L = n x (0.0821 atm L mol-1K-1) x 293.15 K

            Or, 1000 atm L = n x 24.067615 atm L mol-1

            Or, n = (1000 atm L) / (24.067615 atm L mol-1) = 41.54 mol

Thus, number of moles of O2 present in the given volume = 41.54 mol

Now,

In part A, moles of O2 required to produce 3 kg gluconic acid is equal to 15.30 mol.

Or,

            Theoretical requirement of O2 = 15.30 mol

            Actual amount of O2 supplied = 41.54 mol

Therefore, O2 is present in excess and more than sufficient to produce 3 kg gluconic acid.

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