Question

Juice is put into bottles and sealed. Each bottle contains 1500 mL of product and has 65 mL headspace of air with 20% by volume of oxygen in it. The specific gravity of the product is 1.04.

During packaging, the dissolved oxygen content of the product is 7.0 ppm. The juice concentrate contributes 5.5 mg Vitamin C per 100 mL to the final product mixture. The processor then adds an unknown amount of vitamin C to the product to bring it to the desired concentration after storage. After storage, the Vitamin C content of the product falls to 55 mg per 100 mL.  15.7mg of Vitamin C are needed to consume 1mL of oxygen.

How much Vitamin C (in grams) would the processor need to add to make enough beverage to fill 1,000 bottles?

Answer 1

Volume of product in each bottle = 1500 mL
Mass of Vitamin C from 100 mL of the juice concentrate = 5.5 mg
Mass of Vitamin C from 1500 mL of the juice concentrate =

Let the additional amount of Vitamin C added to each bottle = x mg
Calculating the volume of O2:
Volume O2 in the head space = 20 % of 65 mL =

Volume O2 dissolved(V) = 7 ppm

V = 0.0105 mL
Total volume of O2 to be consumed = 13 + 0.0105 = 13.0105 mL
Quantity of Vitamin C required to consume 100 mL of O2 = 15.7 mg
Quantity of Vitamin C required to consume 13.0105 mL of O2 =

Mass of Vitamin C from 100 mL of the final product = 55 mg
Mass of Vitamin C from 1500 mL of the final product =

Therefore, the final equation is:
(Mass. of Vitamin C in the Concentrate + Mass. of Vitamin C added) - Mass. of Vitamin C used up to consume the O2 = Mass. of Vitamin C in the final product

x = 825 + 204.26485 - 82.5 = 946.76485 mg in each bottle
Mass of vitamin C required for 1000 bottles =