The final answer is written below the question. I need the step-by-step solution

Question

The final answer is written below the question. I need the step-by-step solution.

In a fruit juice stand, orange juice is produced at a rate of 2 bottles per minute. Each bottle has average of 500 ml of orange juice. All of the bottles were placed to the ice bath immediately after produced. However, worker forget to place juices to ice bath for 1 hour at 30 degree C and put all 120 bottle together. the degradation of vitamin C in products follows first order reaction kinetics with a rate constant of vitamin C at 30 degree C is 3.43*10^-4 (s^-1), and degradation of %50 of vitamin C content in a bottle is considered as faulty determine the number of the bottles that will be regarded as faulty.

Explanation / Answer

Solution:

Orange juice production rate: 2 bottles/min

1 bottle = 500 mL juice

Total no. of bottles = 120

For a first order kinetics, t = 2.303/k log a/(a-x)

Given: k = 3.43x10-4 s-1

Now,

Half-life, t1/2 = 0.693/k = 2020.4 s = 33.67 min

Therefore, 50% degradation of Vitamin-C requires 33.67 min

Thus, first (60 min – 33.67 min) = 26.33 min of juice production would be faulty and

The no. of bottles of juices would be = 2x26.33 = 52.66; [science, production rate = 2 bottles/min]

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