lactose + H20 ----> glucose + galactose Problem: Suppose you have developed a ne

Question

lactose + H20 ----> glucose + galactose

Problem:

Suppose you have developed a new treatment for lactose intolerance. To test its effectiveness, you decide to run a simulation using a bioreactor. Lactose dissolved in water is added to the bioreactor at a rate of 100g/min. Reaction products, water, and undigested lactose are removed at the same rate. Assume that reactants and products are both at standard conditions (25 C and 1 atm). If 125 J/s heat is removed to keep the bioreactor temperature constant, what percentage of the lactose is broken down into glucose and galactose?

I'm not sure how to continue, please help.

Explanation / Answer

Assuming the delta Hr value you have calculated for the above reaction is correct, let's find out how many moles of lactose we are adding

100 g / min * 1 mol/ 342 g = 0.292 mol/ min

0.292 moles of lactose is added per minute

In order to keep the temperature constant, we are removing 125 J/s heat. This indicates that 125 J is the amount of heat that is getting formed per second.

Let's find out amount of heat getting formed in 1 minute

1 minute * 60 sec/ 1 min * 125 J/s = 7500 J * 1 kJ/ 1000 J = 7.5 kJ

Amount of heat getting formed actually is 7.5 kJ

Let's find theoretical amount of heat

0.292 mol * 37.6 kJ/ mol = 10.98 kJ

Amount heat that should be formed theoretically is 10.86 kJ

% conversion = Actual amount / Theoretical amount * 100

% conversion = 7.5 kJ/ 10.98 kJ * 100

% conversion = 68.3%

68.3 % lactose is broken down into glucose and galactose

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