\"What is the rough length of the comumn that would be required to complete remo

Question

"What is the rough length of the comumn that would be required to complete removal of lactose in one passage?"

The information I have is:

-The concentration of lactose was measured by the measurement of glucose and it is assumed that one molecule of lactose produces one molecule of glucose

- Based on the final max concentration of glucose (.376 g/dL), the concentraion of lactose in the volume of milk used in mg/dL was 174.4 mg/dL

-16 cycles were performed with a column length of 0.8cm to get the max concentration of 376 mg/dL of glucose/ 174.4 mg/dL of lactose

I found the equation (# of cycles)(Capsule Column Height)=removal of lactose but im not sure if that is right and even if so, I do no know how to make the units work out?

Explanation / Answer

Concentration of Lactose at the beginning = 174.4 mg/dL
Concentration of Glucose formed = 376 ml/dL

It is given that with 16 cycles and column length of 0.8 cm we get Lactose conc as 174.4 mg/dL and Glucose conc as 376 mg/dL.

Moles of Lactose left to be used = 174.4 / 342 moles = 0.5087
Moles of Glucose formed = 376 / 180 moles = 2.09

So,
2.09 moles are formed with 16 cycles
0.5087 moles are formed with (16/2.09) * 0.5087 = 3.897 cycles.

So in total, 16 + 3.897 = 19.897 cycles are required with 0.8 cm length column.
In one go length column, 19.897 * 0.8 cm = 15.918 cm.

Let me know, if you need to understand anything else.

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