How do I calculate the concentration of lactose in the original milk sample. In

Question

How do I calculate the concentration of lactose in the original milk sample. In the experiment I mixed 2 microliters of milk with 0.5 mL of water and 0.5 mL of glucose reagent. Incubated that soulton for 5 mins and read the absorbance at 340 nm. The absorbance was 0.257 and the glucose cocnetration was calculated to be 0.0413. To answr this qustion I was told that the concentration of lactose in the original sample is calculated from the glucose concentration data by applying the dilution factor. Each lactose molecule has one glucose (1:1 ratio). however I still do not know how to answer the question. Please help.

Explanation / Answer

An. Total volume of reaction mixture (whose Abs is recorded) =

            2.0 uL (milk) + 500.0 uL (water) + 500.0 uL (glucose reagent)

            = 1002.0 uL

# Given, [Glucose] in the reaction mixture = 0.0143 AU

Since the unit of [Glucose] is NOT specified, it’s taken to be AU (arbitrary unit).

# Now, using             C1V1 (original milk sample) = C2V2 (reaction mixture)

            Or, C1 x 2.0 uL = 0.0143 AU x 1002.0 uL

            Or, C1 = (0.0143 AU x 1002.0 uL) / 2.0 uL

            Hence, C1 = 7.1643 AU

Therefore, [Glucose] in milk sample = 7.1643 AU.

Since 1 mol glucose is derived from 1 mol lactose, the concertation of lactose must be equal to that of glucose in the sample. It’s assumed that the original milk sample does not have glucose.

# Therefore, [Lactose] in original milk sample = 7.1643 AU* see NOTE below-

Note: If the unit of [Glucose] is in terms of molarity or moles per unit volume, there is no need of further unit conversion because 1 mol of glucose is derived from 1 mol of glucose.

However, you would need to do further calculations if the unit of concertation is in terms of mass.

# For example, if the concertation is in terms of g of glucose per 100 mL milk sample, you would need to do further calculations as follow-

# We have, [Glucose] = 7.1643 g glucose / 100 mL milk sample.

Now,

            Moles of glucose = Mass/ Mw = 7.1643 g / (180.156 g/ mol) = 0.0398 mol

# Since 1 mol glucose is derived from 1 mol lactose, the number of moles of lactose in 100 mL milk sample = 0.0398 mol’

# Mass of lactose = Moles x MW = 0.0398 x (342.3 g/ mol) = 13.61 g

Therefore, amount of lactose in 100 mL milk sample = 13.61 g

So,

            [Lactose] = 13.61 g / 100 mL

# Note: You would need to calculate [Lactose] accordingly if the unit of [Glucose] in the graph is in terms of mass of glucose per unit volume or mass of milk sample – or so on.

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