Could someone please explain the steps, especially how the dilution factor happe

Question

Could someone please explain the steps, especially how the dilution factor happened?

You are tasked with determining the concentration of aflatoxin B1 in a sample of suspect milk. There are two problems with directly measuring absorption of these samples: aflatoxin B1 does not readily absorb in the visible region: milk has a lot of components, making it optically opaque. A recent report showed that gold nanoparticles bind tightly to the toxin, forming a complex that readily absorbs 550 nm photons. Use the following information to determine the concentration of aflatoxin B1 in the milk sample. a) How many nanograms of aflatoxin B1 would be in a 1.0 liter bottle of milk?

Explanation / Answer

In order to find the concentration of aflatoxin, first, we have to calculate the extinction coefficient of the gold nanoparticle-aflatoxin at 550 nm. This can be calculated from the rate of change in absorbance with the concentration of aflatoxin. From the given data it is clear that gold nanoparticle-aflatoxin readily absorbs at 550 nm (absorbance got increased from 0.65 to 0.89 ) and it is also given that aflatoxin B1 does not absorb in the visible region.

extinction coefficient = 0.24/(0.5*5) = 0.096 (ng/mL)-1 (pathlength of the cuvette)-1

Milk sample with aflatoxin B1 shows an absorption of 0.65.

using Beer-Lamberts law we can calculate the concentration of aflatoxin B1 in the sample.  

absorbance = extinction coefficient * pathlength of the cuvette * concentration of the sample (Let us take path length as 1. Since we are using the same cuvette for both the measurements, it will not affect our result)

0.65 = 0.096 * 1* concentration of the sample

or concentration of the sample = 0.65/0.096 = 6.77 ng/mL

a). The solution used to measure absorbance has 50 mL it contains 6.77 ng/mL. basically, this came from 25 mL milk thus the milk has double concentration. 13.54 ng/mL.

or in 1 L milk contains 13540 ng of aflatoxin. B1.

Initially, you have mentioned about dilution factor. In order to avoid dilution factor, both the solutions should be of the same volume. that is in the second experiment, we haven't added aflatoxin B1. Thus in order to make it as the same volume, we have added 20 mL water.Whereas in the other experiment we have added 15 mL water and 5 mL aflatoxin B1 solution.

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