Question

Question #9ef4e

Answer 1

Use the Beer-Lambert Law to establish the unknown protein concentration using the absorbance values and the molar extinction coefficient for both the standard sample and the unknown sample:

`A = εlc`

Explanation:

Where:
`A` = absorbance
`ε` = molar extinction coefficient
`l` = length
`c` = concentration

The absorbance value for the 0.25ml in 2.25ml 0.9% NaCl sample = 0.42

The absorbance for a 0.5mg/ml sample = 0.25

The length of the cuvette (the tube that the sample is placed in order to find the absorbance via spectrophotometry is usually 1cm) so we will use that for `l`, and for any given system, `εl` forms a constant.

Therefore we can then find `c` of the unknown, using the standard that underwent spectrophotometry under the same conditions by setting up equations for both sets of data, and dividing the right side of each by `c` to get:

`A/c = εl`

So we''ll have:

`(A(Standard))/(c (Standard)) = εl`

`(A(Unknown))/(c (Unknown)) = εl`

Since `εl` is going to be constant in both equations, the right side will be equal for both the unknown and the standard solution, so we can cancel it out, leaving us with:

`(A(Standard))/(c (Standard)) = (A(Unknown))/(c (Unknown))`

We want to find `c (unknown)`, so rearrange the equation such that:

`c (unknown)` = `(A (unknown) * c(standard))/ (A (standard)`

Plugging in what we have:

`c(unknown) = ((0.42*0.5 (mg)/(mL))/(0.25)) = 0.84 (mg)/(mL)`

Since this concentration was from a dilution made from 0.25ml serum and 2.25ml of a 0.9% NaCl solution, which formed a total of 2.50ml we must find the original concentration using the dilution equation:

`c_1V_1 = c_2V_2`

Rearranged, this gives:

`c_1 = (c_2V_2)/(V_1) = (0.84(mg)/(mL)*(2.50(mL))/(0.25(mL))) = 8.4 (mg)/(mL)`