Question #9ef4e

1 Answer

Answer:

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)#