Question

A student prepares a series of solutions of caffeine of known concentration and measures their absorbance values. A linear regression analysis was conducted on the data from Experiment 5 using Excel and produced the following equation for the line:
Y = 0.4399 X + 0.125

The absorbance value for the student's unknown sample is 2.500 units. The student dilutes the unknown by placing 1.00 mL of the unknown solution into a 25.0 mL volumetric flask and diluting to the fill line with water. If the absorbance of the diluted sample is 0.55, what is the concentration of the unknown in the original (undiluted) sample?
(Report your answer using decimal format to the correct number of significant figures. Include leading zeros if appropriate. Do not include units)

Answer 1

Ans. The trendline (linear regression) equation for the graph “y = 0.4399x + 0.125” is in form of y = mx + c.

In the graph, Y-axis indicates absorbance and X-axis depicts concentration. That is, according to the trendline (linear regression) equation y = 0.4399x + 0.125 obtained from the graph, 1 absorbance unit (1 Y = Y) is equal to 0.4399 units on X-axis (concentration) plus 0.125.

Given, absorbance of diluted unknown, y = 0.55

Putting y = 0.55 in trendline equation-

            0.55 = 0.4399x + 0.125

            Or, 0.55 – 0.125 = 0.4399x

            Or, 0.425 = 0.4399x

            Or, x = 0425 / 0.4399 = 0.96613

Therefore, concentration of diluted unknown = 0.96613 units

Note: Put the correct unit of concertation used to define [Caffeine] in aliquots.

# Calculating concertation of undiluted unknown sample:

1.00 mL (V1) of original (undiluted) unknown is diluted to 25.0 mL (V2) with distilled water.

Now, using-

            C1V1 (undiluted solution) = C2V2 (diluted solution)

            Or, C1 x 1.0 mL = 0.99613 units x 25.0 mL

            Or, C1 = (0.99613 units x 25.0 mL) / 1.0 mL

            Hence, C1 = 24.153 units

Hence, concertation of undiluted solution = 24.153 units