An unknown solution containing a mixture of two compounds is being analyzed by U

Question

An unknown solution containing a mixture of two compounds is being analyzed by UV/visible spectrometry in order to determine the amounts of compounds A and B in the sample. Both compounds absorb to some extent at 525 and 630 nm. The calibration curve data obtained during the experiment were analyzed using linear regression analysis. The linear equations for each compound at the various wavelengths are provided in the table below.

Results of Linear Regression Analysis

Pathlength (cm)

525 nm

630 nm

Compound A

y = 3.600 x + 0.02

y=1.200 x + 0.11

1.00

Compound B

y = 1.200 x + 0.05

y =0.600 x + 0.15

1.00

The absorbance of the unknown solution was 0.7550 at 525 nm and 0.2532 at 630 nm. Calculate the concentrations (M) of compound A and B in the unknown sample. For full credit, you must show the steps in the calculation – not just the answer. Report your answer to two significant figures.

Results of Linear Regression Analysis

Pathlength (cm)

525 nm

630 nm

Compound A

y = 3.600 x + 0.02

y=1.200 x + 0.11

1.00

Compound B

y = 1.200 x + 0.05

y =0.600 x + 0.15

1.00

Explanation / Answer

Ans. Let-

the concertation of A in unknown solution = A M

            the concertation of B in unknown solution = B M

# At 525 nm:

The sum of absorbance of A and B must be equal to the total absorbance.

In the graph, Y-axis indicates absorbance and X-axis depicts concentration. The linear regression equation in in form of “ y = mx + x”                    , where-

            y = Y-axis value, depicts absorbance

            x = X-axis value, depicts concertation with respect to its absorbance

            m = slope ; (y/x) ration.

So,

            0.7550 = Absorbance of A (y1) + Absorbance of B (y2)

            Or, 0.7550 = (3.600A + 0.02) + (1.200B + 0.05)

            Or, 0.7550 – 0.07 = 3.600A + 1.200B

            Hence, 3.600A + 1.200B = 0.6850                       - equation 1

# At 630 nm:

            0.2532 = (1.200A + 0.11) + (0.600B + 0.15)

            Or, 0.2532 – 0.26 = 1.200A + 0.600B

            Hence, 1.200A + 0.600B = -0.0068                     - equation 2

# Comparing (equation 1) – (2 x equation 2)

            3.600A + 1.200B = 0.6850

      (-) 2.400A + 1.200B = -0.0136

            ------------------------------

            1.200A = 0.6986

            Or, A = 0.6986/ 1.200

            Hence, A = 0.5822

Therefore, concertation of A in the unknown solution = A M = 0.5822 M

# Putting the value of A in equation 1-

            3.600 x 0.5822 + 1.200B = 0.6850

            Or. 1.200B = 0.6850 - 2.09592

            Or, B = (-1.41092) / 1.200

            Hence, B = -1.1758

Therefore, concertation of B in the unknown solution = B M = (-)1.1758 M

# Note: Concertation can’t be negative. Since the calculated concertation of B is a NEGATIVE value, there must be some erroneous values in the question. Please recheck if the value of intercepts in linear regression equations are 0.11 and 0.15 or any other value is incorrectly written. Get the correct values in question and follow the steps to get the correct calculated concertation of A and B.

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