Question

The ultraviolet spectra of o- and p- cresol overlap extensively. A 5.0ml sample containing the two compounds was dissolved and diluted to 50.0ml with isoctane. This solution had absorbances of 0.716 at 264nm and 0.318 at 272nm. a solution of 4.63x10^-4M o-cresol had absorbances of 0.730 at 264nm and 0.718 at 272nm. A solution of the para isomer of the same concentration had absorbances of 0.548 at 264nm and 0.433 at 272nm. If all measurements were made in 1cm cells, calculate the molar concentration of each isomer in the sample.

Answer 1

Ans.

Ans. Beer-Lambert’s Law, A = e C L             - equation 1,              

where,

                                                A = Absorbance

                                                e = molar absorptivity at specified wavelength (M^-1cm^-1)

                                                L = path length (in cm)

                                                C = Molar concentration of the solute

Let the concentration of species M = M   molar; and

     the concentration of species R = R molar

Step 1: Calculate molar extinction coefficient of both the isomers are the two wavelength:

# molar absorptivity of o-cresol at 264 nm

            Molar absorptivity, e = A / Cl = 0.730 / (4.63 x 10^-4 M x 1.0 cm)

                                    Or, e = 1576.674 M^-1 cm^-1

* Rest molar absorptivity values are calculated in excel as shown.

# Step 2: Let the [o-cresol] be Q molar    ; and [p-cresol] = P molar

#At 264 nm

Absorbance due to O-cresol alone = eCL

= 1576.674 M^-1 cm^-1 x Q M x 1.0 cm

= 1576.674Q

Absorbance due to P-cresol alone = 1183.585 M^-1 cm^-1 x P M x 1 cm = 1183.585P

Since the absorbance is additive, the sum of absorbance of species Q and P is equal to the total absorbance of the sample.

So,      

            1576.674Q + 1183.585P = 0.716                                    - equation 1

#At 264 nm

Absorbance due to O-cresol alone = 1550.756 M^-1 cm^-1 x Q M x 1 cm = 1550.756Q

Absorbance due to P-cresol alone = 935.205 M^-1 cm^-1 x P M x 1 cm = 935.205P

Since the absorbance is additive, the sum of absorbance of species Q and P is equal to the total absorbance of the sample.

So,      

            1550.756Q + 935.205P = 0.716                           - equation 2

##. Comparing (equation 1 x 1550.756) – (equation 2 x 1576.674)

            2445036.363Q + 1835451.954P = 1110.341

     (-)[ 2445036.363Q + 1474513.57P = 501.382]

                                       360938.382P = 608.959

                                    Or, P = 608.959 / 360938.382 = 0.001687

Thus, concentration of P-cresol = 0.001687 M = 1.687 x 10^-3 M

# Putting the value of P in equation 1-

            1576.674Q + (1183.585 x 0.001687) = 0.716

            Or, 1576.674Q + 1.997 = 0.716

            Or, 1576.674Q = 0.716 – 1.997 = -1.281

The concertation can’t be negative.

Please re-check the values you have provided in the question. Some data provided in the question are NOT in accordance with the calculations. Please re-check the values.