Question

When measured in a 1.00 cm cuvet, a 8.50 x 10-5 M solution of species A exhibited absorbances of 0.129 and 0.764 at 475 nm and 700 nm, respectively. A 4.65 X 10-5 M solution of species B gave absorbances of 0.567 and 0.083 at 475 nm and 700 nm, respectively. Both species were dissolved in the same solvent, and the solvent's absorbance was 0.005 and 0.000 at 475 nm and 700 nm, respectively, in either a 1 or 1.25 cm cuvet. What is the correct expression for a mixture of A and B, if the solution yielded the following absorbance data in a 1.25 cm cuvet: 0.502 at 475 nm and 0.912 at 700 nm.

(a) At 475 nm: (0.497)/1.00 cm = (1459 cm-1M-1 cA) + (12,086 cm-1M-1 cB) At 700 nm: (0.912)/1.00 cm = (8988 cm-1M-1 cA) + (1785 cm-1M-1 cB)

(b) At 475 nm: (0.502)/1.00 cm = (1459 cm-1M-1 cA) + (12,086 cm-1M-1 cB) At 700 nm: (0.912)/1.00 cm = (8988 cm-1M-1 cA) + (1785 cm-1M-1 cB)

(c) At 475 nm: (0.497)/1.25 cm = (1459 cm-1M-1 cA) + (12,086 cm-1M-1 cB) At 700 nm: (0.912)/1.25 cm = (8988 cm-1M-1 cA) + (1785 cm-1M-1 cB)

Answer 1

Beer’s law is given as

A = ε*C*l

where A = absorbance of a solution having concentration C and path length l.

For a solution of species A, we have,

0.129 = ε_1,A*(8.50*10^-5 M)*(1.00 cm)

=====> ε_1,A = (0.129)/(8.50*10^-5 M)(1.00 cm)

=====> ε_1,A = 1517.65 M^-1.cm^-1

0.764 = ε_2,A*(8.50*10^-5 M)*(1.00 cm)

=====> ε_2,A = (0.764)/(8.50*10^-5 M)(1.00 cm)

=====> ε_2,A = 8988.23 M^-1.cm^-1

For the solution of species B, we have,

0.567 = ε_1,B*(4.65*10^-5 M)*(1.00 cm)

=====> ε_1,B = (0.567)/(4.65*10^-5 M)(1.00 cm)

=====> ε_1,B = 12193.55 M^-1.cm^-1

0.083 = ε_2,B*(4.65*10^-5 M)*(1.00 cm)

=====> ε_2,B = (0.083)/(4.65*10^-5 M)(1.00 cm)

=====> ε_2,B = 1784.95 M^-1.cm^-1

The absorbance of the solvent at 475 nm and 700 nm are 0.005 and 0.000 respectively. The absorbance of the mixture of A and B are 0.502 and 0.912 respectively. Since the solvent absorbs at the same wavelength as well, hence, the corrected absorbance is (0.502 – 0.005) = 0.497 and (0.912 – 0.000) = 0.912 respectively.

Let C_A and C_B are the concentrations of A and B. Therefore, we have,

0.497 = (1517.65 M^-1.cm^-1)*C_A*(1.25 cm) + (12193.55 M^-1.cm^-1)*C_B*(1.25 cm)

=====> (0.497)/(1.25 cm) = (1517.65 M^-1.cm^-1)*C_A + (12193.55 M^-1.cm^-1)*C_B ……(1)

Again,

0.912 = (8988.23 M^-1.cm^-1)*C_A*(1.25 cm) + (1784.95 M^-1.cm^-1)*C_B*(1.25 cm)

=====> (0.912)/(1.25 cm) = (8988.23 M^-1.cm^-1)*C_A + (1784.95 M^-1.cm^-1)*C_B ……(2)

The values 1517.65, 12193.55, 8988.23 and 1784.95 are close to 1459, 12086, 8988 and 1785. Therefore, (c) is the correct expression.