Ligand X forms a complex with both cobalt and copper, each of which has a maximu

Question

Ligand X forms a complex with both cobalt and copper, each of which has a maximum absorbance at 510 nm and 645 nm, respectively. A 0.295-g sample containing cobalt and copper was dissolved and diluted to a volume of 100.0 mL. A solution containing ligand X was added to a 50.0 mL aliquot of the sample solution and diluted to a final volume of 100.0 mL. The measured absorbance of the unknown solution was 0.479 at 510 nm and 0.350 at 645 nm, when measured with a 1.00-cm cell. The molar absorptivities of the cobalt and copper complexes at each wavelength are shown in the table below.

Ligand X forms a complex with both cobalt and copper, each of which has a maximum absorbance at 510 nm and 645 nm, respectively. A 0.295-g sample containing cobalt and copper was dissolved and diluted to a volume of 100.0 mL. A solution containing ligand X was added to a 50.0 mL aliquot of the sample solution and diluted to a final volume of 100.0 mL. The measured absorbance of the unknown solution was 0.479 at 510 nm and 0.350 at 645 nm, when measured with a 1.00-cm cell. The molar absorptivities of the cobalt and copper complexes at each wavelength are shown in the table below. Wavelength Molar Absorptivity (E, M cm 1 Co Cu A, nm 510 5731 37789 18160 645 1287 What is the concentration of cobalt and copper in the final diluted solution? Number Number M 2 M Co Cu sample? Number Number

Explanation / Answer

Use Beer’s law:

A = *c*l where = molar absorptivity of the compound and c = concentration of the sample and l = path length of the solution.

Given l = 1.00 cm and 1 = 37789 M-1cm-1 and 2 = 5731 M-1cm-1 (510 nm),

0.479 = (37789 M-1cm-1)*[Co2+]*(1 cm) + (5731 M-1cm-1)*[Cu2+]*(1.0 cm) …..(1)

Again, 1 = 1287 M-1cm-1 and 2 = 18160 M-1cm-1 (645 nm),

0.350 = (1287 M-1cm-1)*[Co2+]*(1.0 cm) + (18160 M-1cm-1)*[Cu2+]*(1.0 cm) ….(2)

Multiply (1) by 1287 and (2) 37789 and subtract

1287*0.479 – 37789*0.350 = (1287*5731 M-1)*[Cu2+] – (37789*18160 M-1)*[Cu2+]

===> 616.473 – 13226.15 = -678892443.0*[Cu2+]

===> [Cu2+] = 1.86*10-5

The concentration of Cu2+ in the dilute sample is [Cu2+] = 1.86*10-5 M (ans).

Plug in [Cu2+] in expression (1) and obtain

0.479 = (37789 M-1cm-1)*[Co2+]*(1.0 cm) + (5731 M-1cm-1)*(1.86*10-5 M)*(1.0 cm)

===> 0.479 = (37789 M-1)*[Co2+] + 0.1066

===> 0.3724 = (37789 M-1)*[Co2+]

===> [Co2+] = (0.3724)/(37789 M-1) = 9.85*10-6 M (ans)

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