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 0.263-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 0.546 at 510 nm and 0.399 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.

What is the concentration of cobalt and copper in the final diluted solution?

What is the weight percent of cobalt (FM = 58.933 g/mol) and copper (FM = 63.546 g/mol) in the 0.263-g sample?

Answer 1

You are missing the molar absorptivities of both Cobalt and Copper. So instead of skipping this question and leave you with doubts, I will give you the main guidelines for you to solve it with your missing data, and write me if you still have doubts.

According to Beer's law:

A = EbC

We have the two absorbance values at different wavelength, but the concentrations of each of the ions is the same, cause we are only varying the wavelength and not concentrations.

For a mixture of two components, beer's law is like this:

A = EbC₁ + EbC₂   let's call C1 concentration of Cobalt and C2 concentration of copper.

So for the first wavelength:

A₁ = EbC₁ + EbC₂   but b = 1 cm so:

A₁ = EC₁ + EC₂   (1)

For the second wavelength, we call E₁' and E₂' for the molar absorptivities of Cobalt and Copper in this wavelength

A₂ = E₁'C₁ + E₂'C₂  (2)

With these two equations, solve for either C₁ or C₂ and then equal the equations. In this case I will solve for C₁ from (1):

C₁ = A₁ - E₂C₂ / E₁ (3)

Then replace in (2)

A₂ = E₁' (A₁ - E₂C₂ / E₁) + E₂'C₂   (4)

From here you can solve for the value of C₂ cause from the table, you have the values for E₁, E₂, E₁' and E₂', the value of A₁ and A₂, so you can know the concentration of Copper (C₂) first, and then, you can replace that value in equation (3) to get the value of C₁ concentration of cobalt, both of them in the final diluted solution.

Now for the Weight percent, you need to first find the original concentrations of copper and cobalt, (before the dillution) and you can do that with the following expression:

C° = C * (final volume / aliquot volume) ----> in this case the final volume is 100 mL and the aliquot is 50 mL.

When you have the concentrations, calculate the moles:

n = C * Valiquot (in Liters)

With the molecular weight of both compounds, calculate the mass of each compound:

m = n * MW

Finally the % would be:

% = (m / m sample) * 100

And that's how you'll calculate the concentrations and % in the sample for each ion. Tell me in a comment if you have doubts with this explanation.

Hope this helps