Question

Titration of M with L to form ML and ML₂. Use theequation from Problem 12-21, where M is Cu²⁺ and L is acetate.Consider adding 0.500 M acetate to 10.00 mL of 0.050 0 M Cu²⁺ atpH 7.00 (so that all ligand is present as ${\mathbf{CH}}_{\mathbf{3}}{\mathbf{CO}}_{\mathbf{2}}^{\mathbf{-}}$, not CH₃CO₂H).Formation constants forCu(CH₃CO₂)⁺ and Cu(CH₃CO₂)₂ aregiven in Appendix I. Construct a spreadsheet in which the inputis pL and the output is [L], V_L, [M], [ML], and [ML₂]. Prepare agraph showing concentrations of L, M, ML, and ML₂as V_L rangesfrom 0 to 3 mL

Short answer

Spreadsheet developed

The graph obtained from the above spreadsheet is as follows

Step-by-step solution

Information Given

The equation obtained from Problem 12-21 need to be used. Here M is considered to be Cu²⁺ and L is considered to be acetate.

Adding 0.500 M acetate to 10.00 mL of 0.0500 M Cu²⁺ at pH 7.00 (so that all ligand is present as${\mathrm{CH}}_3{\mathrm{CO}}_2^{-}$, not CH₃CO₂H). Formation constants for Cu(CH₃CO₂)⁺ and Cu (CH₃CO₂)₂ are obtained from Appendix I.

Equation need to be used to develop spreadsheet

Following equation need to be used to develop spreadsheet

$\mathrm{\varphi }=\frac{{\mathrm{C}}_{\mathrm{L}}{\mathrm{V}}_{\mathrm{L}}}{{\mathrm{C}}_{\mathrm{M}}{\mathrm{V}}_{\mathrm{M}}}=\frac{{\mathrm{\alpha }}_{\mathrm{ML}}+2{\mathrm{\alpha }}_{{\mathrm{ML}}_2}+{\displaystyle \frac{\mathrm{L}}{{\mathrm{C}}_{\mathrm{M}}}}}{1-{\displaystyle \frac{\mathrm{L}}{{\mathrm{C}}_{\mathrm{L}}}}}$

Other equations need to be used

$$\begin{gathered} \mathrm{L}={10}^{-\mathrm{pL}} \\ {\mathrm{\alpha }}_{\mathrm{M}}=\frac{1}{1+{\mathrm{\beta }}_1\left[\mathrm{L}\right]+{\mathrm{\beta }}_2{\left[\mathrm{L}\right]}^2} \\ {\mathrm{\alpha }}_{\mathrm{ML}}=\frac{{\mathrm{\beta }}_1\left[\mathrm{L}\right]}{1+{\mathrm{\beta }}_1\left[\mathrm{L}\right]+{\mathrm{\beta }}_2{\left[\mathrm{L}\right]}^2} \\ {\mathrm{\alpha }}_{{\mathrm{ML}}_2}=\frac{{\mathrm{\beta }}_2{\left[\mathrm{L}\right]}^2}{1+{\mathrm{\beta }}_1\left[\mathrm{L}\right]+{\mathrm{\beta }}_2{\left[\mathrm{L}\right]}^2} \\ \left[\mathrm{ML}\right]={\mathrm{\alpha }}_{\mathrm{ML}}\frac{{\mathrm{C}}_{\mathrm{M}}{\mathrm{V}}_{\mathrm{M}}}{{\mathrm{V}}_{\mathrm{M}}+{\mathrm{V}}_{\mathrm{L}}} \\ \left[{\mathrm{ML}}_2\right]={\mathrm{\alpha }}_{{\mathrm{ML}}_2}\frac{{\mathrm{C}}_{\mathrm{M}}{\mathrm{V}}_{\mathrm{M}}}{{\mathrm{V}}_{\mathrm{M}}+{\mathrm{V}}_{\mathrm{L}}} \end{gathered}$$

Spreadsheet Developed

The following spreadsheet was developed in order to determine the desired concentration

Graph Plot

From the data obtained from the above spreadsheet the graph is plotted below.