EDTA binds metal ions to form complex ions (see Problem 19.142 ) , so it is used to determine the concentrations of metal ions in solution: $$ \mathrm{M}^{n+}(a q)+\mathrm{EDTA}^{4-}(a q) \longrightarrow \mathrm{MEDTA}^{n-4}(a q) $$ A \(50.0-\mathrm{mL}\) sample of \(0.048 M \mathrm{Co}^{2+}\) is titrated with \(0.050 M\) EDTA \(^{4-}\). Find \(\left[\mathrm{Co}^{2+}\right]\) and \(\left[\mathrm{EDTA}^{4-}\right]\) after addition of (a) \(25.0 \mathrm{~mL}\) and \((b) 75.0 m L\) of \(E D T A^{4-}\left(\log K_{f}\right.\) of \(\left.C o E D T A^{2-}=16.31\right)\)

Complex ions are formed when simple ions bind to molecules or ions, creating a larger ion. In the context of EDTA titration, the Co\textsuperscript{2+} ion binds with the EDTA\textsuperscript{4-} ion to form the complex ion CoEDTA\textsuperscript{2-}. This occurs according to the chemical equation: \[\text{Co}^{2+}(aq) + \text{EDTA}^{4-}(aq) \rightarrow \text{CoEDTA}^{2-}(aq)\] This reaction is essential in determining the concentration of metal ions, such as Co\textsuperscript{2+}, in a given solution. The stability of these complex ions is crucial, and it can be determined using the formation constant (\text{log K_{f}}). For CoEDTA\textsuperscript{2-}, the \text{log K_{f}} is 16.31, indicating a very stable complex. Understanding this interaction helps explain why Co\textsuperscript{2+} and EDTA\textsuperscript{4-} react fully until one of them is completely used up.

Molarity (\text{M}) is a way to express the concentration of a substance in a solution. It's defined as the number of moles of a solute per liter of solution. In the EDTA titration exercise, calculating molarity helps us determine the amounts of Co\textsuperscript{2+} and EDTA\textsuperscript{4-} present at different stages. For instance, to find the initial moles of Co\textsuperscript{2+}: \[\text{Moles of Co}^{2+} = \text{Volume (L)} \times \text{Molarity (M)} = 0.050 \text{ L} \times 0.048 \text{ M} = 0.0024 \text{ moles}\] These calculations are repeated for the EDTA\textsuperscript{4-} added at each step to understand how the reaction progresses and to account for the remaining moles, which are then used to calculate final concentrations after the titration.

A limiting reagent is the reactant that is completely consumed in a reaction, thereby limiting the extent of the reaction and determining the amount of products formed. In the case of the EDTA titration: For the addition of 25.0 mL EDTA\textsuperscript{4-}, the moles of EDTA\textsuperscript{4-} added are calculated: \[\text{Moles of EDTA}^{4-} = 0.025 \text{ L} \times 0.050 \text{ M} = 0.00125 \text{ moles}\] Since 0.00125 moles of EDTA\textsuperscript{4-} is less than 0.0024 moles of Co\textsuperscript{2+}, EDTA is the limiting reagent. Similarly, for 75.0 mL EDTA\textsuperscript{4-}, Co\textsuperscript{2+} becomes the limiting reagent: \[\text{Moles of EDTA}^{4-} = 0.075 \text{ L} \times 0.050 \text{ M} = 0.00375 \text{ moles}\] Since 0.0024 moles of Co\textsuperscript{2+} is less than 0.00375 moles of EDTA\textsuperscript{4-}, Co\textsuperscript{2+} is the limiting reagent. Identifying the limiting reagent helps determine the remaining quantities of reactants after the reaction and is crucial in subsequent concentration calculations.

Determining the concentration of reactants or products after a reaction involves calculating the number of moles remaining and dividing by the total volume of the solution. Following the EDTA titration exercise: For the 25.0 mL EDTA addition, the total volume is the initial Co\textsuperscript{2+} solution plus added EDTA: \[\text{Total volume} = 50.0 \text{ mL} + 25.0 \text{ mL} = 75.0 \text{ mL} = 0.075 \text{ L}\] Now, calculating the concentration of the remaining Co\textsuperscript{2+}: \[\text{[Co}^{2+}\text{]} = \frac{0.00115 \text{ moles}}{0.075 \text{ L}} = 0.0153 \text{ M}\] All EDTA is used up, so the concentration of EDTA\textsuperscript{4-} is 0. For the case of 75.0 mL addition: \[\text{Total volume} = 50.0 \text{ mL} + 75.0 \text{ mL} = 125.0 \text{ mL} = 0.125 \text{ L}\] Therefore, the concentration of remaining EDTA\textsuperscript{4-} is: \[\text{[EDTA}^{4-}\text{]} = \frac{0.00135 \text{ moles}}{0.125 \text{ L}} = 0.0108 \text{ M}\] Understanding these calculations ensures accurate determination of concentration changes through the titration process.