The total concentration of Ca^2+ and Mg^2+ in a sample of hard water was determined by titrating

step 1 The total concentration of calcium ion and magnesium ion in a sample of hard water was determine

The total concentration of Ca^2+ and Mg^2+ in a sample of...

The total concentration of $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ in a sample of hard water was determined by titrating a $0.100-\mathrm{L}$ sample of the water with a solution of EDTA $^{4-}$. The EDTA $^{4-}$ chelates the two cations: $$ \begin{aligned} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\ \mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{aligned} $$ It requires $31.5 \mathrm{~mL}$ of $0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}$ solution to reach the end point in the titration. A second $0.100-\mathrm{L}$ sample was then treated with sulfate ion to precipitate $\mathrm{Ca}^{2+}$ as calcium sulfate. The $\mathrm{Mg}^{2+}$ was then titrated with $18.7 \mathrm{~mL}$ of $0.0104 \mathrm{M}$ $[\mathrm{EDTA}]^{4-},$ Calculate the concentrations of $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ in the hard water in $\mathrm{mg} / \mathrm{L}$.

The total concentration of $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ in a sample of hard water was determined by titrating a $0.100-\mathrm{L}$ sample of the water with a solution of EDTA $^{4-}$. The EDTA $^{4-}$ chelates the two cations:
$$
\begin{aligned}
\mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\
\mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow &[\mathrm{Ca}(\mathrm{EDTA})]^{2-}
\end{aligned}
$$
It requires $31.5 \mathrm{~mL}$ of $0.0104 \mathrm{M}[\mathrm{EDTA}]^{4-}$ solution to reach the end point in the titration. A second $0.100-\mathrm{L}$ sample was then treated with sulfate ion to precipitate $\mathrm{Ca}^{2+}$ as calcium sulfate. The $\mathrm{Mg}^{2+}$ was then titrated with $18.7 \mathrm{~mL}$ of $0.0104 \mathrm{M}$ $[\mathrm{EDTA}]^{4-},$ Calculate the concentrations of $\mathrm{Mg}^{2+}$ and $\mathrm{Ca}^{2+}$ in the hard water in $\mathrm{mg} / \mathrm{L}$.

Key Concepts

Conversion of Moles to Concentration Units

After determining the number of moles of a metal ion through titration, it is essential to convert this value into concentration units such as mg/L. This conversion involves multiplying the moles by the molar mass of the ion and then dividing by the sample volume, providing a practical measure of ion concentration in the context of water quality analysis.

Stoichiometry in Titration

Stoichiometry in titration involves calculating the molar relationships between the titrant and the analyte based on the reaction's balanced chemical equation. This principle ensures that the volume of titrant used corresponds accurately to the number of moles of the target ions present in the solution.

EDTA as a Chelating Agent

EDTA (ethylenediaminetetraacetic acid) is a multifunctional ligand that binds strongly to metal ions to form stable complexes. Its ability to chelate ions like Ca²? and Mg²? in a 1:1 molar ratio makes it particularly useful in water hardness analysis, where it serves as the titrant to accurately quantify the amount of these metal ions.

Complexometric Titration

Complexometric titration is an analytical method that uses a chelating agent, such as EDTA, to form a stable, stoichiometric complex with metal ions. This technique is commonly used to quantitatively determine the concentration of divalent or trivalent metal ions in a solution by measuring the amount of titrant needed to react completely with the metal ions.

Precipitation Reactions in Analysis

Precipitation reactions, which involve converting soluble ions into an insoluble form, are employed to selectively remove or separate specific ions from a solution. In water analysis, a precipitating agent can be added to form an insoluble salt with one ion (e.g., Ca²?), thereby allowing the unaffected ion (e.g., Mg²?) to be measured independently.

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