Problem 98 - Chemistry The Central Science

Question

The total concentration of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Mg}^{2+}\) in a sample of hard water was determined by titrating a 0.100-L sample of the water with a solution of EDTA \(^{4-} .\) The EDTA \(^{4-}\) chelatesthe two cations: $$\begin{array}{c}{\mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-}} \\\ {\mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{4-} \longrightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-}}\end{array}$$ 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-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 \(M[\mathrm{EDTA}]^{4-} .\) Calculate the concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in the hard water in \(\mathrm{mg} / \mathrm{L} .\)

Step-by-Step Solution

Answer

The concentrations of Ca²⁺ and Mg²⁺ in the hard water are 53.47 mg/L and 47.26 mg/L, respectively.

Step 1: Calculate moles of Total metal ions

Since we know the volume and molarity of the EDTA4- solution required for the first titration, we can calculate the moles of total metal ions (Ca²⁺ and Mg²⁺). Moles of EDTA4- = volume × molarity Moles of Total metal ions = 31.5mL × 0.0104M \(= 0.3276\times10^{-3} mol\) Since 1 mole of EDTA4- reacts with 1 mole of metal ion, we have the same number of moles of Total metal ions.

Step 2: Calculate moles of Mg²⁺ ions

We are given the volume and molarity of the EDTA4- solution required for the second titration with Mg²⁺ ions. We can calculate the moles of Mg²⁺ ions. Moles of Mg²⁺ =18.7mL × 0.0104M \(= 0.1943\times10^{-3} mol\)

Step 3: Calculate moles of Ca²⁺ ions

We can subtract the moles of Mg²⁺ from the total moles of metal ions to get the moles of Ca²⁺ ions. Moles of Ca²⁺ = Moles of Total metal ions - Moles of Mg²⁺ Moles of Ca²⁺ = 0.3276×10⁻³ mol - 0.1943×10⁻³ mol \(= 0.1333\times10^{-3} mol\)

Step 4: Calculate concentrations of Ca²⁺ and Mg²⁺

Now we can calculate the concentrations of Ca²⁺ and Mg²⁺. Concentration of Ca²⁺ = Moles of Ca²⁺ / 0.100 L Concentration of Ca²⁺ \(=1.333\times10^{-3} M\) Concentration of Mg²⁺ = Moles of Mg²⁺ / 0.100 L Concentration of Mg²⁺ \(=1.943\times10^{-3} M\)

Step 5: Convert concentrations to mg/L

Once we have the molar concentrations, we can convert them to mg/L by multiplying the molar concentration by the molar mass of the metal ion and \(10^{3}\). Molar mass of Ca = 40.08 g/mol Molar mass of Mg = 24.31 g/mol Concentration of Ca²⁺ in mg/L = Concentration of Ca²⁺(mol/L) × 40.08 (g/mol) × 1000 (mg/g) Concentration of Ca²⁺ in mg/L \(=1.333\times10^{-3}\times 40.08 \times 1000 = 53.47 mg/L\) Concentration of Mg²⁺ in mg/L = Concentration of Mg²⁺(mol/L) × 24.31 (g/mol)× 1000 (mg/g) Concentration of Mg²⁺ in mg/L \(=1.943\times10^{-3}\times 24.31 \times 1000 = 47.26 mg/L\) The concentrations of Ca²⁺ and Mg²⁺ in the hard water are 53.47 mg/L and 47.26 mg/L, respectively.

Key Concepts

EDTA Titration

Complexometric titration using Ethylenediaminetetraacetic acid, commonly known as EDTA, is an essential process in determining the concentration of metal ions in a sample. A distinct feature of EDTA titration is its ability to bind selectively with metal ions forming a stable complex, known as chelation.

The process involves adding a standard solution of EDTA to the sample containing the metal ions until the reaction is complete, which is indicated by a color change with the help of an appropriate indicator. In context of hard water analysis, this method is precise for measuring concentrations of calcium (Ca²⁺) and magnesium (Mg²⁺) ions, the two primary contributors to water hardness.

To ensure accurate results, it's crucial to carry out the titration under optimal pH conditions since the stability of the metal-EDTA complexes is pH-dependent. Furthermore, each mole of EDTA can chelate one mole of metal ion, allowing direct stoichiometric calculations.

Calcium and Magnesium Concentration

The presence of calcium and magnesium in water is a key determinant of water hardness. High levels of these minerals can cause scaling in pipes and reduce the effectiveness of soaps and detergents.

By employing the EDTA titration technique, we can precisely evaluate the concentration of these ions. After the titration is complete, the volume of EDTA used provides a quantitative measure of the total hardness of the water due to both Ca²⁺ and Mg²⁺ ions. A subsequent titration, after selectively precipitating one of the ions (such as calcium with sulfate), allows the determination of each ion's individual concentration.

Understanding the individual and total concentrations of these ions is crucial for water treatment processes and to prevent the detrimental effects of hard water in various domestic and industrial settings. The results usually expressed in milligrams per liter (mg/L), give an indication of the water's suitability for different uses.

Chelation Chemistry

Chelation chemistry plays a fundamental role in EDTA titration. In chelation, a single ligand, such as EDTA, forms multiple bonds with a metal ion, creating a closed ring structure known as a chelate. EDTA works as a superb chelating agent due to its four carboxylate and two amine groups, capable of seizing metal ions tightly within its structure.

This multi-dentate mode of binding makes the resulting metal complex more stable compared to those formed with mono-dentate ligands, which bind through a single site. The term 'chelate' derives from the Greek word 'chele,' which means claw, reflecting the way the ligand surrounds the metal ion like the claw of a crab.

In hard water analysis, the chelates formed with calcium and magnesium are particularly stable, allowing for highly accurate titrations. The robustness of these complexes is vital for the sharp endpoint observed during titration, which heralds the precise moment when the stoichiometric reaction is complete.

Molar Concentration Calculations

Molar concentration calculations are a vital piece in quantifying the levels of ions present in a solution after performing a titration. The concentration, expressed in molarity (M), represents the moles of solute per liter of solution.

After determining the moles of metal ions in the sample through titration with EDTA, these values can be converted into molar concentrations by dividing the moles of ions by the volume of the sample in liters. This fundamental step allows chemists to communicate concentration in a standardized way, making it easier to compare and interpret the results across different analyses.

Once the molar concentrations are known, they can be further converted into mg/L, a more practical unit for reporting water hardness. This conversion involves multiplying the concentration (in moles per liter) by the molar mass of the ion and then by 1000 to convert grams to milligrams, providing an intuitive measure for practical applications.