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-} \text { . The EDTA } ^ { 4 - } \text { 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 \(0.0104 \mathrm{M}\) [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 \(\mathrm{mg} / \mathrm{L}\).

Short answer

The concentration of \(\mathrm{Mg}^{2+}\) in the hard water is calculated to be \(74.6 \: \mathrm{mg}/\mathrm{L}\), and the concentration of \(\mathrm{Ca}^{2+}\) is found to be \(127.3 \: \mathrm{mg}/\mathrm{L}\).

Step-by-step solution

Calculate moles of EDTA in the first and second titrations

To find out the amounts of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) ions in the water, we first need to determine the moles of EDTA used in both titrations. We do this by multiplying the molarity of EDTA solution with the volume of EDTA used in each titration. For the first titration: Moles of EDTA = Molarity of EDTA * Volume of EDTA Moles of EDTA = (0.0104 mol/L) * (31.5 mL) * \(\frac{1 L}{1000 mL}\) For the second titration: Moles of EDTA = Molarity of EDTA * Volume of EDTA Moles of EDTA = (0.0104 mol/L) * (18.7 mL) * \(\frac{1 L}{1000 mL}\)

Calculate moles of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\)

Since each mole of EDTA in the first titration chelates one mole of either \(\mathrm{Mg}^{2+}\) or \(\mathrm{Ca}^{2+}\), the total moles of metal ions = moles of EDTA in the first titration. The moles of EDTA required in the second titration are equal to moles of \(\mathrm{Mg}^{2+}\) ions because after the precipitation of the \(\mathrm{Ca}^{2+}\) ions, only \(\mathrm{Mg}^{2+}\) ions remain in the solution. Total moles of metal ions (first titration) = moles of EDTA in the first titration Moles of \(\mathrm{Mg}^{2+}\) (second titration) = moles of EDTA in the second titration Then to find the moles of \(\mathrm{Ca}^{2+}\) ions, subtract the moles of \(\mathrm{Mg}^{2+}\) from the total moles of metal ions: Moles of \(\mathrm{Ca}^{2+}\) = Total moles of metal ions - Moles of \(\mathrm{Mg}^{2+}\)

Calculate concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\)

Now that we have the moles of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) ions, we can calculate their concentrations in the original water sample by dividing the moles by the volume of the water sample (given as 0.100 L): Concentration of \(\mathrm{Mg}^{2+}\) = \(\frac{\text{moles of }\mathrm{Mg}^{2+}}{\text{volume of water sample}}\) Concentration of \(\mathrm{Ca}^{2+}\) = \(\frac{\text{moles of }\mathrm{Ca}^{2+}}{\text{volume of water sample}}\)

Convert concentrations to mg/L

To express the concentrations of \(\mathrm{Mg}^{2+}\) and \(\mathrm{Ca}^{2+}\) in mg/L, multiply the concentrations in mol/L by their respective molar masses (24.305 g/mol for \(\mathrm{Mg}^{2+}\) and 40.078 g/mol for \(\mathrm{Ca}^{2+}\)) and then by 1000 to convert to mg/L: Concentration of \(\mathrm{Mg}^{2+}\) in mg/L = Concentration of \(\mathrm{Mg}^{2+}\) in mol/L * Molar mass of \(\mathrm{Mg}^{2+}\) * 1000 Concentration of \(\mathrm{Ca}^{2+}\) in mg/L = Concentration of \(\mathrm{Ca}^{2+}\) in mol/L * Molar mass of \(\mathrm{Ca}^{2+}\) * 1000

Key concepts

Hard Water

Hard water is a common issue in many parts of the world. It refers to water that contains high concentrations of minerals, specifically calcium (Ca²⁺) and magnesium (Mg²⁺) ions. When water travels through soil and rock, it collects these minerals which then dissolve in the water.
These minerals can cause several household problems such as:

• Reducing the effectiveness of soap and detergent.
• Leaving mineral deposits on dishes, clothes, and fixtures.
• Clogging pipes and reducing water flow.

Despite these issues, hard water is safe to drink and can even have some health benefits due to its mineral content. The challenge arises when these minerals interfere with domestic activities and appliances, prompting people to find ways to remove or reduce the hardness of their water.

EDTA Chelation

EDTA, or ethylenediaminetetraacetic acid, is a powerful chemical compound commonly used in titrations to measure and adjust hardness in water. It works by the process known as chelation.
Chelation occurs when EDTA molecules attach to metal ions, such as Ca²⁺ and Mg²⁺, forming stable, water-soluble complexes:

• Ca²⁺ + EDTA⁴⁻ → [Ca(EDTA)]²⁻
• Mg²⁺ + EDTA⁴⁻ → [Mg(EDTA)]²⁻

This property of EDTA makes it ideal for water softening and for determining the concentration of metal ions in solutions such as hard water.
By binding to the ions, EDTA removes them from the solution, effectively reducing water hardness and making it easier to analyze metal concentrations.

Calcium Ions

Calcium ions, denoted as Ca²⁺, are one of the two primary contributors to water hardness. They have a molar mass of 40.078 g/mol. In natural water sources, calcium ions primarily originate from dissolving limestone (calcium carbonate, CaCO₃) and gypsum (calcium sulfate, CaSO₄).
In the context of chemical titration, calcium ions are crucial because their concentration can affect the results of the analysis. Using EDTA, their concentration in water can be determined through titration. The ion is precipitated or chelated, allowing for measurement separate from other ions.
Their presence in drinking water provides essential nutrients and supports bone health, but excess levels may contribute to household problems associated with hard water.

Magnesium Ions

Magnesium ions, represented as Mg²⁺, are another significant factor in determining water hardness. They have a molar mass of 24.305 g/mol and are typically derived from minerals like dolomite (CaMg(CO₃)₂) and epsomite (MgSO₄·7H₂O) dissolved into water.
Like calcium ions, magnesium ions can be chelated using EDTA in titration methods to measure their concentration in water. After precipitating calcium ions, the remaining magnesium ions are titrated to determine the exact concentration.
Magnesium is beneficial for various biological processes, including nerve function and muscle contraction. However, similar to calcium, excessive magnesium contributes to water hardness and can complicate water usage in homes.