To determine the hardness of the water sample in terms of ppm of CaCO3, we need to analyze the precipitation of magnesium fluoride (MgF2) and how it relates to the hardness caused by dissolved magnesium sulfate (MgSO4). Let's break this down step by step.
Understanding Hardness in Water
Water hardness is primarily caused by the presence of divalent metal ions, such as calcium (Ca²⁺) and magnesium (Mg²⁺). In this case, the hardness is attributed solely to dissolved magnesium sulfate (MgSO4). The hardness can be expressed in terms of calcium carbonate (CaCO3) equivalents.
Precipitation of MgF2
The solubility product constant (Ksp) of MgF2 at 25°C is given as 8 × 10⁻⁸. The reaction for the precipitation of MgF2 can be represented as:
- Mg²⁺(aq) + 2F⁻(aq) ⇌ MgF2(s)
The Ksp expression for this equilibrium is:
Calculating Required Concentration of F⁻
Given that the concentration of NaF required to start precipitation is just more than 0.02 M, we can assume that at this concentration, the fluoride ions (F⁻) are sufficient to initiate the precipitation of MgF2.
Let’s denote the concentration of Mg²⁺ as [Mg²⁺]. At the point of precipitation, we can set up the Ksp equation:
Now, we can solve for [Mg²⁺]:
- [Mg²⁺] = 8 × 10⁻⁸ / (0.02)²
- [Mg²⁺] = 8 × 10⁻⁸ / 0.0004
- [Mg²⁺] = 2 × 10⁴ M
Converting to Hardness in ppm of CaCO3
The hardness of water is often expressed in parts per million (ppm) of CaCO3. To convert the concentration of Mg²⁺ to ppm of CaCO3, we need to consider the molar mass of CaCO3, which is approximately 100 g/mol.
Since 1 mole of Mg²⁺ contributes to the hardness equivalent of 1 mole of CaCO3, we can calculate the hardness as follows:
- Hardness (ppm) = [Mg²⁺] (mol/L) × Molar mass of CaCO3 (g/mol) × 1000 (L to mL conversion)
- Hardness (ppm) = 2 × 10⁴ mol/L × 100 g/mol × 1000 mL/L
- Hardness (ppm) = 2 × 10⁴ × 100 × 1000
- Hardness (ppm) = 2 × 10⁹ ppm
Final Thoughts
Thus, the hardness of the water sample due to the dissolved MgSO4, when expressed in terms of ppm of CaCO3, is approximately 2 × 10⁹ ppm. This indicates a very high level of hardness, primarily due to the presence of magnesium ions in the solution.
