Problem 98 - Chemistry The Central Science In Si Units

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 - \(\mathrm{L}\) 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 -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

Concentration of \(\mathrm{Mg}^{2+}\) is 47.23 mg/L, and \(\mathrm{Ca}^{2+}\) is 53.37 mg/L.

Step 1: Calculate Moles of EDTA from First Titration

First, calculate the moles of EDTA used in the first titration which titrated both \(\mathrm{Ca^{2+}}\) and \(\mathrm{Mg^{2+}}\). Use the formula: \(\text{moles} = \text{Molarity} \times \text{Volume (L)}\). Here, the molarity of \([\mathrm{EDTA}]^{4-}\) is \(0.0104 \text{ M}\) and the volume is \(31.5 \text{ mL} = 0.0315 \text{ L}\). The moles of EDTA are \(0.0104 \times 0.0315 = 0.0003276 \text{ moles}\).

Step 2: Calculate Moles of EDTA from Second Titration

Next, calculate the moles of EDTA used in the second titration, which titrated only \(\mathrm{Mg^{2+}}\). This uses the same formula: \(\text{moles} = \text{Molarity} \times \text{Volume (L)}\). The molarity of \([\mathrm{EDTA}]^{4-}\) remains \(0.0104 \text{ M}\), and the volume used is \(18.7 \text{ mL} = 0.0187 \text{ L}\). Therefore, the moles of EDTA are \(0.0104 \times 0.0187 = 0.00019448 \text{ moles}\).

Step 3: Calculate Moles of \(\mathrm{Ca^{2+}}\)

Subtract the moles of \(\mathrm{Mg^{2+}}\) from the total moles of cations titrated in the first titration to find the moles of \(\mathrm{Ca^{2+}}\). Thus, \(\text{moles of } \mathrm{Ca^{2+}} = 0.0003276 - 0.00019448 = 0.00013312 \text{ moles}\).

Step 4: Calculate Concentration of \(\mathrm{Mg^{2+}}\)

Convert the moles of \(\mathrm{Mg^{2+}}\) to concentration in \(\text{mg/L}\). Moles of \(\mathrm{Mg^{2+}}\) are \(0.00019448 \text{ moles}\). The molar mass of \(\mathrm{Mg}\) is \(24.305 \text{ g/mol}\), so the mass is \(0.00019448 \times 24.305 = 0.004723 \text{ g} = 4.723 \text{ mg}\). Since the volume of water is \(0.100 \text{ L}\), the concentration is \(\frac{4.723}{0.100} = 47.23 \text{ mg/L}\).

Step 5: Calculate Concentration of \(\mathrm{Ca^{2+}}\)

Similarly, convert the moles of \(\mathrm{Ca^{2+}}\) to concentration in \(\text{mg/L}\). Moles of \(\mathrm{Ca^{2+}}\) are \(0.00013312 \text{ moles}\). The molar mass of \(\mathrm{Ca}\) is \(40.08 \text{ g/mol}\), so the mass is \(0.00013312 \times 40.08 = 0.005337 \text{ g} = 5.337 \text{ mg}\). Since the volume of water again is \(0.100 \text{ L}\), the concentration is \(\frac{5.337}{0.100} = 53.37 \text{ mg/L}\).

Key Concepts

EDTA Complexation

Ethylenediaminetetraacetic acid, commonly known as EDTA, is a chelating agent that forms stable complexes with metal ions. This property is particularly useful in titration procedures, as EDTA can precisely target and bind with metal ions such as calcium ( \(\text{Ca}^{2+}\)) and magnesium ( \(\text{Mg}^{2+}\)).

The process of EDTA complexation involves the EDTA molecule wrapping around the metal ions, effectively masking their charges and preventing them from participating in unwanted reactions. This capability is crucial in water analysis, where determining specific metal ion concentrations is required.

During titration, the gradual addition of EDTA solution continues until all the target ions are complexed, which is identified by a noticeable change in indicator color at the endpoint. This indicates that the reaction is complete.

• EDTA combines with metal ions in a 1:1 molar ratio.
• The endpoint of an EDTA titration is often detected using an appropriate indicator that signals when all ions are bound.

By understanding how EDTA complexes with different ions, it becomes possible to differentiate between multiple ions in a solution, especially in complex mixtures like hard water.

Hard Water Analysis

Hard water contains high concentrations of calcium and magnesium ions, which can lead to scaling in pipes and appliances. Analyzing hard water involves determining the concentrations of these metal ions.

To effectively measure these concentrations, a titration method using EDTA is employed. EDTA complexes with calcium and magnesium ions, allowing for precise quantification of the level of these ions.

• The total concentration is determined by a first titration involving both \(\text{Ca}^{2+}\) and \(\text{Mg}^{2+}\) ions.
• A second titration is performed to establish the concentration of \(\text{Mg}^{2+}\) specifically, after \(\text{Ca}^{2+}\) has been precipitated out.

This approach is beneficial as it allows for the accurate measurement of the ions individually, providing detailed insights into the hardness of water. Recognizing the level of water hardness is important for both domestic and industrial applications, as it influences water treatment processes.

Calcium and Magnesium Concentration

Determining the concentration of calcium ( \(\text{Ca}^{2+}\)) and magnesium ( \(\text{Mg}^{2+}\)) in water is crucial for assessing water hardness. Each cation’s concentration is evaluated by the number of moles it forms in reaction with EDTA.

First, the moles of EDTA used in titrating both ions are determined. Then, the separate amount of EDTA required to titrate only magnesium ions is subtracted to find the concentration of just calcium ions.

• The moles of calcium ions in the sample are calculated by difference.
• The concentrations in mg/L are found by converting these mole values using the respective molar masses: 40.08 g/mol for calcium and 24.305 g/mol for magnesium.

Finally, these concentration values allow for an assessment of the hard water degree and the necessary treatments to remove or reduce such levels, improving water quality.