Problem 77 - 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 \(0.100-\mathrm{L}\) sample of the water with a solution of EDTA \(^{4-}\). The EDTA \(^{4-}\) chelates the two cations: $$ \begin{array}{r} \mathrm{Mg}^{2+}+[\mathrm{EDTA}]^{4-}--\rightarrow[\mathrm{Mg}(\mathrm{EDTA})]^{2-} \\\ \mathrm{Ca}^{2+}+[\mathrm{EDTA}]^{--}--\rightarrow[\mathrm{Ca}(\mathrm{EDTA})]^{2-} \end{array} $$ It requires \(31.5 \mathrm{~mL}\) of \(0.0104 M[\mathrm{EDTA}]^{4-}\) 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 \(\mathrm{mg} / \mathrm{L}\).

Step-by-Step Solution

Answer

The concentrations of \(Ca^{2+}\) and \(Mg^{2+}\) in the hard water sample are \(106 \, \text{mg/L}\) and \(46.7 \, \text{mg/L}\), respectively.

Step 1: Calculate moles of EDTA used in the first titration

Using the volume and molarity of EDTA in the first titration, we can determine the moles of EDTA: Moles of EDTA = Volume of EDTA (L) × Molarity of EDTA (moles/L) Moles of EDTA = (31.5 mL × (1 L / 1000 mL)) × 0.0104 M

Step 2: Calculate moles of EDTA used in the second titration

Following the same procedure as in step 1, we can determine the moles of EDTA used in the second titration: Moles of EDTA = Volume of EDTA (L) × Molarity of EDTA (moles/L) Moles of EDTA = (18.7 mL × (1 L / 1000 mL)) × 0.0104 M

Step 3: Calculate concentrations of Ca2+ and Mg2+

In the first titration, the moles of EDTA are equal to the moles of \(Ca^{2+}\) and \(Mg^{2+}\) combined. In the second titration, the moles of EDTA are equal to the moles of \(Mg^{2+}\). 1. Subtract the moles of EDTA from the second titration from the moles of EDTA in the first titration to obtain moles of \(Ca^{2+}\). 2. Use the moles of \(Ca^{2+}\) and \(Mg^{2+}\) separately and divide by the volume of the water sample in liters (0.100 L) to find the concentrations in moles per liter.

Step 4: Convert concentrations to mg/L

To convert the concentrations of \(Ca^{2+}\) and \(Mg^{2+}\) to mg/L, we need to multiply by the molar mass of the ions: 1. \(Ca^{2+}\) concentration (mg/L) = \(Ca^{2+}\) concentration (moles/L) × molar mass of \(Ca^{2+}\) (40.08 g/mol) × (1000 mg/g) 2. \(Mg^{2+}\) concentration (mg/L) = \(Mg^{2+}\) concentration (moles/L) × molar mass of \(Mg^{2+}\)(24.31 g/mol) × (1000 mg/g) After calculating these values, you will have the concentrations of \(Ca^{2+}\) and \(Mg^{2+}\) in the hard water sample in mg/L.

Key Concepts

Complexometric Titration

Complexometric titration is a form of volumetric analysis in which a complexing agent is used to react with a specific ion to form a stable complex. It is often used to determine the concentration of metal ions in a solution. During the titration, an indicator is typically used, which changes color when all the metal ions have been complexed, indicating the endpoint of the titration. A common complexing agent used in these titrations is ethylenediaminetetraacetic acid (EDTA), which can form four or six bonds with a metal ion, creating a very stable complex.

This method is particularly effective because the metal-ligand complexes are highly stable, and the endpoint can be sharply defined. Additionally, EDTA is capable of complexing with a wide range of metal ions, making it a versatile reagent in different kinds of complexometric titrations. To understand the results, stoichiometry is used to relate the known concentration of the titrant (the EDTA solution) to the concentration of the metal ions in the sample.

EDTA Titration

EDTA titration is a specific type of complexometric titration that uses the chelating agent EDTA. EDTA stands for ethylenediaminetetraacetic acid, which is a hexadentate ligand, meaning it can bind to a metal ion at six different points, forming a highly stable chelate complex. The strength of EDTA titrations lies in the high specificity and tight binding of EDTA to many different metal cations.

Detecting the Endpoint in EDTA Titration

Indicators, such as Eriochrome Black T for calcium and magnesium ions, are used to signal the endpoint of the titration visually. The indicator itself binds to the metal ions and then is displaced by EDTA as it is added, causing a color change that indicates that all available metal ions have reacted with the EDTA.

Calculating Results

The calculation of ion concentration following an EDTA titration involves determining the moles of EDTA used and then relating that to the moles of metal ions present based on the stoichiometry of the reaction.

Hard Water Analysis

Hard water contains high levels of mineral ions, particularly calcium (\( \text{Ca}^{2+} \) ) and magnesium (\( \text{Mg}^{2+} \) ), which can lead to scale formation and reduce the effectiveness of soaps and detergents. In a hard water analysis, the concentration of these metal ions is measured to determine the hardness of the water.

Importance of Hard Water Analysis

This analysis is important because it affects various sectors, from domestic to industrial. In homes, hard water can cause limescale buildup in pipes and appliances, while industrially, it can impact processes like heating and cooling systems, leading to increased maintenance costs.

Using Titration for Hard Water Analysis

Complexometric titration, particularly with EDTA, is a common and effective method for quantifying the concentrations of \text{Ca}^{2+} and \text{Mg}^{2+} ions in water samples. Precipitation methods can also be employed to isolate specific ions for individual measurements, which provides a more detailed profile of the water's hardness.

Concentration Calculation

In the context of complexometric titration and hard water analysis, concentration calculation involves using the stoichiometry of the titration reaction and the volume of titrant used to determine the molar concentration of ions in the sample. A clear understanding of molarity, which is moles of solute per liter of solution, is essential for this process.

Steps for Calculating Concentration

The general steps involve calculating the moles of EDTA used during the titration and then relating those moles to the moles of the ions of interest. The final concentration is expressed in mol/L (molarity), which may then be converted to mg/L or parts per million (ppm) for practical uses, such as complying with water quality standards. By following this process carefully and ensuring accurate measurement and precise calculations, one can determine the levels of specific ions in hard water samples and many other types of samples in chemical analysis.