Question

Standard solutions of calcium ion used to test for water hardness are prepared by dissolving pure calcium carbonate, \(\mathrm{CaCO}_{3}\), in dilute hydrochloric acid. A 1.745 -g sample of \(\mathrm{CaCO}_{3}\) is placed in a \(250.0-\mathrm{mL}\) volumetric flask and dissolved in \(\mathrm{HCl}\). Then the solution is diluted to the calibration mark of the volumetric flask. Calculate the resulting molarity of calcium ion.

Short answer

The resulting molarity of calcium ions in the solution prepared by dissolving 1.745 g of CaCO3 in a 250.0 mL volumetric flask is 0.06972 M.

Step-by-step solution

Find the moles of CaCO3

First, we need to determine the number of moles of CaCO3. To do this, we'll use the mass and molar mass of CaCO3: Moles of CaCO3 = (Mass of CaCO3) / (Molar Mass of CaCO3) The molar mass of CaCO3 is: 40.08 (Ca) + 12.01 (C) + 3 * 16.00 (O) = 100.09 g/mol So, the moles of CaCO3 = (1.745 g) / (100.09 g/mol) = 0.01743 mol

Determine the moles of Ca2+ ions

Now, for each mole of CaCO3, there is one mole of Ca2+ ions (1:1 ratio). Therefore, the moles of Ca2+ ions are equal to the moles of CaCO3: Moles of Ca2+ ions = 0.01743 mol

Calculate the molarity of Ca2+ ions

Finally, we'll use the moles of Ca2+ ions and the volume of the solution to determine the molarity: Molarity of Ca2+ ions = (Moles of Ca2+ ions) / (Volume of solution in liters) The volume of the solution is given as 250.0 mL, which is equal to 0.2500 L. Molarity of Ca2+ ions = (0.01743 mol) / (0.2500 L) = 0.06972 M So, the resulting molarity of calcium ions in the solution is 0.06972 M.

Key concepts

Water Hardness

Water hardness is an important property that indicates the concentration of certain minerals in water. It is primarily a measure of the concentration of calcium (\(\text{Ca}^{2+}\)) and magnesium ions(\(\text{Mg}^{2+}\)) in the water. Hard water is known to cause scaling and reduce the effectiveness of soaps and detergents.
These minerals often originate from dissolved limestone and other mineral deposits. In water testing, standard solutions are used to identify and calculate the hardness. Typically, calcium is measured using calcium carbonate equivalents because calcium carbonate (\(\text{CaCO}_3\)) is a common form found in natural water systems.

• Importance of Measuring Hardness: Understanding water hardness helps in preventing scale buildup in pipes and appliances.
• Environmental Impact: Hard water can sometimes lead to higher energy costs as appliances work harder and longer to heat the water.

By preparing standard solutions of calcium, technicians can determine the purpose and concentration of these minerals effectively.

Calcium Carbonate

Calcium carbonate (\(\text{CaCO}_3\)) is a chemical compound commonly found in rocks as minerals like calcite and aragonite. It is a key ingredient in the shells of marine organisms, snails, and eggs, and is widely used in water testing.
When it comes to determining water hardness, calcium carbonate plays a fundamental role because it directly equates the amount of calcium responsible for hardness to its weight. This correlation makes it easier for water technicians to measure and express hardness levels using calcium carbonate as a reference.

• Role in Water Testing: Calcium carbonate dissolves in water to release calcium ions, crucial for measuring hardness.
• Normalization Factor: It provides a standard measurement for the amount of calcium when assessing water hardness.

Utilizing calcium carbonate simplifies the conversion process into the molarity and therefore standardizes water hardness testing.

Volumetric Flask

Volumetric flasks are essential laboratory equipment used for preparing precise chemical solutions. They are specifically designed to accurately contain a definite volume of liquid at a particular temperature, marked by the calibration line etched around the neck.
In the context of the molarity calculation of calcium ions, a volumetric flask helps ensure that the solution is diluted correctly and uniformly to 250 mL, ensuring accuracy for lab experiments.

• Design: The flask has a narrow neck to reduce the error during the measurement of liquids.
• Usage: It is often used when preparing solutions to ensure exact concentrations, such as calibrating standard solutions for experiments.

The use of a 250.0 mL volumetric flask in the exercise ensures that the molarity reflects the true concentration of dissolved ions.

Hydrochloric Acid

Hydrochloric acid (\(\text{HCl}\)) is a strong, highly acidic solution of hydrogen chloride in water. It is a fundamental reagent in many chemical processes and is often used in laboratories to dissolve compounds, as in the exercise described.
The role of hydrochloric acid in this specific task is to dissolve calcium carbonate completely, thereby releasing calcium ions into the solution. This is an essential step to prepare the water sample for hardness measurement.

• Reactivity: It reacts readily with calcium carbonate, resulting in calcium chloride, water, and carbon dioxide, which simplifies the ionization process.
• Function in Molarity Calculation: It ensures the complete dissolution of the sample, leading to accurate molarity determination.

By using hydrochloric acid, the preparation of standard solutions for determining calcium ion molarity is more efficient and precise.