Problem 23 - Chemistry: An Atoms-Focused Approach

Question

Tap water in North America from groundwater sources contains an average of \(48 \mathrm{mg} / \mathrm{L} \mathrm{Ca}^{2+}\) ion. What is the molarity of calcium ion in this water?

Step-by-Step Solution

Answer

Answer: The molarity of calcium ions in the tap water is approximately 0.001198 M.

Step 1: Find the molar mass of calcium ion

First, we need to find the molar mass of the calcium ion (Ca²⁺). The atomic mass of calcium is 40.08 g/mol. Therefore, the molar mass of Ca²⁺ ion is also 40.08 g/mol.

Step 2: Convert mass concentration to moles

Next, we need to convert the given mass concentration of 48 mg/L to moles. To do this, we can use the equation: moles = (mass concentration) / (molar mass) We have the mass concentration as 48 mg/L and the molar mass of Ca²⁺ as 40.08 g/mol. However, the mass concentration is given in mg, so we need to convert it to grams to match the unit in the denominator: 48 mg = 0.048 g Now we can calculate the moles: moles = (0.048 g) / (40.08 g/mol) = 0.001198 mol

Step 3: Calculate molarity

Now that we have the moles of Ca²⁺ ions, we can calculate the molarity using the equation: Molarity (M) = moles of solute / volume of solution (L) The volume of the solution, in this case, is 1 L (since the mass concentration is given in mg/L). Thus, Molarity (M) = 0.001198 mol / 1 L = 0.001198 M So, the molarity of calcium ions in the tap water is approximately 0.001198 M.

Key Concepts

Calcium Ion

When we talk about ions in chemistry, we refer to atoms or molecules that have an electric charge due to the loss or gain of electrons. Calcium ions, specifically symbolized as \(\text{Ca}^{2+}\), are formed when a calcium atom loses two electrons. This changes the neutral calcium atom into a positively charged ion. Calcium ions are particularly important in groundwater as they contribute to water hardness, which can affect everything from soap efficiency to the health of aquatic environments.

Mass Concentration

Mass concentration is a way to express how much solute is present in a solution. It is given as the mass of solute present per unit volume of solution. In the context of our exercise, the mass concentration of calcium ions in tap water is given as \(48\ \text{mg/L}\). This tells us how much calcium is in each liter of water. Understanding mass concentration is crucial for converting measurements into molarity, as it provides the base for calculating moles, which is the next step in solving these types of problems. Some useful tips include:

• Always pay attention to the units given and ensure they are consistent with what is required for calculations.
• Commonly used units include milligrams per liter (mg/L) for solutions like water.

Molar Mass

Molar mass is a fundamental concept in chemistry, representing the mass of one mole of a given substance. It is expressed in grams per mole (g/mol). For calcium ions \(\text{Ca}^{2+}\), the molar mass is the same as that of a neutral calcium atom, at \(40.08\ \text{g/mol}\). Knowing the molar mass allows us to bridge the gap between mass concentration and molarity, as it enables the conversion of mass to moles. This conversion is crucial because molarity relies on the number of moles of solute, not just the mass. To remember:

• Molar mass is derived from the atomic mass found on the periodic table.
• This is important for calculating the moles from given mass concentrations in solutions.

Solution Volume

The concept of solution volume is equally significant when it comes to calculating molarity. It represents the total volume of the solvent plus the solute within a solution, usually measured in liters (L) when dealing with molarity. In our scenario, the solution volume is implicitly considered to be \(1\ \text{L}\) because the mass concentration is specified per liter of water—\(48\ \text{mg/L}\). This simplifies the calculation because it means the mol value calculated directly translates into molarity without additional conversion. Key considerations:

• Always double-check the unit of volume to ensure it is suitable for molarity calculations (L is the standard).
• Volume consistency helps maintain accuracy in converting between different concentrations and when performing dilution calculations.