Problem 20 - Chemistry Matter and Change

Question

How many grams of \(\mathrm{CaCl}_{2}\) would be dissolved in 1.0 \(\mathrm{L}\) of a 0.10 \(\mathrm{M}\) solution of \(\mathrm{CaCl}_{2} ?\)

Step-by-Step Solution

Answer

Approximately 11.10 grams of CaCl2 would be dissolved in 1.0 L of a 0.10 M solution of CaCl2.

Step 1: Write down the given information

We are given: - Molarity (M) = 0.10 M - Volume (V) = 1.0 L

Step 2: Find the moles of CaCl2

To determine the moles of CaCl2, we can use the formula: moles = molarity × volume moles = 0.10 mol/L × 1.0 L moles = 0.10 mol

Step 3: Calculate the molar mass of CaCl2

CaCl2 consists of 1 calcium atom and 2 chlorine atoms. The molar mass of each element is: - Molar mass of Calcium (Ca) = 40.08 g/mol - Molar mass of Chlorine (Cl) = 35.45 g/mol So, the molar mass of CaCl2 is: Molar mass of CaCl2 = (1 × 40.08) + (2 × 35.45) Molar mass of CaCl2 = 40.08 + 70.90 Molar mass of CaCl2 = 110.98 g/mol

Step 4: Calculate the mass of CaCl2

Now that we have the moles and molar mass, we can determine the mass: mass = moles × molar mass mass = 0.10 mol × 110.98 g/mol mass = 11.098 g

Step 5: Round the answer

Let's round the answer to two decimal places: mass ≈ 11.10 g So, approximately 11.10 grams of CaCl2 would be dissolved in 1.0 L of a 0.10 M solution of CaCl2.

Key Concepts

Moles calculation

Calculating moles is a key step in understanding solutions in chemistry. The mole is a standard unit for amount of substance used in chemistry, often symbolized as \( n \). To find the number of moles for a given chemical solution, you can use the formula:

\( \text{moles (n)} = \text{molarity (M)} \times \text{volume (V)} \)

Molarity refers to the concentration of the solution, expressed as moles per liter (mol/L), while volume should be in liters.Let's apply this using our example: If we have a solution with a molarity of \(0.10 \text{ M}\) and a volume of \(1.0 \text{ L}\), the number of moles of \(\mathrm{CaCl}_{2}\) is calculated as:

\( \text{moles} = 0.10 \text{ mol/L} \times 1.0 \text{ L} = 0.10 \text{ mol} \)

It's important to ensure that volumes are always converted to liters to match the units of molarity. This calculation provides the basis for understanding how much of a substance is present in a chemical solution.

Molar mass

Molar mass is the weight of one mole of a given substance and is expressed in grams per mole (g/mol). To determine the molar mass, you add up the atomic masses of each element in a molecule based on its chemical formula.In the case of \(\mathrm{CaCl}_{2}\), we need to consider:

• The atomic mass of calcium (Ca), which is \(40.08 \text{ g/mol}\).
• The atomic mass of chlorine (Cl), which is \(35.45 \text{ g/mol}\).

For \(\mathrm{CaCl}_{2}\), consisting of one calcium and two chlorines, the calculation becomes:

\( \text{Molar mass of } \mathrm{CaCl}_{2} = (1 \times 40.08) + (2 \times 35.45) = 110.98 \text{ g/mol} \)

Understanding molar mass allows us to convert between moles and grams, facilitating the calculation of how much material we need or have.

Chemical solution preparation

Preparing a chemical solution requires knowledge of both the concentration (molarity) and the total volume you want to create. This process involves calculating the precise amount of solute - in grams - to be dissolved in a solvent.To determine how many grams of \(\mathrm{CaCl}_{2}\) you need, follow these steps:

• First, calculate the moles required using the desired molarity and volume: \(0.10 \text{ mol/L} \times 1.0 \text{ L} = 0.10 \text{ mol}\).
• Then, convert moles to grams using the molar mass calculated:\( \text{mass} = \text{moles} \times \text{molar mass} \).
• For \(\mathrm{CaCl}_{2}\), with a molar mass of \(110.98 \text{ g/mol}\), the calculation is: \( \text{mass} = 0.10 \text{ mol} \times 110.98 \text{ g/mol} = 11.10 \text{ g}\).

Now you know how to formulate a solution with the right concentration, which is crucial for experiments and reactions in chemistry.