Question

How many grams of ${\mathrm{CaCl}}_2$ would be dissolved in 1.0 $\mathrm{L}$ of a 0.10 $\mathrm{M}$ solution of ${\mathrm{CaCl}}_2?$

Short answer

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

Step-by-step solution

Write down the given information

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

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

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

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

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.