Question

A 12.5-gram sample of CaCl2 is dissolved in enough water to produce a solution of 0.50 M. What is the volume of the solution?

Answer 1

To find the volume of the solution when a 12.5-gram sample of CaCl₂ is dissolved to achieve a 0.50 M concentration, we first need to determine the number of moles of CaCl₂ in 12.5 grams.

1. **Calculate the molar mass of CaCl₂**:

- Calcium (Ca): 40.08 g/mol
- Chlorine (Cl): 35.45 g/mol (there are 2 Cl atoms)

\[
\text{Molar mass of CaCl}_2 = 40.08 \, \text{g/mol} + 2 \times 35.45 \, \text{g/mol}
\]
\[
= 40.08 \, \text{g/mol} + 70.90 \, \text{g/mol} = 110.98 \, \text{g/mol}
\]

2. **Calculate the number of moles of CaCl₂ in 12.5 grams**:

\[
\text{Moles of CaCl}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{12.5 \, \text{g}}{110.98 \, \text{g/mol}} \approx 0.112 \, \text{mol}
\]

3. **Use the concentration to find the volume of the solution**:

We know that molarity (M) is defined as:

\[
M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\]

We can rearrange this to find the volume:

\[
\text{Volume of solution (L)} = \frac{\text{moles of solute}}{M}
\]

Substituting in the values:

\[
\text{Volume} = \frac{0.112 \, \text{mol}}{0.50 \, \text{mol/L}}
\]
\[
= 0.224 \, \text{L}
\]

4. **Convert the volume to milliliters**:

\[
0.224 \, \text{L} \times 1000 \, \text{mL/L} = 224 \, \text{mL}
\]

Therefore, the volume of the solution is **224 mL**.