Questions: 67 g CaCl2 is dissolved in water to generate a 0.50 M solution. What is the volume of the solution, in liters?

Transcript text: $67 \mathrm{~g} \mathrm{CaCl}_{2}$ is dissolved in water to generate a 0.50 M solution. What is the volume of the solution, in liters?

Solution

Solution Steps

Step 1: Determine the Molar Mass of CaCl$_2$

First, we need to calculate the molar mass of calcium chloride (CaCl$_2$):

Calcium (Ca): $40.08 \, \text{g/mol}$
Chlorine (Cl): $35.45 \, \text{g/mol}$

The molar mass of CaCl$_2$ is: \[ 40.08 + 2 \times 35.45 = 40.08 + 70.90 = 110.98 \, \text{g/mol} \]

Step 2: Calculate the Number of Moles of CaCl$_2$

Next, we calculate the number of moles of CaCl$_2$ in 67 grams: \[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{67 \, \text{g}}{110.98 \, \text{g/mol}} = 0.6037 \, \text{mol} \]

Step 3: Calculate the Volume of the Solution

We know the molarity (M) of the solution is 0.50 M, and we have the number of moles. The volume $V$ in liters can be found using the formula: \[ M = \frac{\text{moles}}{V} \] Rearranging for $V$: \[ V = \frac{\text{moles}}{M} = \frac{0.6037 \, \text{mol}}{0.50 \, \text{M}} = 1.2074 \, \text{L} \]

Step 4: Round to Two Significant Figures

Finally, we round the volume to two significant figures: \[ 1.2074 \, \text{L} \approx 1.2 \, \text{L} \]