To calculate the molarity (M) of a solution, we use the formula:

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

Step 1: Calculate moles of $\text{CaCl}_2$

To find the moles of calcium chloride ($\text{CaCl}_2$), use its molar mass:

$\text{{moles}} = \frac{{\text{{mass}}}}{{\text{{molar mass}}}}$

Given:

• Mass of $\text{CaCl}_2$ = 82.0 g
• Molar mass of $\text{CaCl}_2$ = 111.1 g/mol

$\text{{moles of }} \text{CaCl}_2 = \frac{{82.0 \, \text{g}}}{{111.1 \, \text{g/mol}}}$

$\text{{moles of }} \text{CaCl}_2 = 0.738 \, \text{mol}$

Step 2: Convert volume to liters

The volume of the solution is given as 812 mL. To convert this to liters:

$\text{{volume in liters}} = \frac{{812 \, \text{mL}}}{{1000}} = 0.812 \, \text{L}$

Step 3: Calculate the molarity

Now, use the moles of solute and the volume of the solution in liters to find the molarity:

$M = \frac{{0.738 \, \text{mol}}}{{0.812 \, \text{L}}}$

$M \approx 0.909 \, \text{M}$

Final Answer:

The molarity of the solution is approximately 0.909 M.

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How does temperature affect the molarity of a solution?
2. What is the difference between molarity and molality?
3. How would you prepare a 1 M solution of $\text{CaCl}_2$?
4. How does the dissolution of $\text{CaCl}_2$ affect the conductivity of the solution?
5. What role does calcium chloride play in industrial applications?

Tip: Always ensure you convert volumes to liters when calculating molarity, as molarity is expressed in moles per liter.