Sure, let's go through the detailed step-by-step process to calculate the concentration of the calcium chloride ([tex]\( \text{CaCl}_2 \)[/tex]) solution:
Step 1: Determine the mass of the salt
You have 5.55 grams of dry calcium chloride crystals.
Step 2: Calculate the molar mass of calcium chloride
Calcium chloride ([tex]\( \text{CaCl}_2 \)[/tex]) consists of calcium (Ca) and chlorine (Cl). The atomic masses are:
- Calcium (Ca): 40.08 g/mol
- Chlorine (Cl): 35.45 g/mol
Since there are two chlorine atoms in calcium chloride, the molar mass of [tex]\( \text{CaCl}_2 \)[/tex] is:
[tex]\[ 40.08 + 2 \times 35.45 = 110.98 \text{ g/mol} \][/tex]
Step 3: Find the moles of [tex]\( \text{CaCl}_2 \)[/tex]
To find the number of moles of calcium chloride, use the formula:
[tex]\[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \][/tex]
[tex]\[ \text{moles} = \frac{5.55 \text{ g}}{110.98 \text{ g/mol}} = 0.050009010632546404 \text{ mol} \][/tex]
Step 4: Convert the volume of the solution from cm³ to liters
Since there are 1000 cm³ in 1 liter, 750 cm³ is:
[tex]\[ 750 \text{ cm}^3 = 0.750 \text{ L} \][/tex]
Step 5: Calculate the concentration of the solution
The concentration or molarity ([tex]\( M \)[/tex]) is defined as the number of moles of solute per liter of solution.
[tex]\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \][/tex]
[tex]\[ \text{Molarity (M)} = \frac{0.050009010632546404 \text{ mol}}{0.750 \text{ L}} \approx 0.0666786808433952 \text{ M} \][/tex]
Result
The concentration of the calcium chloride solution is approximately 0.0667 M (to four significant figures).
