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.
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Calculate the molar mass of CaCl₂:
- Calcium (Ca): 40.08 g/mol
- Chlorine (Cl): 35.45 g/mol (there are 2 Cl atoms)
\[ \text{Molar mass of CaCl}_2 = 40.08 , \text{g/mol} + 2 \times 35.45 , \text{g/mol} \] \[ = 40.08 , \text{g/mol} + 70.90 , \text{g/mol} = 110.98 , \text{g/mol} \]
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Calculate the number of moles of CaCl₂ in 12.5 grams:
\[ \text{Moles of CaCl}_2 = \frac{\text{mass}}{\text{molar mass}} = \frac{12.5 , \text{g}}{110.98 , \text{g/mol}} \approx 0.112 , \text{mol} \]
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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:
\[ \text{Volume} = \frac{0.112 , \text{mol}}{0.50 , \text{mol/L}} \] \[ = 0.224 , \text{L} \]
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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.