To determine the volume of a 1.5 M [tex]\( \text{CaCl}_2 \)[/tex] solution that can be prepared using 1200.0 g of [tex]\( \text{CaCl}_2 \)[/tex], follow these steps:
1. Calculate the number of moles of [tex]\( \text{CaCl}_2 \)[/tex]:
- Given the mass of [tex]\( \text{CaCl}_2 \)[/tex] is 1200.0 grams.
- The molecular weight of [tex]\( \text{CaCl}_2 \)[/tex] is 110.98 g/mol.
The formula to find the number of moles is:
[tex]\[
\text{moles of } \text{CaCl}_2 = \frac{\text{mass of } \text{CaCl}_2}{\text{molecular weight of } \text{CaCl}_2}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of } \text{CaCl}_2 = \frac{1200.0 \text{ g}}{110.98 \text{ g/mol}} \approx 10.813 \text{ moles}
\][/tex]
2. Calculate the volume of the solution in liters:
- Given the molarity (M) of the [tex]\( \text{CaCl}_2 \)[/tex] solution is 1.5 M.
- The formula for molarity is:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
Rearrange this formula to find the volume of the solution:
[tex]\[
\text{volume of solution in liters} = \frac{\text{moles of solute}}{\text{molarity}}
\][/tex]
Substituting the known values:
[tex]\[
\text{volume of solution in liters} = \frac{10.813 \text{ moles}}{1.5 \text{ M}} \approx 7.209 \text{ liters}
\][/tex]
Therefore, the volume of a 1.5 M [tex]\( \text{CaCl}_2 \)[/tex] solution that can be made using 1200.0 g of [tex]\( \text{CaCl}_2 \)[/tex] is approximately 7.209 liters.
