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Answer :
To find the volume of a 0.758 M solution of CaCl₂ that contains 1.28 grams of solute, we can follow these steps:
1. Calculate the Molar Mass of CaCl₂:
The molar mass of CaCl₂ is the sum of the molar masses of one calcium (Ca) atom and two chlorine (Cl) atoms.
- Calcium (Ca) has a molar mass of approximately 40.08 g/mol.
- Chlorine (Cl) has a molar mass of approximately 35.45 g/mol.
So, the molar mass of CaCl₂ = 40.08 + 2 * 35.45 = 110.98 g/mol.
2. Determine the Moles of CaCl₂:
Use the mass of CaCl₂ to find the number of moles.
[tex]\[
\text{Moles of CaCl}_2 = \frac{\text{mass of CaCl}_2}{\text{molar mass of CaCl}_2} = \frac{1.28 \, \text{g}}{110.98 \, \text{g/mol}} \approx 0.01153 \, \text{moles}
\][/tex]
3. Use Molarity to Find Volume:
Recall that molarity (M) is defined as moles of solute per liter of solution. We can rearrange this definition to find the volume of the solution:
[tex]\[
\text{Volume of solution} = \frac{\text{moles of solute}}{\text{Molarity}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Volume of solution in liters} = \frac{0.01153 \, \text{moles}}{0.758 \, \text{M}} \approx 0.0152 \, \text{L}
\][/tex]
4. Convert Volume to Milliliters:
Since 1 liter = 1000 milliliters, convert the volume from liters to milliliters:
[tex]\[
\text{Volume in milliliters} = 0.0152 \, \text{L} \times 1000 \approx 15.2 \, \text{mL}
\][/tex]
Therefore, the volume of a 0.758 M solution of CaCl₂ that contains 1.28 grams of solute is approximately 15.2 mL.
1. Calculate the Molar Mass of CaCl₂:
The molar mass of CaCl₂ is the sum of the molar masses of one calcium (Ca) atom and two chlorine (Cl) atoms.
- Calcium (Ca) has a molar mass of approximately 40.08 g/mol.
- Chlorine (Cl) has a molar mass of approximately 35.45 g/mol.
So, the molar mass of CaCl₂ = 40.08 + 2 * 35.45 = 110.98 g/mol.
2. Determine the Moles of CaCl₂:
Use the mass of CaCl₂ to find the number of moles.
[tex]\[
\text{Moles of CaCl}_2 = \frac{\text{mass of CaCl}_2}{\text{molar mass of CaCl}_2} = \frac{1.28 \, \text{g}}{110.98 \, \text{g/mol}} \approx 0.01153 \, \text{moles}
\][/tex]
3. Use Molarity to Find Volume:
Recall that molarity (M) is defined as moles of solute per liter of solution. We can rearrange this definition to find the volume of the solution:
[tex]\[
\text{Volume of solution} = \frac{\text{moles of solute}}{\text{Molarity}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Volume of solution in liters} = \frac{0.01153 \, \text{moles}}{0.758 \, \text{M}} \approx 0.0152 \, \text{L}
\][/tex]
4. Convert Volume to Milliliters:
Since 1 liter = 1000 milliliters, convert the volume from liters to milliliters:
[tex]\[
\text{Volume in milliliters} = 0.0152 \, \text{L} \times 1000 \approx 15.2 \, \text{mL}
\][/tex]
Therefore, the volume of a 0.758 M solution of CaCl₂ that contains 1.28 grams of solute is approximately 15.2 mL.
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