Answer :
Certainly! Let's solve this step-by-step:
1. Determine the Volume of Solution per Beaker in Liters:
Each beaker must contain 250 mL of solution.
Since there are 1000 milliliters in a liter, we convert 250 mL to liters:
[tex]\[ 250 \, \text{mL} = \frac{250}{1000} \, \text{L} = 0.25 \, \text{L} \][/tex]
2. Calculate the Total Volume of Solution Needed:
There are 10 beakers, and each beaker contains 0.25 liters of solution. So, the total volume [tex]\( V_{\text{total}} \)[/tex] is:
[tex]\[ V_{\text{total}} = 10 \times 0.25 \, \text{L} = 2.5 \, \text{L} \][/tex]
3. Determine the Moles of [tex]\( \text{CaCl}_2 \)[/tex] Needed:
We are given that the molarity [tex]\( M \)[/tex] of the [tex]\( \text{CaCl}_2 \)[/tex] solution is 0.720 M. Molarity is defined as moles of solute per liter of solution:
[tex]\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Solving for moles of solute [tex]\( n \)[/tex]:
[tex]\[ n = M \times V_{\text{total}} = 0.720 \, \text{M} \times 2.5 \, \text{L} = 1.8 \, \text{moles} \][/tex]
4. Calculate the Mass of [tex]\( \text{CaCl}_2 \)[/tex] Needed:
The molar mass of [tex]\( \text{CaCl}_2 \)[/tex] is 110.98 g/mol. To find the mass [tex]\( m \)[/tex]:
[tex]\[ m = \text{moles} \times \text{molar mass} = 1.8 \, \text{moles} \times 110.98 \, \text{g/mol} \][/tex]
Performing this calculation:
[tex]\[ m \approx 199.76 \, \text{g} \][/tex]
Therefore, the mass of [tex]\( \text{CaCl}_2 \)[/tex] needed for the solution is approximately 200 grams. Thus, the correct choice from the given options is:
[tex]\[ \boxed{200 \, \text{g}} \][/tex]
1. Determine the Volume of Solution per Beaker in Liters:
Each beaker must contain 250 mL of solution.
Since there are 1000 milliliters in a liter, we convert 250 mL to liters:
[tex]\[ 250 \, \text{mL} = \frac{250}{1000} \, \text{L} = 0.25 \, \text{L} \][/tex]
2. Calculate the Total Volume of Solution Needed:
There are 10 beakers, and each beaker contains 0.25 liters of solution. So, the total volume [tex]\( V_{\text{total}} \)[/tex] is:
[tex]\[ V_{\text{total}} = 10 \times 0.25 \, \text{L} = 2.5 \, \text{L} \][/tex]
3. Determine the Moles of [tex]\( \text{CaCl}_2 \)[/tex] Needed:
We are given that the molarity [tex]\( M \)[/tex] of the [tex]\( \text{CaCl}_2 \)[/tex] solution is 0.720 M. Molarity is defined as moles of solute per liter of solution:
[tex]\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Solving for moles of solute [tex]\( n \)[/tex]:
[tex]\[ n = M \times V_{\text{total}} = 0.720 \, \text{M} \times 2.5 \, \text{L} = 1.8 \, \text{moles} \][/tex]
4. Calculate the Mass of [tex]\( \text{CaCl}_2 \)[/tex] Needed:
The molar mass of [tex]\( \text{CaCl}_2 \)[/tex] is 110.98 g/mol. To find the mass [tex]\( m \)[/tex]:
[tex]\[ m = \text{moles} \times \text{molar mass} = 1.8 \, \text{moles} \times 110.98 \, \text{g/mol} \][/tex]
Performing this calculation:
[tex]\[ m \approx 199.76 \, \text{g} \][/tex]
Therefore, the mass of [tex]\( \text{CaCl}_2 \)[/tex] needed for the solution is approximately 200 grams. Thus, the correct choice from the given options is:
[tex]\[ \boxed{200 \, \text{g}} \][/tex]
