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In a group assignment, students are required to fill 10 beakers with [tex]$0.720 \, M \, CaCl_2$[/tex]. If the molar mass of [tex]CaCl_2[/tex] is [tex]110.98 \, g/mol[/tex] and each beaker must have [tex]250 \, mL[/tex] of solution, what mass of [tex]CaCl_2[/tex] would be used?

Use [tex]\text{molarity} = \frac{\text{moles of solute}}{\text{liters of solution}}[/tex].

A. [tex]3.13 \, g[/tex]
B. [tex]38.5 \, g[/tex]
C. [tex]200 \, g[/tex]
D. [tex]617 \, g[/tex]

Sagot :

GinnyAnswer
To determine the mass of CaCl₂ needed, we can follow a step-by-step approach:

1. Determine the total volume of the solution:
- Given: Each beaker must have 250 mL of solution and there are 10 beakers.
- First, we convert 250 mL to liters since the molarity is given in terms of liters.
[tex]\[ 250 \text{ mL} = 0.250 \text{ liters} \][/tex]
- Thus, for 10 beakers:
[tex]\[ \text{Total volume} = 10 \times 0.250 \text{ liters} = 2.5 \text{ liters} \][/tex]

2. Calculate the moles of CaCl₂ required:
- The molarity (M) is given as 0.720 M, which means there are 0.720 moles of CaCl₂ in 1 liter of solution.
- To find the number of moles in 2.5 liters:
[tex]\[ \text{Moles of CaCl₂} = \text{Molarity} \times \text{Total volume} \][/tex]
[tex]\[ \text{Moles of CaCl₂} = 0.720 \text{ M} \times 2.5 \text{ liters} = 1.8 \text{ moles} \][/tex]

3. Calculate the mass of CaCl₂ required:
- Given: The molar mass of CaCl₂ is 110.98 g/mol, which means each mole of CaCl₂ weighs 110.98 grams.
- To find the mass for 1.8 moles:
[tex]\[ \text{Mass of CaCl₂} = \text{Moles of CaCl₂} \times \text{Molar mass} \][/tex]
[tex]\[ \text{Mass of CaCl₂} = 1.8 \text{ moles} \times 110.98 \text{ g/mol} = 199.764 \text{ grams} \][/tex]

Hence, the mass of CaCl₂ that would be used is approximately 200 g.

Thus, the correct answer is: [tex]$200 g$[/tex].
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