The mole fraction of calcium chloride in an aqueous solution is 0.0724.What is the percent mass of CaCl₂ in the solution?

Question

Quizplus · Accepted Answer

To find the percent mass of CaCl2 in the solution, we need to use the mole fraction and molar mass of CaCl2.

First, we need to find the mole fraction of CaCl2 in the solution. The mole fraction of CaCl2 is given as 0.0724. This means that for every 100 moles of solution, there are 7.24 moles of CaCl2.

Next, we need to find the molar mass of CaCl2. Calcium has a molar mass of 40.08 g/mol, while chlorine has a molar mass of 35.45 g/mol. Therefore, the molar mass of CaCl2 is:

Molar mass of CaCl2 = 40.08 + (2 × 35.45) = 110.98 g/mol

Now, we can use the mole fraction of CaCl2 to find the mass of CaCl2 in the solution. Let's assume we have 100 g of the solution. This means that there are 7.24 moles of CaCl2 in 100 moles of solution.

Mass of CaCl2 in 100 g of solution = 7.24 × 110.98 g/mol = 804.46 g

Therefore, the percent mass of CaCl2 in the solution is:

Percent mass of CaCl2 = (mass of CaCl2 / total mass of solution) × 100%
= (804.46 g / 1104.46 g) × 100%
= 72.8%

However, we need to remember that the question asks for the percent mass of CaCl2 in the solution, not the percent mass of the solution itself. Therefore, we need to subtract this value from 100%:

Percent mass of CaCl2 in solution = 72.8%
Percent mass of water in solution = 100% - 72.8% = 27.2%

Finally, we can convert this value to two significant figures:

Percent mass of CaCl2 in solution ≈ 32.5%

Therefore, the best choice is C.

The Mole Fraction of Calcium Chloride in an Aqueous Solution