Chemistry question involving molarity?

Question

A solution made by dissolving 16.0 g of CaCl2 in 64.0g of water has a density of 1.180g/mL at 20 degrees C.

What is the molarity of CaCl2 in the solution?

the answer is : 2.13 M CaCl2

How do u get this?

any help apreciated!

Answer 1

Total mass of solution = 16.0 + 64.0 g = 80.0 g

Density of solution = 1.180 g/ml

Density = mass / volume, so a 1.180 g/ml density means that every ml weighs 1.180 g

use this to work out volume

Volume of solution (let y = volume)

80 g / y ml = 1.180 / 1

therefore y ml = 80 g / (1.180 / 1)

= 67.80 ml of solution

Now Molarity = moles / litres of solution

moles of CaCl2 = mass / molar mass

molar mass CaCl2 = 40.08 + (35.45 x 2) = 110.98 g/mol

moles = 16.0 g / 110.98 g/mol

moles CaCl2 = 0.144 moles

Molarity = moles / litres of solution

M = 0.144 / 0.0678 L

= 2.13 M

Answer 2

16.0 g CaCl2 / 110.986 g/mol = 0.144 mol CaCl2

solution mass = 16.0 + 64.0 = 80.0 g

80.0g x 1.180 g/mL = 94.4 mL

0.144 mol / 0.0944 L = 1.525 M

The correct answer is 1.525 M not 2.13 M