Question

A 325-mL sample of solution contains \(25.3 \mathrm{~g}\) of \(\mathrm{CaCl}_{2}\). (a) Calculate the molar concentration of \(\mathrm{Cl}^{-}\) in this solution. (b) How many grams of \(\mathrm{Cl}^{-}\) are in \(0.100 \mathrm{~L}\) of this solution?

Short answer

The molar concentration of Cl- ions is 1.403 M and there are 4.97 g of Cl- ions in 0.100 L of the solution.

Step-by-step solution

Calculate the molar mass of CaCl2 and Cl-

To solve these types of problems, you first need to find the molar mass of the compound (CaCl2) and the ion (Cl-) itself. For CaCl2, it can be calculated as \((40.08 \mathrm{~g/mol~Ca} + 2(35.453 \mathrm{~g/mol~Cl})) = 110.986 \mathrm{~g/mol}\). For Cl-, it's \(35.453 \mathrm{~g/mol}\).

Calculate the moles of CaCl2

Next, calculate the moles of CaCl2 in the solution using the formula, moles=\(mass/molar~mass\), plug the values into the formula: \(moles = 25.3 \mathrm{~g} / 110.986 \mathrm{~g/mol} = 0.228 \mathrm{~mol}\).

Calculate the molar concentration of Cl-

Next, you need to calculate the molar concentration of Cl-. Since \(\mathrm{CaCl}_2\) dissociates into one \(\mathrm{Ca}^{2+}\) ion and two \(\mathrm{Cl}^{-}\) ions, there will be twice as many moles of \(\mathrm{Cl}^{-}\) ions as there are moles of \(\mathrm{CaCl}_2\). So, the number of moles of Cl is \(0.228 \mathrm{~mol} × 2 = 0.456 \mathrm{~mol}\). Now, calculate the molar concentration by dividing the moles of Cl by the volume of the solution in liters. The volume of the solution is 325 mL, which is equal to 0.325 L. So, the molar concentration of Cl is \(0.456 \mathrm{~mol} / 0.325 \mathrm{~L} = 1.403 \mathrm{~M}\).

Calculate the mass of Cl- in 0.100 L of the solution

For the second part of the problem, you are asked to calculate the mass of Cl- ions in a 0.100 L sample of the solution. Using the molarity calculated earlier, the number of moles of Cl- in 0.100 L of the solution can be found, which is \(1.403 \mathrm{~M} × 0.100 \mathrm{~L} = 0.1403 \mathrm{~mol}\). Now, change the moles of Cl- to grams using the molar mass of Cl- (\(35.453 \mathrm{~g/mol}\)). The mass of Cl- ions is \(0.1403 \mathrm{~mol} × 35.453 \mathrm{~g/mol} = 4.97 \mathrm{~g}\).