An aqueous solution is prepared by adding 110 mg of calcium chloride (CaCl2) and 50 mg of calcium sulfate (CaSO4) to 500 mL of water. The solution pH is 8.0 ([H+] = 10^-8 M; [OH-]... An aqueous solution is prepared by adding 110 mg of calcium chloride (CaCl2) and 50 mg of calcium sulfate (CaSO4) to 500 mL of water. The solution pH is 8.0 ([H+] = 10^-8 M; [OH-] = 10^-6 M). (a) Assuming that the salts dissociate completely, express the concentration of each of the dissociation products (Ca2+, Cl-, and SO42-) in mg/L, millimolar, and normal (N) units. (b) If the total molar concentration of all species in the solution is the same as in pure water, what are the mole fractions of H+, OH-, Ca2+, Cl-, and SO42-, and H2O? Read more

Steps to Solve

1. Calculate moles of calcium chloride (CaCl2)

First, we need to find the number of moles of calcium chloride (CaCl2).

The formula to calculate moles is given by

$$ \text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} $$

The molar mass of CaCl2 is approximately 110.98 g/mol.

For a given mass of ( m ) grams of CaCl2, the number of moles is

$$ \text{moles of CaCl2} = \frac{m}{110.98} $$

2. Calculate moles of calcium sulfate (CaSO4)

Next, we calculate the moles of calcium sulfate (CaSO4) using the same formula.

The molar mass of CaSO4 is approximately 136.14 g/mol.

For a given mass of ( n ) grams of CaSO4, the number of moles is

$$ \text{moles of CaSO4} = \frac{n}{136.14} $$

3. Dissociation products of CaCl2

Calcium chloride dissociates into calcium ions and chloride ions in a 1:2 ratio:

$$ \text{CaCl2} \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- $$

Thus, the concentration of Ca²⁺ ions is equal to the moles of CaCl2, and the concentration of Cl⁻ ions is twice the moles of CaCl2.

4. Dissociation products of CaSO4

Calcium sulfate dissociates into calcium ions and sulfate ions in a 1:1 ratio:

$$ \text{CaSO4} \rightarrow \text{Ca}^{2+} + \text{SO4}^{2-} $$

So, the concentration of Ca²⁺ ions from CaSO4 is equal to the moles of CaSO4, and the concentration of SO₄²⁻ ions is also equal to the moles of CaSO4.

5. Total concentrations of ions

Now, we need to sum up the contributions of all ions. Let's denote ( C_{Ca²+} ) as the total concentration of calcium ions, ( C_{Cl^-} ) as the concentration of chloride ions, ( C_{SO₄²-} ) as the concentration of sulfate ions.

Using the above dissociation data:

$$ C_{Ca^{2+}} = \text{moles of CaCl2} + \text{moles of CaSO4} $$

$$ C_{Cl^-} = 2 \times \text{moles of CaCl2} $$

$$ C_{SO₄^{2-}} = \text{moles of CaSO4} $$

6. Convert units of concentration

Next, we convert the concentrations into other units like mg/L, millimolar (mM), and normal units (N).

For mg/L:

$$ \text{mg/L} = \text{molar concentration (mol/L)} \times \sqrt{ \text{molar mass (g/mol)} } \times 1000 $$

For millimolar:

$$ \text{millimolar} = \text{mol/L} \times 1000 $$

For normal:

$$ N = \text{equivalents/L} = \text{moles/L} \times \text{valence} $$

7. Calculate mole fractions

Finally, we calculate the mole fractions of different ions and water using:

$$ \text{mole fraction of } A = \frac{\text{moles of } A}{\text{total moles}} $$

For example, the mole fraction of ( Ca^{2+} ) will be:

$$ X_{Ca^{2+}} = \frac{C_{Ca^{2+}}}{C_{Ca^{2+}} + C_{Cl^-} + C_{SO₄^{2-}} + C_{H2O}} $$

Where ( C_{H2O} ) represents the moles of water in the solution.