(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.... (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?
Understand the Problem
The question is asking us to calculate the concentrations of the dissociation products of calcium chloride and calcium sulfate in three different units (mg/L, millimolar, and normal). Additionally, we need to determine the mole fractions of several ions and water in the solution given that the total molar concentration is the same as in pure water.
Answer
Concentration calculations depend on the input values; typically, you can find concentrations in mg/L, mM, and normality. Mole fractions for ions follow the dissociation relation shown above.
Answer for screen readers
The concentrations of the dissociation products can vary based on the input values, but generally, you would calculate:
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Concentration of $Ca^{2+}$ in mg/L = (moles of $\text{CaCl}_2 + \text{CaSO}_4$) * (molar mass of calcium) * 1000
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Concentration in millimolar (mM) = Concentration in molarity (mol/L) * 1000 for respective ions.
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Normality (N) = Concentration in molarity (mol/L) for $\text{Ca}^{2+}$.
The mole fractions will depend on the total number of moles you compute as described.
Steps to Solve
- Identify the dissociation of compounds
Calcium chloride ($\text{CaCl}_2$) dissociates into calcium ions ($\text{Ca}^{2+}$) and chloride ions ($\text{Cl}^-$).
The dissociation can be represented as: $$ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- $$
Calcium sulfate ($\text{CaSO}_4$) dissociates into calcium ions and sulfate ions ($\text{SO}_4^{2-}$): $$ \text{CaSO}_4 \rightarrow \text{Ca}^{2+} + \text{SO}_4^{2-} $$
- Calculate total moles of ions
For calcium chloride, you get 3 moles of ions for every mole of $\text{CaCl}_2$ (1 $\text{Ca}^{2+}$ and 2 $\text{Cl}^-$).
For calcium sulfate, you get 2 moles of ions for every mole of $\text{CaSO}_4$ (1 $\text{Ca}^{2+}$ and 1 $\text{SO}_4^{2-}$).
For a solution with mixtures of these salts, the total number of dissolves ions will be the sum of their contributions.
- Calculate concentrations in mg/L
To convert to mg/L, use the molar mass of each compound:
- Molar mass of $\text{CaCl}_2 \approx 110.98 \text{ g/mol}$
- Molar mass of $\text{CaSO}_4 \approx 136.14 \text{ g/mol}$
For a given concentration $C$ in mol/L, the concentration in mg/L would be calculated as: $$ \text{Concentration (mg/L)} = C \times \text{Molar Mass (g/mol)} \times 1000 $$
- Convert to millimolar (mM) and normal (N)
1 millimolar (mM) is equal to 0.001 mol/L. For normality (N), since these are diprotic systems for calcium chloride and calcium sulfate, normality will equal molarity in this case as they both give 2 equivalents of reactants (1 for $\text{Ca}^{2+}$ and 1 for each chloride and sulfate).
- Calculate mole fractions
The mole fraction ($X$) of an ion is calculated as: $$ X_{ion} = \frac{\text{moles of } ion}{\text{total moles of all dissolved species}} $$
Make sure to account for all ions and water, which can be approximated as having a concentration based on the total molarity of water.
The concentrations of the dissociation products can vary based on the input values, but generally, you would calculate:
-
Concentration of $Ca^{2+}$ in mg/L = (moles of $\text{CaCl}_2 + \text{CaSO}_4$) * (molar mass of calcium) * 1000
-
Concentration in millimolar (mM) = Concentration in molarity (mol/L) * 1000 for respective ions.
-
Normality (N) = Concentration in molarity (mol/L) for $\text{Ca}^{2+}$.
The mole fractions will depend on the total number of moles you compute as described.
More Information
The calculations involve understanding how salts dissociate in solution and how to convert between different concentration units. Calcium chloride and calcium sulfate are common compounds studied in chemistry, especially in contexts involving ionic solutions and solubility.
Tips
- Forgetting to account for the total number of ions produced from dissociation can lead to underestimating concentrations.
- Miscalculating molar masses or units during conversion can lead to incorrect final answers.
- Neglecting the contribution of water to the total volume when calculating mole fractions can result in errors.
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