Calculation of Chloride Ion Concentration in Mixed Sodium Chloride and Calcium Chloride Solutions

In this article, we will discuss how to determine the natural concentration of chloride ions (Cl-) in a solution formed by mixing 100 mL of NaCl (N/10) and 100 mL of CaCl2 (M/10) solutions. This process involves understanding the dissociation of these salts in water and calculating the moles of chloride ions contributed by each solution.

Introduction to the Problem

We start with a 100 mL N/10 NaCl (Sodium Chloride) solution and a 100 mL M/10 CaCl2 (Calcium Chloride) solution. Our goal is to find the concentration of chloride ions in the resulting solution after mixing the two solutions.

Step-by-Step Calculation

Step 1: Calculate Moles of Chloride Ions from NaCl

NaCl dissociates in water as follows:

nNaCl → Na Cl-

Given:

Normality (N) of NaCl solution: N/10 0.1 N Volume of NaCl solution: 100 mL 0.1 L

The number of equivalents of NaCl is:

Equivalents Normality × Volume L 0.1 eq/L × 0.1 L 0.01 eq

Since each mole of NaCl produces 1 mole of Cl- ions:

Moles of Cl- 0.01 eq 0.01 mol

Step 2: Calculate Moles of Chloride Ions from CaCl2

Calcium Chloride dissociates in water as follows:

nCaCl2 → Ca2 2 Cl-

Given:

Molarity (M) of CaCl2 solution: M/10 0.1 M Volume of CaCl2 solution: 100 mL 0.1 L

The number of moles of CaCl2 is:

Moles of CaCl2 Molarity × Volume L 0.1 mol/L × 0.1 L 0.01 mol

Since each mole of CaCl2 produces 2 moles of Cl- ions:

Moles of Cl- 0.01 mol × 2 0.02 mol

Step 3: Total Moles of Chloride Ions

Now, we add the moles of Cl- ions from both solutions:

Total moles of Cl- 0.01 mol (from NaCl) 0.02 mol (from CaCl2) 0.03 mol

Step 4: Calculate the Total Volume of the Mixed Solution

The total volume after mixing the two solutions is:

Total Volume 100 mL 100 mL 200 mL 0.2 L

Step 5: Calculate the Concentration of Chloride Ions

Finally, the concentration of chloride ions in the resulting solution can be calculated using the formula:

Concentration C frac{Total moles of Cl-}{Total Volume L} frac{0.03 mol}{0.2 L} 0.15 M

Conclusion

The natural concentration of chloride ions in the resulting solution is 0.15 M.

Additional Information

Understanding the dissociation of salts in water and the calculation of ion concentrations is crucial in various scientific and industrial applications. This process is not only useful in educational contexts but also in practical settings such as water treatment, soil chemistry, and pharmaceutical manufacturing.