Calculating the Final Concentration of Chloride Ions in a Barium Chloride Solution

The calculation of the final concentration of chloride ions in a solution after dilution is a common problem in chemistry, particularly in the context of understanding solubility and concentration principles. To understand how to calculate this concentration, we will delve into a specific example involving barium chloride (BaCl2).

Example Problem

Let's consider the following scenario: How would you calculate the final concentration of chloride ions in a solution when 15.0 mL of a 6.00 M solution of barium chloride (BaCl2) is diluted to 100.0 mL?

Step 1: Determine the Number of Moles of Barium Chloride (BaCl2) in the Original Solution

The first step is to find the number of moles of barium chloride in the original solution. This can be done using the formula:

Moles of BaCl2 Concentration (M) × Volume (L)

In the initial solution:

Concentration of BaCl2 6.00 M Volume 15.0 mL 0.0150 L (Note: 1 mL 0.001 L)

Moles of BaCl2 6.00 M × 0.0150 L 0.0900 moles

Step 2: Calculate the Number of Moles of Chloride Ions (Cl-) Produced

Each mole of barium chloride (BaCl2) produces 2 moles of chloride ions (Cl-). Therefore, we can calculate the total moles of chloride ions:

Moles of Cl- 2 × Moles of BaCl2 2 × 0.0900 moles 0.1800 moles

Step 3: Calculate the Final Concentration of Chloride Ions

The final volume of the solution after dilution is 100.0 mL 0.1000 L. We can now find the final concentration of chloride ions using the formula:

Final Concentration (M) Moles of Cl- / Final Volume (L)

Final Concentration (M) 0.1800 moles / 0.1000 L 1.80 M

Conclusion

The final concentration of chloride ions in the solution will be 1.80 M.

Let's explore another example with different values to further illustrate this concept.

Additional Example

Consider an example where the concentration of barium chloride (BaCl2) is 1.15 M and the volume is 35 mL. The initial number of moles can be calculated as:

VM mol

0.035 L × 1.15 M 0.04 mol BaCl2

If the solution is then diluted till 100 mL, the new molarity can be calculated using:

0.04 mol / 0.1 L 0.4 mol/L BaCl2

Therefore, the concentration of chloride ions in the new solution would be:

[Cl-] 0.4 x 2 0.8 mol/L

Final Note

It is important to note that in practice, it can be challenging to achieve very high concentrations of barium chloride due to its solubility limits. However, for the purpose of this discussion, we are focusing on the calculation method.

Understanding how to dilute solutions and calculate concentrations is crucial in various chemical applications, including pharmaceuticals, environmental testing, and more. By mastering these calculations, chemists can ensure accurate and precise work, which is vital for reproducibility and reliability in experiments and research.