Concentration of Ions in a Mixed Solution: A Detailed Calculation

In this article, we will delve into the process of calculating the final concentrations of various ions in a mixed solution, specifically when 9.45 grams of NaCl are dissolved into 1.0 liter of water and then mixed with 800.0 mL of 0.75 M AlCl3 solution. Understanding these calculations is crucial in chemistry and applicable across numerous scientific fields. This article will provide a detailed step-by-step guide to solve the problem.

Problem

Given:

9.45 grams of NaCl are dissolved into 1.0 L of water. 800.0 mL of 0.75 M AlCl3 solution is added.

We need to determine the final concentrations of all ions in the resulting solution.

Calculation of Initial Concentrations

First, let's calculate the concentration of NaCl in the initial solution:

Calculate the number of moles of NaCl: Molecular weight of NaCl: 58.5 g/mol Number of moles: ( frac{9.45 , text{g}}{58.5 , text{g/mol}} 0.162 , text{mol} ) Initial concentration of NaCl: ( frac{0.162 , text{mol}}{1.0 , text{L}} 0.162 , text{M} )

Mixing the Solutions

Now, we will mix these two solutions. The total volume of the resulting solution is 1.8 L (1.0 L 0.8 L), and we need to calculate the concentrations of the ions after mixing.

Na Ions

Na ions come from the NaCl solution:

Initial concentration of NaCl: 0.162 M Total volume: 1.8 L Final concentration of NaCl: ( frac{0.162 , text{M} times 1.0 , text{L}}{1.8 , text{L}} 0.0897 , text{M} )

Al3 Ions

Al3 ions come from the AlCl3 solution:

Initial concentration of AlCl3: 0.75 M Initial volume of AlCl3: 0.8 L Total volume: 1.8 L Final concentration of AlCl3: ( frac{0.75 , text{M} times 0.8 , text{L}}{1.8 , text{L}} 0.33 , text{M} )

Since each AlCl3 molecule dissociates into 1 Al3 and 3 Cl-, the concentration of Al3 ions will be:

Final concentration of Al3 : 0.33 M

Cl- Ions

Cl- ions come from both NaCl and AlCl3 solutions:

From NaCl: ( text{Initial concentration of NaCl} times frac{text{Volume of NaCl solution}}{text{Total volume}} 0.0897 , text{M} ) From AlCl3: ( text{Final concentration of AlCl3} times 3 0.33 , text{M} times 3 0.99 , text{M} ) Total concentration of Cl-: ( 0.0897 , text{M} 0.99 , text{M} 1.0797 , text{M} )

Summary of Final Concentrations

N : 0.0897 M Al3 : 0.33 M Cl-: 1.0797 M

Conclusion

This detailed calculation demonstrates how to determine the final concentrations of ions in a mixed solution. Understanding these concepts is fundamental in various chemical processes and helps in solving complex problems in laboratory settings and real-world applications. These calculations are important in fields such as environmental science, pharmaceuticals, and industrial chemistry.