Final answer:
Use the molar mass of CuCl₂ to find the number of moles in 4.73 g, then calculate the concentration in 50.0 ml of the diluted solution. Finally, apply the dilution formula (C₁1V₁1 = C₁2V₁2) with given initial concentration and volume to find the total volume needed to obtain the proper dilution.
Step-by-step explanation:
The goal is determining the volume of a diluted solution when a certain mass of solute is required in a given final volume of that solution. We have an initial volume and concentration of CuCl₂ solution (124 ml of an 8.10 M) and a desired mass of CuCl₂ (4.73 g) in a 50.0 ml sample of the final diluted solution. To solve this, we need to find the final volume (V₂) of the diluted solution.
First, calculate the number of moles in 4.73 g of CuCl₂ using its molar mass.
Number of moles = mass (g) ÷ molar mass (g/mol)
Then, using the desired concentration in the 50.0 ml sample, find the concentration of the entire solution (C₂).
C₂ = moles ÷ volume (L)
Finally, apply the dilution formula (C₁1V₁1 = C₁2V₁2) where C₁1 and V₁1 are the concentration and volume of the initial solution, C₁2 is the concentration of the diluted solution, and V₁2 is the unknown total volume needed.
Using the calculated concentration (C₂) and the initial solution's properties, solve for V₁2 to get the total volume needed to reach the desired concentration.