To determine the required volume to dilute the 43.5mL of a 4.20M KI solution, we need to use the concept of dilution and the formula:
CiVi = CfVf
Where:
Ci = initial concentration of the solution before dilution
Vi = initial volume of the solution before dilution
Cf = final concentration of the solution after dilution
Vf = final volume of the solution after dilution
Given:
Ci = 4.20M
Vi = 43.5mL
We need to solve for Vf, the final volume of the solution after dilution.
Step 1: Convert mL to L
To maintain consistent units, we need to convert mL to L:
Vi = 43.5mL * (1L / 1000mL)
Vi = 0.0435L
Step 2: Calculate the final concentration (Cf) after dilution.
We have the final concentration (Cf) as 2.80g/L, and we need to find the final volume, Vf.
Step 3: Substitute the values into the formula and solve for Vf.
CiVi = CfVf
(4.20M)(0.0435L) = (2.80g/L)(Vf)
Step 4: Convert grams to moles
Since we are given the mass in grams, we need to convert it to moles using the molar mass.
Molar mass of KI:
K (potassium) = 39.10 g/mol
I (iodine) = 126.90 g/mol
Molar mass of KI = 39.10 g/mol + 126.90 g/mol = 166.00 g/mol
Step 5: Calculate the number of moles of KI required.
Number of moles = mass / molar mass
Number of moles = 2.80g / 166.00 g/mol
Step 6: Calculate the final volume (Vf).
(4.20M)(0.0435L) = (2.80g / 166.00 g/mol)(Vf)
Vf = (4.20M)(0.0435L)(166.00 g/mol) / (2.80g)
Vf ≈ 35.359 L
Therefore, you need to dilute the 43.5mL of a 4.20M KI solution to a volume of approximately 35.359 L so that 24.0mL of the diluted solution contains 2.80g of KI.