To what volume should you dilute 124 mL of an 8.10 M CuCl2 solution so that 52.0 mL of the diluted solution contains 5.9 g CuCl2
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To find the volume to which you should dilute the original solution, we can use the formula for dilution:
C1V1 = C2V2
Where:
C1 = initial concentration of the solution
V1 = initial volume of the solution
C2 = final concentration of the solution
V2 = final volume of the solution
Given:
C1 = 8.10 M
V1 = 124 mL
C2 = concentration is not given, but we can find it using the mass of CuCl2
V2 = 52.0 mL
Mass of CuCl2 = 5.9 g
First, we need to find the concentration of the diluted solution. The molar mass of CuCl2 is calculated as follows:
Cu: atomic mass = 63.55 g/mol
Cl: atomic mass = 35.45 g/mol
2 x Cl: 2 x 35.45 g/mol = 70.90 g/mol
The molar mass of CuCl2 is 63.55 + 70.90 = 134.45 g/mol.
Next, we can calculate the moles of CuCl2 in the 5.9 g sample:
moles = mass / molar mass
moles = 5.9 g / 134.45 g/mol = 0.0438 mol
To find the concentration of the diluted solution, we will divide the number of moles by the volume given:
C2 = moles / V2
C2 = 0.0438 mol / (52.0 mL / 1000) = 0.8438 M
Now we can plug in the values into the dilution formula:
C1V1 = C2V2
(8.10 M)(124 mL) = (0.8438 M)(V2)
Solving for V2 gives us:
(8.10 M)(124 mL) / (0.8438 M) = V2
V2 = 1193.21 mL
Therefore, you should dilute the 124 mL of the 8.10 M CuCl2 solution to a volume of approximately 1193.21 mL (or 1.19 L) to obtain a final volume of 52.0 mL containing 5.9 g of CuCl2.
You want 5.9 g CuCl2 in 52.0 mL. The molar mass CuCl2 is 134.451 so
5.9/134.451 = 0.0439 moles.
That in 52.0 mL = 0.0439 moles/0.052 L = 0.844 M is the concn of the solution you want to end up with.
124 mL x 8.10M = ?? mL x 0.844M
Solve for ?? mL and that will be the volume needed for the dilution. Then you should check it to see that 52.0 mL contains 5.9 g of CuCl2.