A chemist dissolves 0.097 g of CuSO4 · 5 H2O

in water and dilutes the solution to the mark
in a 500-mL volumetric flask. A 13.6-mL
sample of this solution is then transferred to a
second 500-mL volumetric flask and diluted.
What is the molarity of CuSO4 in the second
solution?
To prepare the second 500 mL of solution
directly, what mass of CuSO4 · 5 H2O would
need to be weighed out?
Answer in units of mg

y=mx+b

-b+or- square root of b^2 -4ac/2a

To find the molarity of CuSO4 in the second solution, we need to first determine the amount of CuSO4 present in the 13.6 mL sample.

Given:
Mass of CuSO4 · 5 H2O = 0.097 g
Volume of solution = 500 mL

To find the molarity, we need to divide the moles of CuSO4 by the volume of the solution in liters.

First, we need to determine the moles of CuSO4:
Molar mass of CuSO4 · 5 H2O = (63.55 g/mol) + (32.07 g/mol) + (4 * 16.00 g/mol) + (5 * (1.01 g/mol * 2))

= 249.68 g/mol

Moles of CuSO4 = Mass / Molar mass

= 0.097 g / 249.68 g/mol

= 0.000389 moles

Now, we need to convert the volume of the solution from milliliters to liters:

Volume = 13.6 mL * (1 L / 1000 mL)

= 0.0136 L

Finally, we can calculate the molarity:

Molarity = Moles / Volume

= 0.000389 moles / 0.0136 L

= 0.0286 M

So, the molarity of CuSO4 in the second solution is 0.0286 M.

To prepare the second 500 mL of solution directly, we need to calculate the mass of CuSO4 · 5 H2O that would need to be weighed out.

Using the molarity calculated above, we can use the formula:

Moles = Molarity * Volume in liters

Moles = 0.0286 mol/L * 0.5 L

= 0.0143 moles

Now, we can calculate the mass:

Mass = Moles * Molar mass

= 0.0143 moles * 249.68 g/mol

= 3.574 mg

Therefore, to prepare the second 500 mL of solution directly, you would need to weigh out 3.574 mg of CuSO4 · 5 H2O.

First, calculate the M of the initial solution.

mols CuSO4.5H2O = grams/molar mass = ?
Then mols/L = M

So the diluted solution is M of first x (13.6/500) = ?

For the last part.
How many mols do you have in the second solution? That's mols = M x L = ?
Then mols = grams/molar msss. You know molar mass and mols, solve for grams.