The concentration of a solution is the amount of solute in a solution.
We have from the question that he mass of manganese = 1.584 g
Hence;
Amount of [tex]Mn^2+[/tex] = 1.584 g/55g/mol = 0.0288 moles
Recall that;
Number of moles = concentration * volume
Let the concentration of the solution be C
0.0288 moles = C * 1 L
C = 0.0288 moles/ 1 L
C= 0.0288 mol/L
Hence concentration of stock solution = 0.0288 mol/L
For solution A
From the dilution formula;
C1V1 = C2V2
where;
C1 = initial concentration
C2 = final concentration
V1 = initial volume
V2= final volume
C1 = 0.0288 mol/L
V1 = 50.00 mL
C2 = ?
V2 = 1000.0 mL
C2 = 0.0288 mol/L * 50.00 mL/1000.0 mL
C2 = 0.00144 mol/L
Hence, concentration of solution A is 0.00144 mol/L
For solution B
C1V1 = C2V2
C1 = 0.00144 mol/L
V1 = 10.00 mL
C2 = ?
V2 = 250.0 mL
C2 = 0.00144 mol/L * 10.00 mL/250.0 mL
C2 = 0.0000576 mol/L
Hence, concentration of solution B is 0.0000576 mol/L
For solution C
C1 = 0.0000576 mol/L
V1 = 10.00 mL
C2 = ?
V2 = 500.0 mL
C2 = 0.0000576 mol/L * 10.00 mL/500.0 mL
C2= 0.000001152 mol/L
Hence, concentration of solution C is 0.000001152 mol/L
To learn more about concentration
https://brainly.com/question/13499062