4.74 (a) How many mL of a stock solution of 10.0 M HNO3 would you have to use to prepare 0.450 L of 0.500 M HNO3?
where Mconc = molarity of concentrated solution, Vconc = volume of concentrated solution, Mdil = molarity after dilution, and Vdil = volume of diluted solution.
A look at the numbers given in the problem reveals that we are trying to make up 450 mL (0.450 L) of 0.500 M HNO3; this is the volume and molarity of the dilute solutions, respectively. The molarity of the concentrated solution is 10.0 M; what we are trying to find is the volume of concentrated (10.0 M HNO3) solution which we need to dilute to 450 mL to get 0.500 M HNO3; thus, we are trying to find Vconc in the relation above.
(b) if you dilute 25.0 mL of the stock solution to a final volume of 0.500 L, what will be the final concentration of the diluted solution?
We use the relation given above, and we solve it for Mdil, molarity of the diluted solution. We're given two volumes and the molarity of the concentrated stock solution (10.0 M), so this is pretty strightforward: