Question

What volume of water must be added to `57*mL` of `0.500*mol*L^-1` solution to make `285*mL` of `0.100*mol*L^-1` solution?

Answer 1

`C_1V_1=C_2V_2`, and thus we must add `228*mL` to the mother solution.

Explanation:

The product `C_1V_1` gives the starting molar quantity; this is clear from the dimensional product, i.e. `mol*L^-1xxL=mol` as req'd.

From the given relationship,

`V_2=(C_1V_1)/C_2=(57.0xx10^-3Lxx0.500*cancel(mol*L^-1))/(0.100*cancel(mol*L^-1))=285*mL`

But we already have a `57*mL` volume, so we add appropriately.