Question

What volume OF SOLVENT must we add to a `500*mL` solution of `1.2*mol*L^-1` concentration to dilute the concentration to `1.0*mol*L^-1`?

Answer 1

Look at this dimensionally...........we must add `100*mL` to the initial volume, to make up to a volume of `600*mL`...........

Explanation:

`C_1V_1=C_2V_2`, if we multiply the DIMENSIONS of concentration and volume, i.e.:

`"Concentration"xx"Volume"-=mol*cancel(L^-1)xxcancelL=mol`, i.e. `CV-="moles, i.e. amount of substance. "`

And so, we solve for `V_2=(C_1V_1)/C_2` (and CLEARLY this has the units of volume, as we require.)

And so..........,

`V_2=(1.2*cancel(mol)*cancel(L^-1)xx500*cancel(mL)xx10^-3*L*cancel(mL^-1))/(1.0*cancel(mol)*cancel(L^-1))`

`=0.60*L`

And so we ADD `100*mL` to the original solution.........

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