Question

What volume of 0.10 M `NaOH` can be prepared from 250 mL of 0.30 M `NaOH`?

Answer 1

`"750 mL"`

Explanation:

The thing to notice here is that the initial solution is `3` times more concentrated than the target solution, since

`(0.30 color(red)(cancel(color(black)("M"))))/(0.10color(red)(cancel(color(black)("M")))) = 3`

This tells you that the volume of the target solution must be `3` times greater than the volume of the initial solution.

That is the case because when you dilute a solution, you decrease its concentration by increasing its volume while keeping the number of moles of solute constant.

This implies that when the concentration of a solution decreases by a factor, which is usually called dilution factor, `"DF"`, upon dilution, the volume of the diluted solution increases by the same factor `"DF"`.

`color(blue)(|bar(ul(color(white)(a/a)"DF" = V_"final"/V_"initial" = c_"initial"/c_"final"color(white)(a/a)|)))`

You thus have

`V_"final" = 3 xx "250 mL" = color(green)(|bar(ul(color(white)(a/a)color(black)("750 mL")color(white)(a/a)|)))`

The answer is rounded to two sig figs.

So, you can decrease the concentration of `"250 mL"` of sodium hydroxide solution from `"0.30 M"` to `"0.10 M"` by adding enough water to get its final volume to `"750 mL"`.