Question

`"750. mL"` of a `"5.0 M"` solution needs to be diluted to `"1.0 M"`. How much water should be added to reach this concentration?

Answer 1

`3.0 * 10^3"mL"`

Explanation:

The trick here is to realize that because the amount of solute must remain constant in a dilution, the decrease in concentration must be equal to the increase in volume.

In other words, diluting a solution will decrease its concentration by a factor `"DF"` and increase its volume by the same factor `"DF"`.

This factor is called the dilution factor and can be written as

`color(blue)(ul(color(black)("DF" = overbrace(c_"concentrated"/c_"diluted")^(color(red)("decrease in concentration")) = overbrace(V_"diluted"/V_"concentrated")^(color(purple)("increase in volume")) )))`

In your case, the concentration decreases by a factor of

`"DF" = (5.0 color(red)(cancel(color(black)("M"))))/(1.0color(red)(cancel(color(black)("M")))) = color(blue)(5)`

which means that the volume must increase by factor of `color(blue)(5)`

`V_"diluted" = color(blue)(5) * "750. mL" = "3750 mL"`

This means that you must add

`"volume of water" = "3750 mL" - "750. mL" = color(darkgreen)(ul(color(black)(3.0 * 10^(3)color(white)(.)"mL")))`

of water to your concentrated solution in order to dilute it from `"5 M"` to `"1 M"`.

The answer is rounded to two sig figs.