Question

How much water must be added to 1500 mL of a 6.0 mol/L `CaCl_2` solution to make the concentration of the resulting solution 2.0 mol/L?

Answer 1

You need to add another `"3 litres"` of water........

Explanation:

The defining relationship for `"concentration"` is,

`"Concentration"` `=` `"Moles of stuff"/"Volume of solution"`, now typically the solvent is water, but it could be other materials, even a gas.

Here we have a molar quantity of `6.0*mol*L^-1`, and a `1500*mL` volume. We wish to dilute this concentration by a THIRD to `2.0*mol*L^-1`.

Now clearly, we cannot get the calcium salt out of solution, but we can add more solvent, more water to dilute it.

And here we can use the old relationship,

`C_1V_1=C_2V_2` where `C="concentration"`, and `V="volume"`.

So we solve for `V_2=(C_1V_1)/C_2=(1500*mLxx6.0*mol*L^-1)/(2.0*mol*L^-1)=4500*mL`.

And since we began with `1500*mL`, another `3000*mL` are required.