# Looking for volume [closed]

The question in my assignment is as follows. You have 5.5 M $$\ce{NaOH}$$. The volume of $$\ce{NaOH}$$ is 0.5 L. How many mL of the 5.5 M $$\ce{NaOH}$$ solution do you need if you would like to make 300 mL of 1.2 M $$\ce{NaOH}$$? I thought you could use the $$C_1V_1= C_2V_2$$ formula and rearrange it in there to get the answer, 720 ml. But that doesn't quite feel right. Does anyone have hints on what I'm doing wrong?

• You may take 65 ml of the solution and top it up with 235 ml of water.
– Shub
Aug 24 at 15:24
• It is very simple algebra of junior high school, just darkened by almighty magic, because it is about chemistry. Aug 24 at 17:16
• @Shub No. That's not how it is done. Aug 24 at 17:27

Take care ! The volumes are not additive! A $$5.5$$ M solution of $$\ce{NaOH}$$ has a density is $$1.205$$ and contains $$18.1$$% $$\ce{NaOH}$$ by weight. So let's start from the beginning!

A volume $$\pu{V}$$ of this concentrated solution has to be taken for the dilution. It contains $$\pu{5.5·V}$$ moles of $$\ce{NaOH}$$. The final solution must contain $$\pu{1.2 mol L^{-1}*~ 0.3 L~ =~ 0.36~ mol}$$ $$\ce{NaOH}$$. As these two number of moles are equal, the volume $$\pu{V}$$ of the concentrated solution to be taken for the final dilution is given by : $$\pu{5.5 mol L^{-1}*V~ =~ 0.36 mol}$$, and $$\pu{~ V = \frac {0.36~ mol}{5.5~ mol~ L^{-1}} =~ 0.0655 L~ =~ 65.5 mL}$$

To obtain the final solution you should not mix it with $$\pu{300 mL - 65.5 mL = 234.5 mL}$$ water, as the volumes are not additives. $$1$$ liter of the concentrated solution plus $$1$$ liter water does not make $$2$$ liters diluted solution. In this case choose a flask containing exactly $$\pu{300 mL}$$. Transfer $$\pu{65.5 mL}$$ of the concentrated solution, and then add some water and mix. Then add enough water and mix to get to the exact final volume $$\pu{300 mL}$$.

Maurice has already explained it nicely!

You have the right dilution formula, but most students even get this wrong anyway. I substitute the indexes and it helps students remember. You should be able to derive this relationship otherwise it will keep haunting as a mystery formula.

$$C_iV_i= C_fV_f$$

where $$C_i$$ is the initial concentration of the stock solution

$$V_i$$ is the initial volume you need from the stock solution

$$C_f$$ is the final desired concentration of the diluted solution

$$V_f$$ is the final desired volume of the diluted solution

If you now plug in the numbers you should the answer right, 65.45 mL or 65.5 mL.