Looking for volume [closed]








**Closed.** This question is [off-topic](/help/closed-questions). It is not currently accepting answers.
 
 






---








 **Homework questions** must demonstrate some effort to understand the underlying concepts. For help asking a good homework question, see: [How do I ask homework questions on Chemistry Stack Exchange?](https://chemistry.meta.stackexchange.com/questions/141/how-do-i-ask-homework-questions-on-chemistry-stack-exchange)




Closed 2 years ago.








[Improve this question](/posts/156117/edit) 



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?




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 $\pu{300 mL}$.


 2

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.


 0