# Question 106e8

Feb 21, 2017

$\text{2.0 L}$

#### Explanation:

The key to any dilution calculation is the dilution factor

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{DF" = V_"diluted"/V_"stock" = c_"stock"/c_"diluted}}}}$

The dilution factor essentially tells you how concentrated the stock solution was compared with the diluted solution.

In your case, the dilution must take you from a concentrated hydrochloric acid solution of $\text{18.5 M}$ to a diluted solution of $\text{1.5 M}$, so the dilution factor must be equal to

"DF" = (18.5 color(red)(cancel(color(black)("M"))))/(1.5color(red)(cancel(color(black)("M")))) = color(blue)(12.333)

So, in order to decrease the concentration of the stock solution by a factor of $\textcolor{b l u e}{12.333}$, you must increase its volume by a factor of $\textcolor{b l u e}{12.333}$ by adding water.

The volume of the stock solution needed for this dilution will be

$\text{DF" = V_"diluted"/V_"stock" implies V_"stock" = V_"diluted"/"DF}$

Plug in your values to find

V_"stock" = "25.0 L"/color(blue)(12.333) = color(darkgreen)(ul(color(black)("2.0 L")))

The answer is rounded to two sig figs, the number of significant figures you have for the concentration od the diluted solution.

So, to make $\text{25.0 L}$ of $\text{1.5 M}$ hydrochloric acid solution, take $\text{2.0 L}$ of $\text{18.5 M}$ hydrochloric acid solution and dilute it to a final volume of $\text{25.0 L}$.

IMPORTANT NOTE! Do not forget that you must always add concentrated acid to water and not the other way around!

In this case, you're working with very concentrated hydrochloric acid, so it would be best to keep the stock solution and the water needed for the dilution in an ice bath before the dilution.

Also, it would be best to perform the dilution in several steps using smaller doses of stock solution. Don't forget to stir as you're adding the acid!

So, to dilute your solution, take several steps to add the concentrated acid solution to enough water to ensure that the final is as close to $\text{25.0 L}$ as possible. If you're still a couple of milliliters short of the target volume, finish the dilution by adding water.

Always remember

• "Water to concentrated acid " -> color(white)(.)color(red)("NO!")

• "Concentrated acid to water " -> color(white)(.)color(darkgreen)("YES!")#