# Question 6a996

Mar 30, 2017

1.24%

#### Explanation:

The trick here is to realize that when you dilute a solution, its volume increases and its concentration decreases by the same factor.

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{\text{DF" = c_"concentrated"/c_"diluted" = V_"diluted"/V_"concentrated}}}} \to$ the dilution factor

In your case, the dilution increases the volume by a factor of

"DF" = (500. color(red)(cancel(color(black)("mL"))))/(17.2color(red)(cancel(color(black)("mL")))) = color(blue)(29.07)

This means that the concentration of the diluted solution must be $\textcolor{b l u e}{29.07}$ times lower than the concentration of the initial solution.

You can thus say that

$\text{DF" = "% concentrated"/"% diluted" implies "% diluted" = "% concentrated"/"DF}$

In your case, the concentration of the diluted solution will be

"% diluted" = "36%"/color(blue)(29.07) = color(darkgreen)(ul(color(black)(1.24%)))#

I'll leave the answer rounded to three sig figs, but keep in mind that you only have two sig figs for the initial concentration of the solution.

IMPORTANT NOTE Concentrated acid solution should never be diluted by adding water to the acid! EVER!

Instead, you should always add very small quantities of acid to the water in multiple steps, giving the solution enough time to cool off between each step.