# An aqueous solution is 40.0% by mass hydrochloric acid, HCl, and has a density of 1.20 g/mL. What is the molarity of hydrochloric acid in the solution?

##### 1 Answer

#### Explanation:

The first thing to do here is pick a sample of this solution.

Since you're going to find its molarity, you can make the calculations easier by picking a *regardless* of the volume you pick.

So, use the density of the solution to determine how many grams you get in that respective volume

#1.00color(red)(cancel(color(black)("L"))) * (1000color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("L")))) * "1.20 g"/(1color(red)(cancel(color(black)("mL")))) = "1200 g"#

Now, you that the percent concentration by mass for this solution is **for every**

The mass of hydrochloric acid you get in that sample will thus be

#1200color(red)(cancel(color(black)("g solution"))) * "40.0 g HCl"/(100color(red)(cancel(color(black)("g solution")))) = "480 g HCl"#

Use hydrochloric acid's molar mass to determine how many moles you have in that many grams

#480color(red)(cancel(color(black)("g"))) * "1 mole HCl"/(36.46color(red)(cancel(color(black)("g")))) = "13.17 moles HCl"#

The molarity of the solution will thus be - remember that we started with a

#c = n/V#

#c = "13.17 moles"/"1.00 L" = color(green)("13.2 M") -># rounded to three sig figs

**SIDE NOTE** *This is very close to the maximum possible concentration for hydrochloric acid in aqueous solution. At this concentration, the solution is actually fuming at a significant evaporation rate.*