# Question 9b1c1

##### 1 Answer
Nov 1, 2015

$\text{11.6 M}$

#### Explanation:

You know that molarity of the solution is defined as the number of moles of solute, which in your case is perchloric acid, ${\text{HClO}}_{4}$, divided by the volume of the solution - expressed in liters.

This means that you're going to have to pick a sample solution to base your calculations on. To keep things simple, pick a $\text{1.00-L}$ sample of perchloric acid.

The first thing to do here is determine what the mass of this solution will be. To do that, use the given density - don't forget to convert the volume of the sample to mililiters, or cubic centimeters

1.00color(red)(cancel(color(black)("L"))) * (10^3color(red)(cancel(color(black)("cm"^3))))/(1color(red)(cancel(color(black)("L")))) * "1.67 g"/(1color(red)(cancel(color(black)("cm"^3)))) = "1670 g"

Now, you know that this solution has a percent concentration by mass of $\text{70%}$. This means that you get $\text{70 g}$ of perchloric acid for every $\text{100 g}$ of solution.

In your case, the sample solution will contain a total of

1670color(red)(cancel(color(black)("g solution"))) * "70 g HClO"_4/(100color(red)(cancel(color(black)("g solution")))) = "1169 g HClO"_4

To determine how many moles of perchloric acid you have, use its molar mass

1169color(red)(cancel(color(black)("g"))) * "1 mole HClO"_4/(100.46 color(red)(cancel(color(black)("g")))) = "11.636 moles HClO"_4

Since the sample solution has a volume of $\text{1.00 L}$, the solution's molarity will be

$c = \frac{n}{V}$

c = "11.636 moles"/"1.00 L" = color(green)("11.6 M")#

The answer is rounded to three sig figs.

So, to find molarity given density and percent cocnentration by mass you need to

• pick a sample solution of whatever volume you want
• calculate the mass of that sample solution
• use the percent cocnentration to find how many moles of solute you have in the sample
• use the molar mass of the solute to determine the number of moles