# How many moles of HNO_3 are needed to prepare 5.0 liters of a 2.0 M solution of HNO_3?

May 22, 2017

$\text{10. moles}$

#### Explanation:

All you have to do here is to use the molarity of the solution as a conversion factor to determine the number of moles of solute that must be dissolved in $\text{5.0 L}$ of solution in order to have a concentration of $\text{2.0 M}$.

As you know, molarity tells you the number of moles of solute present in $\text{1 L}$ of solution. In your case, a $\text{2.0 M}$ solution will contain $2.0$ moles of solute for every $\text{1 L}$ of solution.

Now, because solutions are homogeneous mixtures, i.e. they have the same composition throughout, you can use the molarity of the solution as a conversion factor to get the moles of solute needed for your solution

$5.0 \textcolor{red}{\cancel{\textcolor{b l a c k}{{\text{L solution"))) * overbrace("2.0 moles HNO"_3/(1color(red)(cancel(color(black)("L solution")))))^(color(blue)("= 2.0 M")) = color(darkgreen)(ul(color(black)("10. moles HNO}}_{3}}}}$

The answer is rounded to two sig figs.

This tells you that dissolving $10.$ moles of nitric acid in enough water to get the total volume of the solution to $\text{5.0 L}$ will give you the same molarity as dissolving $2.0$ moles of nitric acid in enough water to get the total volume of the solution to $\text{1.0 L}$.