# Question 33e61

May 14, 2016

$\text{25 L}$

#### Explanation:

Molarity is simply a measure of how many moles of solute you get per liter of solution.

In this regard, a $\text{1 molar}$ solution will contain $1$ mole of solute for every liter of solution. Right from the start, you should be able to tell that since the $\text{2 molar}$ solution si less concentrated than the $\text{5 molar}$ solution, you're going to need a bigger volume to get the same number of moles of solute.

The $\text{10 molar}$ solution contains $10$ moles of solute per liter of solution, which means that $\text{5 L}$ of solution will contain

5color(red)(cancel(color(black)("L solution"))) * "10 moles solute"/(1color(red)(cancel(color(black)("L solution")))) = "50 moles solute"#

Now, the $\text{2 molar}$ solution contains $2$ moles of solute per liter of solution, which means that $50$ moles of solute will correspond to

$50 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles solute"))) * "1 L solution"/(2color(red)(cancel(color(black)("moles solute")))) = color(green)(|bar(ul(color(white)(a/a)"25 L solution} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Notice that since the first solution is five times as concentrated as the second solution

$\textcolor{b l u e}{\text{10 molar") color(white)(a)"vs."color(white)(a) color(red)("2 molar}}$

the volume of the second solution that will contain the same number of moles as the first solution will be five times bigger than the volume of the first solution

$\textcolor{red}{\text{25 L")color(white)(a) "vs." color(white)(a) color(blue)("5 L}}$