# Question 42082

Apr 19, 2015

You'd need 250. mL of your solution to get that many moles of hydrochloric acid.

As you know, molarity is defined as moles of solute, in your case hydrochloric acid, divided by liters of solution.

This means that, if you get 1 mole of something in 1 L of solution you'll get a 1 M solution.

Let's play a little with this concept. By the same reasoning, if you get 12 moles of $H C l$ in 12 L of solution, you'll once again have a 1 M solution.

Now let's say you get 12 moles of $H C l$ in 1 L of solution. You'd have the same number of moles as in the previous case, but now the volume is 12 times smaller$\to$ the molarity of the solution will be 12 times higher, so you'd get a 12 M solution.

If you start with 3 moles of $H C l$, you'd need 1 L to get a 3-M solution. If you want to keep the number of mole constant and increase the molarity, you'll have to decrease the volume.

THis means that, to get a molarity that's 4 times bigger, you need a volume 4 times smaller. Automatically, this means that you'd need 250. mL, or 1/4th of aliter, to get a 12 M solution with 3 moles of solute.

For more complex calculations, you'll have to use the formula for molarity

$C = \frac{n}{V} \implies V = \frac{n}{C}$

In this case, you'd get

V = (3.00cancel("moles"))/(12.0cancel("mol")/"L") = "0.250 L"#

Expressed in mL, the answer will be

$V = \textcolor{g r e e n}{\text{250. mL}}$