# What volume of solution is needed to make a 3.0 M solution containing 109.5 g of hydrochloric acid?

Mar 20, 2015

You'd need a solution with a volume of $\text{1.0 L}$.

Since molarity is defined as the number of moles of solute (in your case, hydrochloric acid) per volume of solution (in liters), the first thing you need to do is figure out how many moles of hydrochloric acid your solution contains.

This is done by using its molar mass - you simply add the molar masses of hydrogen and chlorine, the elements that make up a molecule of HCl"

$\text{109.5 g HCl" * "1 mole HCl"/"36.46 g" = "3.003 moles HCl}$

So, your solution must contain approximately 3 moles of $H C l$. This means that its volume must be

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

V_("solution") = ("3.003"cancel("moles"))/("3.0"(cancel("mol"))/"L") = "1.001 L"

Rounded to two sig figs, the answer will be

V_("solution") = "1.0 L"