# How many mL of 6.0 M HCl solution will provide 164 g of HCl?

Nov 18, 2015

$\text{0.75 L}$

#### Explanation:

The idea here is that you need to determine how many moles you get in $\text{164 g}$ of hydrochloric acid, then use the given solution's molarity to figure out the volume that would contain that many moles.

So, hydrochloric acid has a molar mass of $\text{36.46 g/mol}$, which means that the $\text{164-g}$ sample will contain

164color(red)(cancel(color(black)("g"))) * "1 mole HCl"/(36.46color(red)(cancel(color(black)("g")))) = "4.498 moles HCl"

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

$\textcolor{b l u e}{\text{molarity" = "moles of solute"/"liters of solution}}$

A $\text{6.0-M}$ hydrochloric acid solution will contain $6$ moles of hydrochloric acid for every liter of solution. This means that $4.498$ moles will come with a volume of

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

V = (4.498color(red)(cancel(color(black)("moles"))))/(6.0color(red)(cancel(color(black)("moles")))/"L") = "0.7497 L"

Rounded to two sig figs, the number of sig figs you have for the molarity of the solution, the answer will be

$V = \textcolor{g r e e n}{\text{0.75 L}}$