# An aqueous solution of concentrated hydrobromic acid contains 48% HBr by mass. If the density of the solution is 1.5 g / mL, What is its concentration?

Jul 31, 2017

(B): $8.9$ $\text{mol/L}$

#### Explanation:

We're asked to find the (molar) concentration of $\text{HBr}$ in solution, given its mass percentage and density.

To do this, we'll first assume there is $1$ $\text{L}$ of solution, so the density is also written as

$1.5$ $\text{g/mL}$ $= 1500$ $\text{g/L}$

We're given that 48% of the mass ($1500$ $\text{g}$) is $\text{HBr}$, so the mass of $\text{HBr}$ is

0.48·1500 $\text{g soln}$ = ul(720color(white)(l)"g HBr"

Now, we use the molar mass of $\text{HBr}$ ($80.912$ $\text{g/mol}$) to calculate the number of moles:

720cancel("g HBr")((1color(white)(l)"mol HBr")/(80.912cancel("g HBr"))) = color(red)(8.9 color(red)("mol HBr"

Molarity equation:

$\text{molarity" = "mol solute"/"L soln}$

= (color(red)(8.9color(white)(l)"mol HBr"))/(underbrace(1color(white)(l)"L soln")_"we assumed 1 L") = color(blue)(8.9color(white)(l)"mol/L"

Thus, option (B) is the correct answer.