# Calculate the concentration of an ammonia (M_M = "17 g/mol") solution that is 15% "NH"_3 and has a density of "0.90 g/mL" ?

Mar 26, 2018

Here's what I got.

#### Explanation:

Let's start by picking a sample of this ammonia solution that has a volume of

$\text{1.0 L" = 1.0 * 10^3 quad "mL}$

Use the density of the solution to convert its volume to mass.

1.0 * 10^3 color(red)(cancel(color(black)("mL solution"))) * "0.90 g"/(1 color(red)(cancel(color(black)("mL solution")))) = "900. g"

Now, you know that the solution is 15% ammonia, presumably by mass. This tells you that every $\text{100 g}$ of this solution contain $\text{15 g}$ of ammonia.

In this case, your sample will contain

900. color(red)(cancel(color(black)("g solution"))) * "15 g NH"_3/(100color(red)(cancel(color(black)("g solution")))) = "135 g NH"_3

Next, use the molar mass of ammonia to convert the mass to moles.

135 color(red)(cancel(color(black)("g"))) * "1 mole NH"_3/(17color(red)(cancel(color(black)("g")))) = "7.94 moles NH"_3

As you know, the molarity of a solution tells you the number of moles of solute present in exactly $\text{1 L}$ of the solution. Since our initial sample had a volume of $\text{1.0 L}$, you can say that you get $7.94$ moles of ammonia, the solute, for every $\text{1.0 L}$ of the solution.

This means that the molarity of the solution is

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{molarity = 7.9 mol L}}^{- 1}}}}$

The answer is rounded to two sig figs, the number of sig figs you have for your values.