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"# ?

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

#"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 #"100 g"# of this solution contain #"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 #"1 L"# of the solution. Since our initial sample had a volume of #"1.0 L"#, you can say that you get #7.94# moles of ammonia, the solute, for every #"1.0 L"# of the solution.

This means that the molarity of the solution is

#color(darkgreen)(ul(color(black)("molarity = 7.9 mol L"^(-1))))#

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