An ammonia solution is 6.00 M and the density is 0.950 g mL. What is the mass/mass percent concentration of #NH_3# (17.03 g/mol)?

The idea here is that you need to pick a sample volume of this solution and calculate

• the total mass of this sample
• the mass of ammonia it contains

To make the calculations easier, let's pick a #"1000 mL"# sample. This solution is said to have a density of #"0.950 g mL"^(-1)#, which means that every milliliter of solution has a mass of #"0.950 g"#.

The sample we've picked will have a mass of

#1000 color(red)(cancel(color(black)("mL"))) * "0.950 g"/(1color(red)(cancel(color(black)("mL")))) = "950 g"#

Now, you know that this solution has a molarity of #"6.00 M"#, which basically means that every liter, which is the equivalent of #"1000 mL"#, will contain #6.00# moles of ammonia.

Since we've picked a sample of #"1000 mL"#, you can say that it will contain #6.00# moles of ammonia. To convert this to grams, use the compound's molar mass

#6.00 color(red)(cancel(color(black)("moles NH"_3))) * "17.03 g"/(1color(red)(cancel(color(black)("mole NH"_3)))) = "102.18 g"#

Now, the solution's percent concentration by mass, #"%m/m"#, tells you how many grams of ammonia, the solute, you get per #"100 g"# of solution.

You already know how many grams of ammonia you have in #"950 g"# of solution, so use this known composition to figure out how many grams of ammonia you'd get in #"100 g"# of solution

#100 color(red)(cancel(color(black)("g solution"))) * "102.18 g NH"_3/(950color(red)(cancel(color(black)("g solution")))) = "10.76 g NH"_3#

Therefore, you can say that the solution's mass by mass percent concentration is

#color(green)(bar(ul(|color(white)(a/a)color(black)("% m/m" = 10.8%"NH"_3)color(white)(a/a)|)))#

The answer is rounded to three sig figs.