Question

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)?

Answer 1

`"10.8 % NH"_3`

Explanation:

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.