Question

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"` ?

Answer 1

Here's what I got.

Explanation:

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.