Question

Question #a4835

Answer 1

`"0.0395 g"`

Explanation:

As you know, Avogadro's constant tells you the number of molecules of ammonia needed in order to have `1` mole of ammonia.

`6.022 * 10^(23) quad "molecules NH"_3 = "1 mole NH"_3`

Now, the molar mass of ammonia, which tells you the mass of exactly `1` mole of ammonia, is equal to `"17.031 g mol"^(-1)`. This means that `1` mole of ammonia has a mass of `"17.031 g"`.

`"1 mole NH"_3 = "17.031 g"`

You can thus say that, for ammonia, you have

`6.022 * 10^(23) quad "molecules NH"_3 = "1 mole NH"_3 = "17.031 g"`

which, of course, implies that

`6.022 * 10^(23) quad "molecules NH"_3 = "17.031 g"`

Your sample contains `2.38 * 10^(22)` molecules of ammonia, so you can say the mass of the sample will be equal to

`2.38 * 10^(22) color(red)(cancel(color(black)("molecules NH"_3))) * "17.031 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules NH"_3)))) = color(darkgreen)(ul(color(black)("0.0395 g")))`

The answer is rounded to three sig figs, the number of significant figures you have for the number of molecules of ammonia.