Question

Question #b3926

Answer 1

`"0.5 gram-atoms"`

Explanation:

The trick here is to realize that you're actually looking for the number of moles of atoms present in, presumably, `"7 g"` of nitrogen gas, `"N"_2`.

For starters, a gram-atom is simply Avogadro's constant of atoms, regardless if those atoms are combined in molecules or formula units or floating around on their own.

This is the important distinction between a mole and a gram-atom: a mole of a given substance contains Avogadro's constant of molecules, formula units, or atoms of said substance, while a gram-atom of a given substance contains Avogadro's constant of atoms, regardless of the nature of the substance (molecular, ionic).

In your case, a mole of nitrogen gas contains `6.022 * 10^(23)` molecules of nitrogen gas, `"N"_2` and `2` moles of nitrogen atoms, `"N"`.

You can thus say that a mole of nitrogen gas is equivalent to `2` gram-atoms of nitrogen, or that `1` gram-atom of nitrogen gas is equivalent to `1/2` moles of nitrogen gas.

Now, a mole of nitrogen gas has a mass of approximately `"28 g"` as given by the molar mass of nitrogen gas, which is equal to `"28 g mol"^(-1)`.

This means that you sample contains

`7 color(red)(cancel(color(black)("g"))) * "1 mole N"_2/(28color(red)(cancel(color(black)("g")))) = "0.25 moles N"_2`

You can thus say that the sample contains

`0.25 color(red)(cancel(color(black)("moles N"_2))) * "2 gram-atoms N"_2/(1color(red)(cancel(color(black)("mole N"_2)))) = color(darkgreen)(ul(color(black)("0.5 gram-atoms N"_2)))`

The answer is rounded to one significant figure.

Notice that you get the same answer is you assume that you're dealing with `"7 g"` of elemental nitrogen, `"N"`.

The molar mass of elemental nitrogen is approximately `"14 g mol"^(-1)`, which means that `"7 g"` will contain

`7 color(red)(cancel(color(black)("g"))) * "1 mole N"/(14color(red)(cancel(color(black)("g")))) = "0.5 moles N"`

Now, a gram-atom of nitrogen atoms simply means Avogadro's number of nitrogen atoms, so you can say that `1` mole of nitrogen atoms is equivalent to `1` gram-atom of nitrogen atoms.

This implies that you once again have

`0.5 color(red)(cancel(color(black)("moles N"))) * "1 gram-atom N"_2/(1color(red)(cancel(color(black)("mole N")))) = color(darkgreen)(ul(color(black)("0.5 gram-atoms N"_2)))`