Question #b3926

1 Answer
Jul 4, 2017

Answer:

#"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)))#