Question #a4823

The first thing to do here is use Avogadro's number to convert the number of molecules of nitrogen gas, #"N"_2#, to moles of nitrogen gas.

As you know, Avogadro's number is basically the definition of one mole

#color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"molecules"color(white)(a/a)|)))#

This means that in order to have one mole of a molecular substance, you need to have #6.022 * 10^(23)# molecules of that substance.

In your case, you have enough molecules of nitrogen gas to account for approximately #2# moles, since

#12.046 * 10^(23)color(red)(cancel(color(black)("molecules N"_2))) * "1 mole N"_2/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules N"_2)))) = "2.0003 moles N"_2#

Now, STP conditions are currently defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#.

Under these conditions, one mole of any ideal gas occupies #"22.7 L"# #-># this is known as the molar volume of a gas at STP.

Since your sample contains approximately #2# moles of nitrogen gas, its volume will be

#2.0003 color(red)(cancel(color(black)("moles N"_2))) * overbrace("22.7 L"/(1color(red)(cancel(color(black)("mole N"_2)))))^(color(purple)("molar volume of a gas at STP")) = color(green)(|bar(ul(color(white)(a/a)color(black)("45.407 L")color(white)(a/a)|)))#

I'll leave the answer rounded to five sig figs, the number of sig figs you have for the number of molecules of nitrogen gas.

SIDE NOTE A lot of text books and online sources still use the old definition of STP conditions, for which pressure is #"1 atm"# and temperature is #0^@"C"#.

Under these conditions, one mole of any ideal gas occupies #"22.4 L"#.

If this is the STP definition given to you, simply redo the last calculation using #"22.4 L"# instead of #"22.7 L"#.