Question #a4823

1 Answer
Jun 26, 2016

"45.407 L"

Explanation:

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".