Question

Question #a4823

Answer 1

`"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"`.