Your strategey here will be to
use the molar mass of the gas to convert the sample to moles
use the molar volume of a gas a STP as a conversion factor
The molar volume of a gas at STP can be used as a conversion factor that helps you go from moles to liters, or vice versa.
As its name suggest, the molar volume of a gas at STP will tell you what volume would one mole of a gas occupy under STP conditions.
Now, STP conditions are currently defined as a pressure of
In other words, a gas kept under STP conditions will have a molar volume of
In your case, the problem provides you with the mass of neon, which means that you're going to have to use its molar mass to convert it to moles.
#33.6 color(red)(cancel(color(black)("g"))) * overbrace("1 mole Ne"/(20.18color(red)(cancel(color(black)("g")))))^(color(brown)("molar mass of Ne")) = "1.665 moles Ne"#
So, if one mole occupies
#1.665color(red)(cancel(color(black)("moles Ne"))) * overbrace("22.7 L"/(1color(red)(cancel(color(black)("mole Ne")))))^(color(purple)("molar volume of a gas at STP")) = color(green)(|bar(ul(color(white)(a/a)"37.8 L"color(white)(a/a)|)))#
The answer is rounded to three sig figs.
SIDE NOTE Many sources still use the old definition of STP, which implies a pressure of
Under these conditions, one mole of any ideal gas occupies
If this is the value given to you for the molar volume of a as at STP, simply redo the calculations using