Hello, Kallista,
I believe you have everything nicely laid out in terms what what needs to be done to find the temperature, in Kelvins. My first attempt at doing the calculation was a bit of a suprise, I'll admit, but I think it is correct, so I'll share the steps.
Is there a particular aspect of this problem that was not clear to you? Perhaps the identity of the gas? The identity makes no difference in this problem The ideal gas law applies to all ideal gases, which we'll assume is true of ethane, C2H6.
Everything is already in the proper units for use with the selected gas constant, R. The units will all cancel, leaving only temperature, in Kelvin.
PV = nRT
Rearrange to find T: T = PV/nR
T = (4.9487atm)*(22.773L)/((0.5388 moles)*( 0.082058 L*atm*K-1mol-1)
T = (4.9487atm)*(22.773L)/((0.5388 moles)*( 0.082058 L*atm*K-1mol-1)
T = 2549 K (4 sig figs)
High, but any gas at STP will occupy a volume of 22.4 liters for 1 mole of that gas. We have 1/2 mole here, so it would require 11.2 liters for STP. But it's in a large container, at 22.8 liters, so it should have plenty of room. But we also see that the pressure is almost 5 atmospheres. So something must be keeping the gas molecules in motion: Heat. 2549K of heat.
Bob
