What the original posting missed was that the number of moles in the sample situation was not one mole. So when using that same amount of gas at STP, they could not have 22.4 L volume.
When analyzing the problem in general it looks like you can look at it as an ideal gas in situation 1 and situation 2.
Mathematically it can be represented by
Situation 1 ---- P1 V1= n1 R T1
Situation 2 ---- P2 V2= n2 R T2
It follows mathematically
Situation 1 ---- R = (P1 V1) / (n1 T1)
Situation 2 ---- R = (P2 V2) / (n2 T2)
Since R is the same in both situations
(P1 V1) / (n1 T1)= (P2 V2) / (n2 T2)
For this problem
Although the the n (number of moles) is not one, it is the same for both situations and can be canceled out of the equation.
(P1 V1) / T1)= (P2 V2) / T2)
You then solve for V2 making sure all the units are the same and the values are absolute.