To determine the final temperature of an ideal gas when the pressure and volume change, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Where: P1 = initial pressure V1 = initial volume T1 = initial temperature P2 = final pressure V2 = final volume T2 = final temperature
Let's plug in the given values into the equation:
(P1 * V1) / T1 = (P2 * V2) / T2
(4.62 ATM * 35.0 L) / (-31.5 °C) = (8.51 ATM * 20.0 L) / T2
Now, let's rearrange the equation to solve for T2:
T2 = (8.51 ATM * 20.0 L) / [(4.62 ATM * 35.0 L) / (-31.5 °C)]
T2 = (8.51 ATM * 20.0 L * (-31.5 °C)) / (4.62 ATM * 35.0 L)
Calculating this expression gives us:
T2 ≈ -54.61 °C
Therefore, the ideal gas would shift to approximately -54.61 °C after the pressure is changed from 4.62 ATM to 8.51 ATM and the volume is changed from 35.0 L to 20.0 L.