To solve this problem, we can use the combined gas law, which states:
(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:
P1 = 5.0 ATM V1 = 1.25 L T1 = -125°C (converted to Kelvin by adding 273.15) = 148.15 K P2 = 50.0 ATM V2 = 325 mL (converted to liters by dividing by 1000) = 0.325 L T2 = final temperature (unknown)
Now we can solve for T2:
(P1 × V1) / T1 = (P2 × V2) / T2
(T2 × P1 × V1) = (T1 × P2 × V2)
T2 = (T1 × P2 × V2) / (P1 × V1)
Substituting the values:
T2 = (148.15 K × 50.0 ATM × 0.325 L) / (5.0 ATM × 1.25 L)
Calculating:
T2 = 19.92 K
However, this result seems unusually low. Please double-check the values provided to ensure they are accurate.