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
Given values: P1 = 1.00 ATM V1 = 17.3 mL T1 = 301 K P2 = 678 torr (convert to ATM: 678 torr / 760 torr/ATM = 0.8926 ATM) V2 = 10.9 mL
Plugging these values into the combined gas law equation, we get:
(1.00 ATM × 17.3 mL) / (301 K) = (0.8926 ATM × 10.9 mL) / (T2)
Simplifying the equation, we have:
17.3 / 301 = 10.9 / T2
Cross-multiplying and rearranging, we find:
T2 = (10.9 × 301) / 17.3
T2 ≈ 189.122 K
Therefore, the final temperature of the argon gas is approximately 189.122 K.