Final answer:
Using the combined gas law, the final volume of the helium-filled balloon when immersed in liquid nitrogen at -196°C and under a pressure of 5.20 atm is calculated to be approximately 0.20 L. Option 2) 0.20 L is the correct answer.
Step-by-step explanation:
The question relates to the behavior of gases under different conditions of temperature and pressure, which is described by the combined gas law. The combined gas law combines Charles's Law, Boyle's Law, and Gay-Lussac's Law and is stated as (P1V1/T1) = (P2V2/T2), where P is pressure, V is volume, and T is temperature (in Kelvin). To solve the problem, we need to find the final volume (V2) of the helium gas when the balloon is submerged in liquid nitrogen at -196°C (which is 77K) and the pressure is increased to 5.20 atm. We will use the initial conditions of 20°C (which is 293K) and 1.00 atm with an initial volume of 3.91 L.
Given: P1 = 1.00 atm, V1 = 3.91 L, T1 = 293K
(20°C + 273 = 293K),
P2 = 5.20 atm, and T2 = 77K (-196°C + 273 = 77K).
By rearranging the combined gas law to solve for V2, we have V2 = (P1 × V1 × T2) / (P2 × T1). Plugging in the known values, V2 = (1.00 atm × 3.91 L × 77K) / (5.20 atm × 293K) = 0.205 L approximately. The final volume of the balloon, when immersed in liquid nitrogen and the pressure is raised, is approximately 0.20 L, thus option 2) 0.20 L is the correct answer.