Final answer:
The final volume of the helium-filled balloon, when cooled from 25°C to -196°C, is approximately 0.51 L, calculated using the combined gas law under constant pressure.
Step-by-step explanation:
To calculate the final volume of a helium-filled balloon cooled by liquid nitrogen, we employ the combined gas law, which assumes that pressure remains constant. Given an initial volume (V1) of 2.20 L and an initial temperature (T1) of 25°C (or 298 K, since temperature must be in Kelvin), we can find the final volume (V2) after the temperature drops to -196°C (or 77 K).
The combined gas law is V1/T1 = V2/T2. Firstly, we add 273 to each Celsius temperature to convert to Kelvin:
T1 = 25°C + 273 = 298 K, and
T2 = -196°C + 273 = 77 K.
Solving for V2, we plug in the values:
V2 = V1 × (T2/T1).
So, V2 = 2.20 L × (77 K / 298 K) = 0.51 L approximately.