Final answer:
To find the volume of a helium balloon when exposed to liquid nitrogen, use the combined gas law. Calculate the initial conditions in Kelvin and apply the law to find the new volume under increased pressure and reduced temperature. The final volume is 0.147unit.
Step-by-step explanation:
To calculate the volume of a helium balloon when it is immersed in liquid nitrogen, we use the combined gas law, which is expressed as (P1 V1)/T1 = (P2 V2)/T2, where P is pressure, V is volume, and T is temperature. The temperatures need to be in Kelvin, so we convert them first. The initial temperature (20°C) is 293.15 K and the final temperature (-196°C) is 77.15 K.
Starting with a volume of 2.91 L at 1.00 atm and 293.15 K, we can solve for the final volume (V2) when the pressure is 5.20 atm and the temperature is 77.15 K as follows:
(1.00 atm × 2.91 L)/293.15 K = (5.20 atm × V2)/77.15 K
This simplifies to V2 = (1.00 × 2.91 × 77.15)/(5.20 × 293.15)
= 224.50/ 1524.38
=0.147
The volume is 0.147 unit giving us the final volume of the helium inside the balloon.