Question

2. A spherical balloon is made from a material whose mass is 3.10 kg. The thickness of the material is negligible compared to the 1.55 m radius of the balloon. The balloon is filled with helium (He) at a temperature of 315 K and just floats in air, neither rising nor falling. The density of the surrounding air is 1.19 kg/m³ and the molar mass of helium is 4.0026×10-3 kg/mol. Find the absolute pressure of the helium gas.

Answer 1

The mass of the balloon is 3.10 kg. Since the balloon is neither rising nor falling, this is the difference in mass of the air and the mass of Helium in the balloon.

Volume of balloon = 4/3 * pi * r^3 = 15.6 m^3

Mass of air = 15.6 m^3 * 1.19 kg/m^3 = 18.56 kg

mass of helium = 18.56 kg – 3.10 kg = 15.46 kg

moles of helium = mas of He/molar mass of HE = 15.46/(4.0026*10^-3) = 3862 moles

P = nRT/V = 3862 moles * 0.08205 Latm/moleK * 315K / 15600 L = 6.398 atm = 6.48 * 10^5 Pa