NCERT Class XI Chemistry States of Matter Solutions

Question : 16

Total: 23

Payload is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the payload when a balloon of radius 10 m, mass 100 kg is filled with helium at 1.66 bar at 27°C. (Density of air =1.2 kgm–3 and R = 0.083 bar dm3K–1mol–1)

Solution:

Volume of balloon =

πr3 , Radius of balloon, r = 10 m
V =

× 3.14 × (10)3 = 4186.7 m3
Mass of displaced air = 4186.7 m3 × 1.2 kgm–3 = 5024.04 kg
Moles of gas present =

1.66×4186.7×103

0.083×300

= 279.11 × 103 moles
Mass of helium present = 279.11 × 103 × 4 = 1116.44 × 103 g = 1116.44 kg
Mass of filled balloon = 100 + 1116.44 = 1216.44 kg
Payload = Mass of displaced air – Mass of balloon
= 5024.04 – 1216.44 = 3807.6 kg

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