Class 11 Chemistry States of Matter: NCERT Solutions for Question 16

This page focuses on the detailed States of Matter question answers for Class 11 Chemistry States of Matter, addressing the question: 'Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load 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 kg m–3 and R = 0.083 bar dm3 K–1 mol–1).'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.
Question 16

Pay load is defined as the difference between the mass of displaced air and the mass of the balloon. Calculate the pay load 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 kg m–3 and R = 0.083 bar dm3 K–1 mol–1).

Payload of the ballon  = mass of the displaced air – mass of the ballon

Radius of the ballon, r  = 10 m

Mass of the ballon, m = 100kg

Therefore volume of the ballon = 4/3πr3 = 4/3 x 22/7 x (10)3 = 4190.5 m3

Now volume of the displaced air = 4190.5 m3

Given,

Density of air = 1.2 kg m–3

Therefore, the mass of the displaced air

= 4190.5 x 1.2  = 5028.6 kg

Let w be the mass of helium gas filled into the ballon,then

PV = (w/m)RT

OR w = PVM/RT

= (1.66 X 4190.5 X 103 X 4) / (0.083 X 300)

= 1117 kg (approx)

Total mass of the balloon filled with He  = 1117 + 100 = 1217 kg

Therefore payload of the balloon  = 5028.6 – 1217 = 3811.6 kg

Hence, the pay load of the balloon is 3811.6 kg.