Ncert Exercises & Solutions

5.17 Calculate the volume occupied by 8.8 g of CO2 at 31.1°C and 1 bar pressure.
R = 0.083 bar L K–1 mol–1.

Given,

Radius of the balloon = r = 10 m

Volume of the balloon =

= \frac{4}{3} {πr}^{3}

= \frac{4}{3} \times \frac{22}{7} \times 10^{3}

= 4190.5 m^{3} (approx)

Thus, the volume of the displaced air is 4190.5

m^{3}

Given,

Density of air = 1.2 kg

m^{- 3}

Then, mass of displaced air = 4190.5

\times

1.2 kg

= 5028.6 kg

Now, mass of the helium (m) inside the balloon is given by,

m = \frac{MpV}{RT}

Here,

M = 4 \times 10^{- 3} {kgmol}^{- 1}

p = 1.66 bar

V = Volume of the balloon

= 4190.5 m^{3}

R = 0.083 bar {dm}^{3} K^{- 1} {mol}^{- 1}

T = 27 ° C = 300 K

Then, m = \frac{4 \times 10^{- 3} \times 1.66 \times 4190.5 \times 10^{3}}{0.083 \times 300}

= 1117.5 kg (approx)

Now, total mass of the balloon filled with helium = (100 + 1117.5) kg
= 1217.5 kg
Hence, pay load = (5028.6 – 1217.5) kg
= 3811.1 kg
Hence, the pay load of the balloon is 3811.1 kg.

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