Question

# A balloon of diameter $$21\:meter$$ weight $$100 kg$$. Calculate its pay-load, if it is filled with $$He$$ at $$1.0\: atm$$ and $$27 ^\circ C$$. Density of air is $$1.2\: kg m^{-3}$$. (Given: $$R = 0.082\: L\: atm\: K^{-1} mol^{-1}$$)

A
4952.42 kg
B
4932.42 kg
C
493.242 kg
D
None of these

Solution

## The correct option is B 4932.42 kgWeight of balloon$$=100\:kg=10 \times 10^{4}\:g$$.Volume of balloon$$= \displaystyle \frac{4}{3} \pi r^{3}$$.$$= \displaystyle \frac{4}{3} \times \displaystyle \frac{22}{7} \times ( \displaystyle \frac{21}{2} )^{3}$$$$=4851 m^{3}=4851 \times 10^{3} \:L$$Weight of gas $$(He)$$ in balloon$$= \displaystyle \frac{PVM}{RT}$$$$= \displaystyle \frac{1 \times 4851 \times 10^{3} \times 4}{0.082 \times 300} =78.878 \times 10^{4}$$$$\therefore$$ Total weight of gas and balloon $$=78.878 \times 10^{4}+10 \times 10^{4}$$$$=88.878 \times 10^{4}g$$ or $$888.78\:kg$$Weight of air displaced$$=1.2 \times 4851$$$$=5821.2\:kg$$$$\therefore$$ Pay load=wt. of air displaced-wt. of (balloon+gas)$$\therefore$$ Pay load$$=5821.2-888.78=4932.42\:kg$$.Chemistry

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