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While constructing a bulb of volume 250 ...

While constructing a bulb of volume `250 cm^3`, it is sealed at `27^@C` temperature and `10^-3` mmHg pressure. Find the number of gas molecules in the bulb. Avogadro number `=6.0 times 10^23`.

Text Solution

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Volume of air inside the bulb `V_1=250 cm^3`, pressure of air , `p_1=10^-3 mmHg=10^-4 cmHg,` temperature
`T_1=27+273=300 K`. Let at STP the volume of air =`v_2 cm^3,p_2=76 cmHg,T_2=273 K`
`therefore ` Using `(p_1V_1)/(T_1)=(p_1V_2)/T_2` we get,
`V_2=(p_1V_1T_1)/(T_1p_2)=(10^-4times250times273)/(300times76)=29.934 times 10^-5 cm^3`
At STP number of molecules in air of volume `22400 cm^3` at `6 times 10^23`
SO that it volume `29.934 times 10^-5 cm^3`
`=(6times10^23)/22400times29.934times10^-5=8.018 times10^15`.
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