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  • We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm kept at NTP. The gas in the chamber is compressed, keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?

We have 0.5 g of hydrogen gas in a cubic chamber of size 3cm kept at NTP. The gas in the chamber is compressed, keeping the temperature constant till a final pressure of 100 atm. Is one justified in assuming the ideal gas law, in the final state?
(Hydrogen molecules can be considered as spheres of radius 1 A ).

Answers (1)

The volume of a sphere = the volume of one molecule

=\frac{4}{3}\pi r^{3}

Here r= 10^{-10} m

So, volume = 4 \times 1.05 \times 10^{-30} = 4.2 \times 10^{-30} m^{3}

For 0.5 g of hydrogen gas, no of moles = \frac{0.5}{2}=0.25 moles

Hence the volume of hydrogen molecules = 0.25 \times 6.023 \times 10^{23} \times 4.2 \times 10^{-30} = 6.3 \times 10^{-7} m^{3}

For a constant temperature, ideal gas à  Pi Vi = Pf Vf

Vf =\frac{P_i V_i}{P_f} = \frac{1}{100}\times (3\times 10^{-2})^{3}

Hence, V_f = 2.7 \times 10^{-7} m^{3}

The gas here will not obey the ideal gas behaviour as the kinetic energy of the molecules will not interact with each other due to compression.

Posted by

infoexpert24

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