question_answer 36)

                  We have 0.5 g of hydrogen gas in a cubic chamber of size 3 cm 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 consider as spheres of radius \[1\,\overset{\text{o}}{\mathop{\text{A}}}\,\]).

Answer:

                  Ideal gas law hold only if the intermolecular force is negligible or zero.                 Here, radius of hydrogen molecule,                 \[r=1,\,\overset{\text{o}}{\mathop{\text{A}}}\,={{10}^{-10}}\,m\]                 \[\therefore \] volume of 1 molecule of hydrogen\[=\,\frac{4}{3}\,\pi \,{{r}^{3}}\]                 \[=\,\frac{4}{3}\,\times \,3.14\,\times \,{{10}^{-30}}\]                 \[=4.19\times {{10}^{30}}{{m}^{3}}\]                 Number of molecule of hydrogen                 \[=0.5\times 6.023\times {{10}^{23}}\]                 \[=\text{3}\times \text{1}{{0}^{\text{23}}}\]                 \[\therefore \] Molecules volume \[=4.19\times {{10}^{30}}\times 3\times {{10}^{23}}\]                 \[=12.6\times {{10}^{7}}{{m}^{3}}\]                 For ideal gas, \[{{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}\]                 \[\therefore \] \[{{V}_{2}}=\,\left( \frac{{{P}_{1}}}{{{P}_{2}}} \right)\,{{V}_{1}}=\frac{1}{100}\,\times \,{{(3\times {{10}^{-2}})}^{3}}\]                 Since final volume is approximately equal to the molecular volume, so intermolecular forces cannot be neglected. Hence, ideal gas law cannot hold good in the final stage.