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?
Volume of 1 molecule =34πr3=34×3.14×(10−10)3 r=1A˚=10−10m(Given) volume of 1 molecule =4×1.05×10−30m3=4.20×10−30m3 Number of mole in 0.5g H2 gas =20.5=0.25 (∴ H2 has 2 mole) Volume of H2 molecules in 0.25 mole =0.25×6.023×10×4.20×10−30m3 =1.05×6.023×10−23−30=6.324×10−23−30=6.3×10−7m3 volume of H2 molecules =6.3×10−7m3 Now for ideal gas at constant temperature PiVi=PfVfVf=PfPiVi=1001×(3×10−2)3 (∵ vol. of cube Vi=(side)3;Pi=1atm at NTP) Vf=10027×10−5=2.7×10−5−2=2.7×10−7m3
