Question

We have $0.5g$ 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 $100atm$. Is one justified in assuming the ideal gas law, in the final state? (Hydrogen molecules can be considered as spheres of radius $1\AA$).

Answer 1

Number of moles, $\mu =\frac{m}{M}$

$\mu =\frac{0.5}{2}=0.25$

From Avogadro's hypothesis, molecules in $\mu$ moles of $H_2$

$=0.25\times 6\times {10}^{23}atoms$

Given, Hydrogen molecules can be considered as spheres of radius $1\AA$.

Volume of hydrogen molecule $V=\frac{4}{3}\pi r^3$

$=\frac{4}{3}\pi (1\times {10}^{-10}{)}^3$

$=4.2\times {10}^{-30}{m}^3$

So, we have $0.25\times 6\times {10}^{23}$ molecules, each of volume approximately $4.2\times {10}^{-30}{m}^3$.


Total volume $=0.25\times 6\times {10}^{23}\times 4.2\times {10}^{-30}{m}^3$

$=6.3\times {10}^{-7}{m}^3$

Supposing Ideal gas law is valid.

Finally, gas will occupy the volume of the container.

$V_i=L^3=(3\times {10}^{-2}{)}^3$

And

$V_f=\frac{P_i{V}_i}{P_f}=\frac{(3\times {10}^{-2}{)}^3}{100}=2.7\times {10}^{-7}{m}^3$

which is about the total molecular volume. Hence, intermolecular forces cannot be neglected. Therefore, the ideal gas situation does not hold.

$\text{Final Answer}:$ No.