Question
(a) How many moles per cubic meter of an ideal gas are there at a pressure of $1.00 \times 10^{14} \textrm{ N/m}^2$ and at $0^\circ\textrm{C}$? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?
1. $4.41 \times 10^{10} \textrm{ mol/m}^3$
2. This is unreasonably large. Suppose the gas is hydrogen, the density would be $4.44 \times 10^7 \textrm{ kg/m}^3$. For comparison, the density of uranium, one of the most dense materials found on Earth, is $1.91 \times 10^4 \textrm{ kg/m}^3$. The hydrogen would be more dense than uranium by a factor of 1000.
3. The ideal gas law doesn't apply at such high pressures.
Solution Video