I'm teaching myself some basics of the ideal gas law and working out simple density equations for atmospheric gases at various altitudes.
When I applied the gas law to Venus' atmosphere at its surface,
$$ \rho = \frac{PM_{mol}}{RT},$$
with a Venusian atmosphere of 96.5% $CO_{2}$ and 3.5% $N_{2}$, and
$$R = 8.31451 \frac{J}{mol \cdot K}$$
$$M_{mol} = 0.04344 \frac{kg}{mol}$$
$$P = 9.3 \times 10^{6} Pa$$
$$T = 735K$$
I get 66.1072 $\frac{kg}{m^{3}}$, which roughly agrees with Wikipedia's page on Venus' atmosphere (67 $\frac{kg}{m^{3}}$).
But I'm curious (and here's my question): With all the discussion on the Wikipedia pages cited above about how Venus' atmosphere is a supercritical fluid at its surface, does the ideal gas law equation still work in this exercise?
Best Answer
After further research, I've concluded that the ideal gas law would work for Venus' supercritical fluid atmosphere, at least reasonably well enough for my curiosity, and certainly as well as it would here on Earth.
My research took me to learning compressibility factor, equations of state, and several other real gas topics.
From what I gather, a gas behaving "ideally" will have a compressibility factor $Z = \frac{P}{nRT}$ of one. While the Wikipedia page mentions that $Z$ will deviate substantially for a gas at extreme pressures, such deviation doesn't become significant until several hundred bars of pressure (more than Venus' surface).
This web page has an online calculator of various physical properties of several gases (sorry, it's an HTTP POST so no direct URL to the calculated data), and it shows the compressibility factor is still near 1 for both gases, even at 93 bar and 735K (1.0048 for $CO_2$ and 1.0391 for $N_2$).
That page also mentions the densities of $CO_2$ and $N_2$ at Venus' surface pressure/temperature are $66.98 \frac{kg}{m^{3}}$ and $41.21 \frac{kg}{m^{3}}$, respectively. Given the fractional amount of each, this yields an overall density of $\rho = 66.08 \frac{kg}{m^{3}}$. Close enough to my original calculation!