Under what pressure will carbon dioxide have the density `rho = 500 g//1` at the temperature `T = 300 K` ? Carry out the calculations both for an ideal and for a Van der Walls gas.

Explanation

For an ideal gas law
`p = (rho)/(M) R T`
So, `p = 0.082 xx 300 xx (500)/(44) atms = 279.5` atmosphere
For Vander Wall gas Eqs.
`(p + (v^2 a)/(V^2))(V - vb) = vRT`, where `V = vV_M`
or, `p = (v RT)/(V - vb) = (av^2)/(V^2) = (m RT//M)/(V -(mb)/(M)) -(am^2)/(V^2 M^2)`
=`(rho RT)/(M - rho b) -(a rho^2)/(M^2) = 79.2 atm`.