deduce van der walls equation of state forreal gases. define critical constants for real gases.?

Question

deduce expressions for them in terms of van der walls constants.

Answer 1

Well, I'll see how far I can get with this. :)

van der Walls looked at the ideal gas equation pv = mRT and tried to improve on it in two ways (can you see the two constants coming?). First, gas molecules have finite volume, so he wanted to take the apparent volume the gas occupied and subtract form that the actual volume of the molecules and then focus on the free volume left that the molecules could interact in, hence passing from pV = mRT to p(V-Npd^3 / 6) = mRT, with N being the number of particles and d their diameter, assuming rigid spheres. With a little experimentation the volume of gas molecules can actually be derived by experimentally measuring b for a substance, with b=NApd^3 / 6, NA = N/n being Avogadro's number. There's one of the constants. Whew!

Now for the other. van der Walls also proposed to replace the actual pressure, p, in pv = mRT, by the ideal pressure the particles would impose on the walls (which would be higher in absence of their mutual attraction), p + pattr, with pattr being proportional to the density of particles, squared to account for the surface effect (i.e. a spherical shell of particles pulling from a central particle, pattrµ1/v2.

That leads, with a little algebra fiddling, to his equation of state:

(p + a/v^2)(v - b) = RT

That's the best I can do. Does that help at all?

HTH

Charles

Answer 2

sorry i don"t know the asnwer but i"m asnwering atleast