Ratio PV/RT dieterici's equation

[Dassinia]

Hello

Homework Statement

Determine the ratio PV/RT at the critical point for a fluid which obeys Dieterici’s equation
p(v-b)=RT exp(-a/RTv)

Homework Equations

The Attempt at a Solution

First ofall i don't really understand this notion of critical point.
I found an equation to find it that is
(dp/dv)=(d²p/dv²)=0 at constant temperature T
I don't have any equation in my book so where did this get from ?
Using it I found that
V=2nb
P=a/(4b²e²)
T=a/4Rb
And then I don't know what to do

Thanks

 

[BOYLANATOR]

The critical point is the minimum or maximum value of a function. At this point the gradient (derivative) of the function is 0.

You are asked to work out the ratio PV / RT .

 

[Dassinia]

The result is supposed to be 2/e² but I get 2n/e² what am i supposed to do with the n ?

 

[BOYLANATOR]

Sometimes the question may ask "per mole".

 

[Chestermiller]

Boylanator is correct. The problem statement clearly implies molar V. When did the n come from anyway? It wasn't in the problem formulation.

Chet