Pressure correction (getting corrected ideal pressure)
Let us consider a container containing ‘n’ number of gaseous molecules. Now consider two gaseous molecule A and B inside it.
At ‘A’ : The gaseous molecule ‘A’ present at the interior of the container and is attracted (disturbed) by all neighboring gaseous directions. Hence the net force exerted by this molecule is zero.
At ‘B’: The gaseous molecule ‘B’ is about to strike the walls of the container, it is influenced by other neighboring molecules as follows.
(a) It is attracted by large number of molecules inward and net effect is an inward pull. This inward force (pressure) is directly proportional to the number of molecules per unit volume (at the bulk of the container) ie., P ∝ 1/V …………(1)
(b) Within the container, there are some molecules that are already striking the wall of the container. Thus there exist pulling of B inward by the molecules striking on the wall. This pressure (force) is directly proportional to the number of molecules striking on unit volume of the walls of the container. P ∝ 1/V…………(2)
From the above two points A and B it is clear that the actual pressure exerted on the wall due to gaseous molecular is less than the ideal pressure.
Actual Pressure (P) = Ideal Pressure (Pi) – Pressure Correction (Pc)
P = Pi – Pc
Pi = P + Pc …………….(3)
Where a is constant, substitute the pressure corrections (4) is (3)
Volume correction: At high pressure the molecules are closer and covering/ occupying a considerable minimum area or volume. (Because the space available for the molecule to move is less than the actual volume of the container. Hence Vander waal accounted for this by subtracting volume correction ‘b’ from the observed volume V.
Ideal Volume (Vi) = V - b ………………(6)
We know that if Pi and Vi are pressure and volume of ideal gas then it satisfies PiVi = RT
But from (5) and (6) the ideal pressure and ideal Volumes are substituted.
Equation (7) is called Vander Waal equation for one mole of gas. This equation for ‘n’ moles of gas is
