Question

derivation of vander wall pressure correction

Answer 1

Van der Waals forces include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces. They differ from covalent and ionicbonding in that they are caused by correlations in the fluctuating polarizations of nearby particles (a consequence of quantum dynamics[4]).

Being the weakest of the weak chemical forces, with a strength between 0.4 and 4kJ/mol, they may still support an integral structural load when multitudes of such interactions are present. Such a force results from a transient shift in electron density. Specifically, the electron density may temporarily shift more greatly to one side of the nucleus. This generates a transient charge to which a nearby atom can be either attracted or repelled. When the interatomic distance of two atoms is greater than 0.6 nm the force is not strong enough to be observed. In the same vein, when the interatomic distance is below 0.4 nm the force becomes repulsive.

Intermolecular forces have four major contributions:

A repulsive component resulting from the Pauli exclusion principle that prevents the collapse of molecules.Attractive It repulsive electrostaticinteractions between permanent charges (in the case of molecular ions), dipoles (in the case of molecules without inversion center), quadrupoles (all molecules with symmetry lower than cubic), and in general between permanent multipoles. The electrostatic interaction is sometimes called the Keesom interaction or Keesom force after Willem Hendrik Keesom.Induction (also known as polarization), which is the attractive interaction between a permanent multipole on one molecule with an induced multipole on another. This interaction is sometimes called Debye force after Peter J.W. Debye.Dispersion (usually named London dispersion interactions after Fritz London), which is the attractive interaction between any pair of molecules, including non-polar atoms, arising from the interactions of instantaneous multipoles.

Answer 2

$Here \: is \: the \: answer \: of \: your \: question$


`$\textbf{1. Pressure Correction}$`

A molecule is pulling inward by molecule B. So, the correct pressure is P + p.

→ [Figure is in Attachment !!]

Now,

p directly proportional to cA × cB

p directly proportional to n/v × n/v

p directly proportional to n² ÷ v²

p = an² ÷ v²

Here a = constant

p = Pressure exerted by gas particle on each other

P = Pressure of gas.

So, net pressure = P + p

p = an² ÷ v² .........(1)


`$\textbf{Correction for Volume}$`

v = volume of container

nb = actual volume of gas particle

v - nb = empty volume ........(2)

[v - nb = correct volume]

Now,


`$\textbf{Vanderwall equation}$`

PV = nRT

(P + p) (v) = nRT

[P + an² ÷ v²] [v - nb] = nRT

= [P + a ÷ v²] [v - nb] = RT



$Hope \: it \: helps \: you.$