equations physical chemistry

vanderwaals interaction
v = -1/r^6(cuu + cuu* +cdisp)
multiply by na to get per mole
average kinetic energy of translation of a particle
Etrans=3/2KT
energy of translation per mole
Etrans,m = 3/2K×nA×T
k×nA=R gas constant
Etrans,m=3/2RT
dispersion interaction
v=-3/2 polarizability vol1 x vol2 × (ionization potential 1 ×potential 2/I1 +I2) ×1/r^6
gas
epsilon<
liquid
etrans~~epsilon
solid
epsilon>>etrans
charge charge interaction
v = Q1 × Q2 / 4piepsilon0 × r
charge dipole interaction colinear
v = -u1 Q2/ 4piepsilon r^2
u* induced dipole interaction
u* = 4pi epsilon0 × polarizability volume × E (electric field)
charge dipole interactions at an angle
v = -u1 Q2 / 4pi epsilon0 × R^2 × costheta
dipole dipole interactions colinear
v = -u1u2/2pie0 r^3
addition of dipole moments
u = (u1^2 + u2^2 + 2u1u1costheta)^0.5
Pythagoras 3d dipole moments
u =(ux^2 + uy^2 +uz^2)^0.5
Keesom interactions
rotating ermanent dipoles
C = 2u1^2 u2^2 / 3(4pie0)^2 KTr^6
if v << kt
keesom interaction holds
dipole induced dipole interaction
V = -μ1^polarizability vol2^2/4pie0 r^6
effect of changing conditions for fixed amount of gas
p1 v1/ t1 = p2 v2/ t2
root mean square speed for n molecules
c = ((s1^2 + s2^2 + … sn^2)/N)^1/2
Phase Rule
F = C – P + 2
F= number of degrees of freedom
P = number of phases at equilibrium with one another
dipole dipole at an angle
v = μ1×μ2(1-3cos^2theta)/4pie0r^3
ideality assumptions for van der waals equation of gases
1. molecular size is negligible
2. no intermolecular interactions
only true at low pressures or high temperatures
corrections to vdw equation for gases
pressure reduced by intermolecular forces
p -> p + a(n/v)^2
excluded volume as molecules cannot occupy the same space
v -> v – nb
a
correction factor to account for intermolecular attractions
b
correction factor to account for finite size of molecule
Categories: Physical Chemistry