som week 8

Question 1

give two equations for weighted average potential of 2 rotating dipoles aka a Keesom interaction

Answer 1

= -Cμμ/r⁶

Cμμ = constant of proportionality, its negative because it’s an attractive energy, and μμ signifies its between two dipoles

Cμμ = -2μ₁²μ₂²/3(4πℇ₀)²kTr⁶

k = Botlzmann constant which is given

Question 2

give two equations for the dipole-induced dipole interaction

Answer 2

V = -Cμμ*/r⁶

Cμμ* = π₁²ɑ₂’/4πℇ₀

Question 3

give two equation for the induced dipole-induced dipole interaction

Answer 3

V = -Cdisp/r⁶

Cdisp = 3/2 x ɑ₁’ɑ₂’ x I₁I₂/I₁ + I₂

I = ionisation potential

Question 4

what are the two components of the total interaction? how is this represented on a graph

Answer 4

total interaction = attraction + repulsion

add the attraction and repulsion functions
V = Cn/rn - Cm/rm
n > m
first term represents the repulsive forces and second term represents the attractive forces

Question 5

on the total interaction energy graph, what is the value of the minimum point?

Answer 5

minimum point V = -ℇ
and r = 2^1/6 x r₀
not vacuum permittivity

Question 6

give the Lennard-jones potential energy equation

Answer 6

V = 4ℇ{(r₀/r)¹² - (r₀/r)⁶}

ℇ = depth of the well
r₀ = separation at which the interaction is 0

Question 7

in the Lennard-jones equation, what happens to the graph when

• r value is changed
• ℇ value is changed
• molecules get larger

Answer 7

• r shifts graph left or right
• ℇ makes a shallower or deeper well
• as molecules get larger, the graph shifts to the right because molecules can get as close together and well gets deeper because they experience a stronger attraction

Question 8

give the equation for van Der Waals interactions

Answer 8

V = -1/r⁶ (Cμμ + Cμμ* + Cdisp)

Cμμ -> electrostatic interaction
Cμμ* -> inductive interaction
Cdisp -> dispersion interaction

all contribute to van der waals interactions§

Question 9

give the equation for the kinetic energy of

• one molecule
• one mole of molecules

Answer 9

• Etrans = 3/2 kT

- Etrans,m = 3/2 NakT = 3/2 RT

Question 10

what is Etrans,m at room temp?

Answer 10

3.716 kJ/mol

Question 11

what is the value of Etrans relative to ℇ in a:

• solid?
• liquid?
• gas?

Answer 11

• SOLID ℇ&raquo_space; Etrans
• LIQUID ℇ ≈ Etrans
• GAS ℇ &laquo_space;Etrans

Question 12

how is state of matter worked out from the interaction energy

Answer 12

if kinetic energy of molecules can overcome interactions it will become a liquid or a gas

if kinetic energy of molecules cannot overcome interaction forces it will remain a solid

use the V =… for the appropriate interaction in J/mol
V = -ℇ
work out Etrans,m and assess relationship between ℇ and Etrans,m