som week 10 Flashcards
what is the symbol and meaning of a collision cross-section?
what are the units?
collision cross-section - σ
it is the area around a particle in which the centre of another particle must be for there to be a collision
distance between the colliding particles < the sum of their radii
units - nm²
nm² = 10⁻¹⁸ m²
what is the equation for the area of the collision cross-section?
two particles of radius r must have a collision cross section of the area of a circle twice their radius
σ = π(2r)² = πd²
collision frequency
- what does it mean
- what are the units
- what is the equation
- give three proportionality equations of collision frequency
- collision freq, z, is how many collisions per second, rate of collision
- units - s⁻¹
- z = √2 Na (cσ)(p/RT)
c - average speed - z ∝ speed
- z ∝ area of collision cross section
- z ∝ 1/T
mean free path
- what is the symbol
- what does it mean
- what is the equation
- λ, m
- average distance a molecule travels before it collides with another molecule
- λ = √2 x c/z
c - average speed
z - collision frequency
what is an isotherm?
describe the difference between an isotherm at high temps and at low temps
what is the reason for this difference
isotherm is a plot generating from plotting pressure (y) against volume (x)
at high temps - experimental and actual results are very similar
but at low temps - actual values deviate from the experimental values
this deviation occurs because of gas liquefaction at high pressures
describe what gas liquefaction is
when pressure on a gas reaches a certain amount, the gas begins to turn to a liquid and when it is a liquid, it is much harder to compress
describe how a gas is behaving at
- a low pressure
- as it changes to a liquid
how does the pressure change once the gas turns to liquid?
- at a low pressure the gas is gaseous, taking up a relatively large volume
- no pressure change from gas to liquid but volume decreases because liquids take up less room
when all the gas is liquefied, it is much harder to compress, pressure is very high
critical temp
- what is the symbol
- what is the meaning
- Tc
- the temperature at which the liquid form of the gaseous molecule can exist under the temperature and pressure condition
- the density of the gas and liquid of the molecule are equal
what are two assumptions made when handling ideal gases?
molecules have negligible size compared to their container
there are no intermolecular forces/interactions
compression factor
- what is the symbol
- what does it mean
- what is the equation
- Z capital Z compared to collision freq which is a small z
- it is the ratio of actual measured gas volume to what we expect in an ideal gas
- Z = Vm/Vm°
Vm - real gas volume
Vm° - ideal gas volume
how do the values of Z, compression factor relate to the forces involved in gas interactions
Z < 1 → attractive forces dominate
Z = 1 → perfect gas
Z > 1 → repulsive forces dominate
correcting the ideal gas equation
- what does the pressure become and why
when correcting the ideal gas equation we need to consider intermolecular forces, these forces work to reduce the pressure of collisions
pressure becomes
p → p + a(n/V)²
a = constant related to strength of forces n/V = moles per unit of volume
correcting the ideal gas equation
- what does volume become and why
at very high pressures, molecules get close together and so no longer have negligible volume
because the molecules have volume, this excludes previously available volume
volume becomes
V → V - nb
b = a constant found in data tables
give the van der Waals equation of state
- as a increases what happens
- as b increases what happens
(p + a(n/V)²)(V - nb) = nRT
as a increases, attractive forces increase
as b increases, excluded volume increases
define polymorphs
solids with different structures but the same composition
eg carbon has structures of diamond and graphite
in close packing structures, what 3 characteristics must the atoms have
- all atoms are the same size
- all atoms are spherical
- all atoms are touching
describe the first 3 layers of cubic close packing/face-centred cubic structure (fcc)
- first is a close packed layer, all touching
- second layer atoms sit in the depressions of the first layer
- third layer lies on the depressions of the second layer that are not above the first layer
ABC pattern
describe the first 3 layers of hexagonal close packing
- first is a close packed layer, all touching
- second layer atoms sit in the depressions of the first layer
- third layer atoms sit in the depressions of the second that are directly above the first layer atoms (identical to layer 1)
ABA pattern
what is the coordination number of
- cubic close packing
- hexagonal close packing
- 12
- 12
each atom is bonded to 12 other atoms
define unit cell
how are they drawn?
smallest repeating unit of a structure
drawn as a cube with atoms placed on the cube depending on how they are packed
describe the unit cell of cubic close packing/face-centred cubic
atoms at each corner
an atom in the middle of each cube face
no atom in the centre of the cube
describe the body-centred cubic unit cell
what is the coordination number
atom at each corner
one atom in the centre
coordination number 8
describe the primitive cubic unit cell
what is the coordination number
just one atom in each corner
coordination number 6
describe hexagonal close packing unit cell
hexagonal prism shape
ABA structure
see w10 vid15 for a visual
why is knowing packing efficiency useful
tells us about stability of a solid
give 3 steps and the equation for working out packing efficiency
- find number of atoms in a unit cell
- find volume of atoms in the unit cell
- find volume of the entire cube
packing efficiency, % = volume of atoms/volume of cube x 100
define interstitial site
what are the 2 different types
spaces in a unit cell or close packed structures where you can fit smaller atoms
octahedral and tetrahedral site
octahedral interstitial site
- describe the layering
- where does the smaller atom sit
- what is the coordination number of this smaller atom
- 3 atoms on top, 3 atoms below, there’s a depression in the middle that does not sit on an atom
- the smaller atom lies in the middle
- coordination number 6
tetrahedral site
- describe the layering
- where does the smaller atom sit
- what is the coordination number of this smaller atom
- 3 atoms and then a single atom in the middle depression of these 3
- the smaller atom lies in the tetrahedral structure, in the middle of the 4 close-packed atoms
- coordination number 4
what is radius ratio and why is it useful
what is the equation
what does a radius ratio of 1 mean
the ratio of anion radius to cation radius in. a close packed solid structure, useful to work out coordination numbers of structures
radius ratio = r+/r-
radius ratio = 1, coordination number is 12, max number of atoms can pack around each other
