THERMO2 Flashcards
Ideal Gas Equation
PV = nRT
P = pressure V = volume n = number of moles R = molar gas constant T = temperature
Assumptions of Kinetic Gas Theory
- Gas contains many molecules
- Molecules are well separated
- Direction of motion of molecules is random
- Molecules exert no force on each other except during collisions
- Collisions between molecules and with walls are elastic
Ideal Gas Constant
R = PV/nT = 8.31
When do real gases behave as ideal gases?
Real gases behave as ideal gases when molecules are well separated i.e. at high temperatures and low pressures
Units of Pressure
1 pascal
1Pa = 1 N/m^2
Units of Pressure
1 bar
1 bar = 10^5 Pa
Units of Pressure
1 atmosphere
1 atm = 1013millibar = 1.013x10^5 Pa
Standard Temperature and Pressure (STP)
0C = 273.15K 1atm = 1.013x10^5 Pa
How does kinetic gas theory explain pressure?
Collisions of molecules with the walls of the container
Change in momentum
Pressure Equation
P = (1/3) * Nm/V * (v^2)av
Kinetic Energy per Molecule
(1/2)mv^2 = (3/2)kT
Dalton’s Law of Partial Pressures
Ptotal = P1 + P2
Pt =RT/V (n1 + n2)
Pressure in a Fluid
P = ρhg
Kinetic Energy per Mole
(1/2)Mv^2 = (3/2)RT
Number of Molecules and Moles Equation
N = n*Na
N = number of molecules n = number of Moles Na = advogadros constant
Mass of Molecules and Moles Equation
M = m*Na
M = mass of a mole
m =mass of a molecule
Na = advogadros Constant
Relationship between advogadros Constant, the molar Gas Constant and Boltzmann Constant
R = k*Na
Root Mean Square Speed Equation
Vrms = √(Vav^2) = √(3kT/m)
Mean Free Path
Definition
The average distance travelled by a Molecule between collisions
Mean Free Path
Equation
λ = 1/(√2nvπ*d²)
λ = mean free path nv = number density d = diameter of a molecule
What does mean free path depend on?
- size of molecules
- particle density of the gas
- doesn’t depend on speed
- depends on geometric factors
Collision Time
Definition
The average time between collisions
Collision Time
Equation
λ = Vav * τ
τ = collision Time λ = mean free path Vav = average velocity
What does collision time depend on?
- mean free path
- speed of molecules
NND
Nearest Neighbour Distance
NND = ∛(volume per molecule) NND = ∛(1/nv) = ∛(V/N) = ∛(kT/P)
Maxwell Boltzmann Distribution
Description of Graph
- bell curve
- steeper on left hand side
- doesn’t touch the y axis
- theoretically the Graph continues to x=∞
- speed on X axis
- fraction of molecules on y axis
Maxwell Boltzmann Distribution
Vmax
Vmax is the speed that the highest proportion of molecules have
I.e. The maxima of the Graph
To find it differentiate the Graph equation and set it equal to zero
Vmax = √(2RT/M)
Maxwell Boltzmann Distribution
Vrms
The square root of the average of the speeds squared
Calculated using an integral
Vrms = √(3kT/m) = √(3RT/M)
Maxwell Boltzmann Distribution
Vav
Average of the velocities of each molecule so accounts for direction
Calculated using an integral
Vav = √(8kT/πm) = √(8RT/πM)
Relationship Between Vmax, Vrms and Vav
Vmax < Vav < Vrms
Maxwell Boltzmann Distribution
Change With Temperature
For a fixed mass of gas, an increase in temperature results in:
- Vmax increases
- peak moves to the right
- height decreases
- area under graph remains constant as the number of molecules has not changed
Maxwell Boltzmann Distribution
Change With Molar Mass
Temperature remains constant but molar mass is increased results in:
- Vmax decreased
- height of graph increases
- area under graph remains constant as the number of molecules has not changed
Maxwell Boltzmann Distribution
Evaporative Cooling - Change With Loss of Fast Molecules
- the fastest molecules are lost
- once thermal equilibrium is achieved again after the initial loss, the graph:
- Vmax decreased
- height decreased and area under the graph has decreased as there are fewer molecules than their were before the evaporative Cooling
