Chapter 13/14 Flashcards
Boyle’s Law
PV = k
Charle’s Law
V/T = k
Pressure Law
P/T = k
Ideal Gas Law (2)
pV = nRT
pV = NkT
equation of state
When does the ideal gas law work well?
Gases at low pressures and high temperatures.
Boltzmann’s constant
k = R/N(A)
Name 4 conditions of kinetic theory
- Particle velocity is proportional to pressure.
- faster particles, larger momentum, larger force on the wall. - Number of particles is proportional to pressure
- Volume of the box is inversely proportional to the pressure.
- Particles travel in random directions at different velocities.
Kinetic theory equation
pV = 1/3 NmC^2
Name a few assumptions of kinetic theory
- Gas contains large number of particles
- Particles move rapidly and randomly
- Motion of particles follow Newton’s laws
- Collisions are perfectly elastic.
- No other forces between particles.
- Forces during collisions are instantaneous.
- Particles have negligible volume compared to container.
Average distance moved of a particle in N steps
proportional to root N
What is specific heat capacity?
Amount of energy needed to raise the temperature of 1kg of the substance by 1K.
E = mc0
3 things about speed distribution of gas particles
As temperature of gas increases:
- Average particle speed increases
- Maximum particle speed increases
- Curve spreads out with same area.
What is internal energy?
Sum of kinetic and potential energy of particles within a system.
Relationship between Boltzmann’s constant and Molar gas constant
k = R/Na
Boltzmann’s constant can be thought of as the gas constant for one particle of gas in contrast to R as the gas constant for one mole of gas
How to find average KE of a gas molecule (ideal monatomic gas)
equate ideal gas equation with kinetic theory equation
nRT = 1/3 Nmc^2
Average distance moved by random walk with N steps
proportional to root N
What is the specific thermal capacity of a substance?
Amount of energy required to raise the temperature of 1kg of a substance by 1K.
J kg^-1 K^-1
Specific thermal capacity equation
ΔE = mcΔθ
What does the shape of the speed distribution of particles in a gas depend on?
Temperature of the gas.
As the temperature increases:
- Average particle speed increases
- Maximum particle speed increases
- Distribution becomes more spread out.
- Areas are equal
What is internal energy?
Sum of the kinetic and potential energy of the particles. (PE in the bonds which is 0 for ideal gases)
The amount of energy contained in a system.
1st Law of Thermodynamics
ΔU = Q + W
Change of internal energy = supply thermal energy + work done on it
Derivation of kinetic theory steps
- Change of momentum of gas molecule per collision with walls of box of length x = 2mv
- Time between collisions with wall = 2x/v (there and back)
- No of collisions per unit time = v/2x
- Force = change in momentum = change in momentum per collision x no of collisions per unit time
- F = 2mv x v/2x = mv^2/x
- For N particles, F = Nmv^2/x
- P = F/A = Nmv^2/Ax = Nmv^2/V
- Molecules all have different velocities so average is taken - mean square speed. PV = 1/3 Nmc^2 (force in only one dimension out of the 3)
What does a rise in absolute temperature result in?
Increase in kinetic energy of each particle and thus a rise in internal energy.
What is the boltzmann factor?
The ratio of the number of particles in energy states e joules apart.
Proportion of particles with activation energy.
How does Boltzmann factor vary with temperature?
S shaped curve.
Low temperatures, boltzmann factor very low so very few particles will have sufficient energy to react.
High temperatures: bf approaches 1 so nearly all particles will have enough energy to react.
In between these two, bf increases rapidly with temperature.
Relationship between boltzmann factor and rate of reaction
Rate of reaction is proportional to Boltzmann factor
