lecture 3 Flashcards
particles have different speeds meaning there is a
distribution
this distribution has a shape
how can we measure the speed of a gas
row of spinning discs with slots
the discs spin at different rates leading to particles of different speeds passing by
measuring the number of particles gives the distribution of speeds
what is the root mean squared speed based on
finding average speed using the pressure the particle it exerts
root mean speed squared and pressure
pV = 1/3n NA m Vrms2
pV = 1/3n M Vrms2
m=mass
M=molar mass
root mean speed squared equation
root 3KBT/m
root 3RT/M
what does root mean square speed allow us to do
determine the average kinetic energy of particles
what is the average kinetic energy of a particle
1/2 m vrms2
what is the total kinetic energy of an ideal gas
3/2 nRT
maxwell distribution graph is
unsymmetrical
3 types of average speed
most probable
mean speed
root mean squared
most probable speed
peak of maxwell distribution
diff of y axis = 0
root 2KBT/m
temp in k
mass: /1000 /avo
ms-1 units
mean speed aka Vmean
higher than most probable
root 8KbT/nm
n is pi
m: /1000 /avo
temp in k
ms-1 units
root mean square speed
higher than most probable and mean speed
root 3KbT/m
root 3RT/M ???
temp in k
m: /1000 /avo
ms-1
what are the 3 speeds and what are they all proportional to
most probable
mean
root mean squared
probable to root(KbT/m)
what do the 3 speeds tell us about the distribution of speeds
based on mass and temp
not on pressure or volume.
same temp = same speed
no matter the vessel theyre in
ratio of T:m determines the speeds of particles: all the speeds have T nominator and m as a denominator
what does changing the temp do to the distribution of speeds
changes them
lower temp = lower most probable speed
changes width and hight but not shape
what changes distribution of speeds
temp: higher temp = wider = larger mist probable speed, change in height and width
mass: lower mass = wider distribution.
low mass == hotter temp shape
distributioon of kinetic energy doesnt depend on what
doesnt depend on the mass
depends on temp only
explains why the ideal gas equation can be applied to all gas - based on temp and not mass aka its identity
on average particles in an ideal gas collide
elastically
total amount of kinetic energy remains the same // unchanged
distribution of kinetic energy graph
more asymmetric than speed maxwell boltzmann graph.
basically a 1s wavefunction - up down
most probable kinetic energy equation
peak of kinetic energy distribution graph
Emp = KbT/2
mean kinetic energy on distribution of kinetic energy graphs
higher than most probable
3KbT/2
same as the Vrms
what affects the distribution of kinetic energys on a distribution graph
look at the equations - the TEMPERATURE
changes the height and width not shape
effect of temp is more pronounced than speed - dependence is linear - there is no square root in the equation but there was for the speed distributions.
why is the effect of temp on kinetic energy distributions more pronounced
dependence is linear
there is no square root in the kinetic energy equations
what does the kinetic energy distributions tell us
how much energy is involved when 2 particles collide
helps us know if they will react or not
how many collisions have above the Ea - proportional to exp(-Ea/RT) - matches the rate constant ‘k’
what describes the distribution of speeds
maxwell boltzman distribution
what affects the maxwell distribution and how
mass and temp
smaller mass + larger temp = shorter and wider = increase in average speeds
what describes the kinetic energy of a particle
distribution graph
what affects the kinetic energy distribution graph and how
increasing the temp widens the graph
larger average kinetic energy
particles with more than the Ea is proportional to
exp(-Ea/RT)
explains temp dependence of rate constant.
