Chapter 15 Gases Flashcards
What is definition for one mole again
The amount of substance equal to the number of entities in 12g of cabron 12
This is a avagadro constant, 6.02 x 10^23
So 1 mol contains this many entities
What is the kinetic theory of matter
This is just a model to describe behaviour of atoms as an IDEAL GAS, as real gases are too complex
This way we are able to use newton law or motion to show how IDEAL gasses cause pressure etc, when before we couldn’t as microscopic scale have different rules
What are the assumptions for an IDEAL GAS (5) list them
1)Atoms/ molecules in gas occupy a negligible volume compared to the volume of the gas
2) the collisions of atoms with each other AND THE container are perfectly elastic (no kinetic energy lost
3) time of collisions between atoms are negligible compared to time without colliding
4) electrostatic forces between atoms or molecules are negligible EXCEPT during collisions
5) has contains atoms molecules moving in random directions and random speeds!
5) gas moves in random directions with random speeds explain why good assumption
Due to brownisn motion
Good sssuption because if it wasn’t random then something would happen = there would be some net movement but there isn’t
1) gases atoms of molecules occupy negligible volume compared to gas volume
Who good
Good because gas can be compressed so they need to have small volume indicually
3) collisions between atoms and containers are perfectly elastic
Why good
Good because we can’t see where the energy would go anyways
4) time spent colliding is negligible compared to time spent without colliding
It just is
Electodstsic forces of attraction between atoms are negligible except when colliding
What does it show
This shows that 1 mol occupies the same amount of volume no matter where and what if at rtp
Again list all 5
1) gases move random speeds and direction
2) time spent collidjg negligible fompsred to time spent without
3) collisions between each other snd container elastic
4) electrostatic force negligent except during collisions
5) occupy negligible volume cl speed to volume of bsd
Okay so using sssumption that collisions are elastic how can we explain how they exert a pressure
Collisions are elastic, so when it hits the wall it’s gonna bounce off with same v as kinetic energy conserved but OPPOSITE DIRECTIOn
As a result change of momentum is = -2mv
And this exerts a force on the particle based on time of contact with wall
However due to newton 3rd law it exerts force on the wall too and at right angles
So sum of all force is total force and over area = pressure
Summary
- elastic Collins so rebounds at same v but opposite direction, this gives a change jnnkknetum and thus force
- due to newton this force applied at surface
# some of force over surface is pressure
What assumptions must be made now when working with pressure etc and gas
1) ideal gas
3) moles of gas constant
For constant TEMPERTAURE moles and ideal gas what relationship with pressure and volume
PV= constant
Pressure properinsl to 1/v
Why must you lower the volume of something slowly or give time after when doing PV = constant experiments?
Entering a force on the molecules does work on them so TEMPERTAURE increases, and with sn increase in TEMPERTAURE you get inc pressure
Do slowly or let it cool down before taking new readings
What happens when you increase TEMPERTAURE, why does pressure increase FOR THE SAME VOLUME?
2 ways
Inc temp = inc ke = inc velocity = inc momentum = so harder forces exerted on wall (so more force = more pressure)
Inc temp = inc ke = inc FREQUENCY OF COLLISIONS= more Collins = more force so more pressure
So what isnrelationship for pressure and TEMPERTAURE
Assuming fixed volume, moles and ideal gas
Pressure promotional to TEMPERTAURE
P=kT (in kelvin)
So P/T = constant
How to find value for absolute zero
Absolute zero when no internal energy do not moving so no pressure
If do graph pressure against temperature and vary temp and record pressure you can extrapolate to temperature at which pressure isn0
This is 0K
Combine the laws to make a new one for pressure volume and temperature
If pressure inversely to volume and proportional to temp
Then it’s proptiomal to T/V
Thus P=KT/V
And here K is NR
If we plot p against 1/V what is the gradient
So if everything constant l whagt would a lower gradient represent for another variable .
As P= KT x 1/V
The gradient is Kt, which is NRT
So a lower gradient, for same moles and R which is constant, means you’re at a LOWER temp
If P= KT/V, how to do changing condisitons questions
Rearrange for constant and equate
PV/T = PV/2 (2)
Another formula relating volume and temp for constant pressure?
List all three gas laws
Volume orooritnsl to temp
For constant volume p prop to t
For constant t p prop to 1/v
For constant pressure t prop to v
How to do an experiment to show PV=nrt but actually how would you change volume, keep pressure constant , moles constant, TEMPERTAURE constant to change each vairblwe
- to keep pressure, put hole in it so that pressure is just by ATMOSPHERIC
- to keep volume constant vary, surface area is constant so length is properinsl to volume so change by this. Keep constant by RIGID CONTAINER
- to keep moles constant, keep plunger closed to keep it
- to keep TEMPERTAURE constant heat it constantly with heating mantle at same tmeleyure , or leave at room temp
What is RMS and why we use
How does this compare to average velocity and average speed
We went to compare average velocities of particles in a gas but assumption is they move in random directions . As a result they would add to 0 as a vector
Instead we square to get rid of negative, then mean of the squares and then square root it too
Average velocity = 0
Average speed just means taking magnitude of velocity and thus it’s not the same as rms , but jus add land divide
Wen do these equations no longer work for gas laws under what conditions (2)
When pressure too big as forces are made and when temp too small as forces are made
What is new equation for PV
PV = 1/3Nm c2 =mean of c2
How do you represent the averages of speed on a BOLTZMANN distribution (chemistry ) and what happens when TEMPERATURE IS INCREASED
Si number of particles with speed v and then sped of particle on x axis
Then maxwell distribution, this means random distribution if speeds, some will be very slow some very fast mist mistlry in middle
Mode first, then mean, then rms (always higher)
2) when temp increases more particles gain more speeds so distribution is more spread out and flattens too (jus like in chem)
Wait Im PV = 1/3 NMC2, what is capital N?
Little n?
Capital is TOTAL AMOUNT OF PARTICLES
So moles x avagadro constant!
Little n is moles
Okay so what is Boltzmann constant
Simply R/ avagadro
How can we rearrange the equation to link TEMPERTAURE and mean kinetic energy together
First off kinetic energy is 1/2mv2, but mean kinetic energy is 1/2mc2
So if PV = 1/3NMc2, we have M and C2, can divide both sides by 1/2 to rearrange for ke
Now expression for ke, remember that N = nxNa
So n cancel out
And R/Na = K
So we now get 1.5KT= mean kinetic energy
And thus ke is PORPTIOMAL TO T ( BUT IN KLEVIN)
Final equation for ke mean and temp in kelvin
1,5KT = mean ke
The fact that they are promotional means if I double ke what happens
And why do different masses at same temp move at different speeds
Finally what must I REMEMBER TO DO TO TEMP FIRST
Must be in kelvin
Fact proptinal is if I double the ke the temp will and vice Verda
And so different masses at same temp will have the same KE, thus will have varying v2 due to their masses
Must be in KELVIM! if I double my room temp the ke will NOT DOUBKE
Another equation of PV in particle form
We know PV = nRT
If we sub in n = N/Na
We get PV = NKT
All three PV equatuins then and 4 gas
PV = nrt
PV = 1/3NMc2
PV = NKT
1.5KT = mean ke
P prop to T at same volume
P prop to 1/V at same temp
V prop to T at same pressure
Finally P= K T/V
Where K = nr
REMMEBER aLl of these only apply to
Ideal gases nothing else with 5 assumptions
How is mass independence of kinetic energy average
Because ke is = 1.5 KT
But having different masses will result in different rms
How to find rms using temp and ke
Equator 1/2mc2 = 1.5KT
And rearrange
How can you use these ideas of ke being prop to t to explain why such a light atoms like helium has escaped earth
Because yh at same temp same ke but small mass so rms is huge and if enough ti can escape grav pull and wscape
Okay finally we said gases have greatest potential energy
However what do we say in an IDEAL GAS
assumption is intermolecular forces between are hegljble except for collisions , thus no bonds at all so ni potential to make bonds so no potential energy
Thus there is no INTERNAL energy in an ideal gas
And as a result all internal energy is in KINETIC store
So doubling temp doubles kinetic and thus doubles INTERNAL ENERGY TOO But only for an IDEAL GAS!
Fact no potential energy means what for internal
So what happens to internal energy if I double temperature in an ideal gas final
That all internal is kinetic
So doubling temp doubles kinetic and thus doubles INTERNAL ENERGY TOO But only for an IDEAL GAS!
Remember if T is propritnsk mean square speed, then what is t proprtinsl to rms
Rms 2! So if rms doubles then 5 multiply by 4 and volume by 4 too
For these factor questions involving differnt pressures, apply laws to BOTH
Sides so both pressures whatever and then add them up
Remember with scales you are
DIVIDING, so if 0.5 on top and 0.25 on bottom that becomes 2!
Always in factor questions first you. Should
So the thing you are calculating,ting isolate of any variables so squares roots whatever, now you can apply the rules
Remember volume of gas and volume of molecules are
Not the same, assumption is volume of gas much bigger compared to volume of molecules, as a lot of space between etc
Equation m is mass of what
Mass of INDICUAL PARTICLE
