Chapter 15 Gases

Question 1

What is definition for one mole again

Answer 1

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

Question 2

What is the kinetic theory of matter

Answer 2

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

Question 3

What are the assumptions for an IDEAL GAS (5) list them

Answer 3

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!

Question 4

5) gas moves in random directions with random speeds explain why good assumption

Answer 4

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

Question 5

1) gases atoms of molecules occupy negligible volume compared to gas volume
Who good

Answer 5

Good because gas can be compressed so they need to have small volume indicually

Question 6

3) collisions between atoms and containers are perfectly elastic
Why good

Answer 6

Good because we can’t see where the energy would go anyways

Question 7

4) time spent colliding is negligible compared to time spent without colliding

Answer 7

It just is

Question 8

Electodstsic forces of attraction between atoms are negligible except when colliding

What does it show

Answer 8

This shows that 1 mol occupies the same amount of volume no matter where and what if at rtp

Question 9

Again list all 5

Answer 9

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

Question 10

Okay so using sssumption that collisions are elastic how can we explain how they exert a pressure

Answer 10

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

Question 11

What assumptions must be made now when working with pressure etc and gas

Answer 11

1) ideal gas
3) moles of gas constant

Question 12

For constant TEMPERTAURE moles and ideal gas what relationship with pressure and volume

Answer 12

PV= constant

Pressure properinsl to 1/v

Question 13

Why must you lower the volume of something slowly or give time after when doing PV = constant experiments?

Answer 13

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

Question 14

What happens when you increase TEMPERTAURE, why does pressure increase FOR THE SAME VOLUME?

2 ways

Answer 14

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

Question 15

So what isnrelationship for pressure and TEMPERTAURE

Assuming fixed volume, moles and ideal gas

Answer 15

Pressure promotional to TEMPERTAURE
P=kT (in kelvin)
So P/T = constant

Question 16

How to find value for absolute zero

Answer 16

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

Question 17

Combine the laws to make a new one for pressure volume and temperature

Answer 17

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

Question 18

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 .

Answer 18

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

Question 19

If P= KT/V, how to do changing condisitons questions

Answer 19

Rearrange for constant and equate

PV/T = PV/2 (2)

Question 20

Another formula relating volume and temp for constant pressure?

List all three gas laws

Answer 20

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

Question 21

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

Answer 21

• 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

Question 22

What is RMS and why we use

How does this compare to average velocity and average speed

Answer 22

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

Question 23

Wen do these equations no longer work for gas laws under what conditions (2)

Answer 23

When pressure too big as forces are made and when temp too small as forces are made

Question 24

What is new equation for PV

Answer 24

PV = 1/3Nm c2 =mean of c2

Question 25

How do you represent the averages of speed on a BOLTZMANN distribution (chemistry ) and what happens when TEMPERATURE IS INCREASED

Answer 25

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)

Question 26

Wait Im PV = 1/3 NMC2, what is capital N?
Little n?

Answer 26

Capital is TOTAL AMOUNT OF PARTICLES
So moles x avagadro constant!

Little n is moles

Question 27

Okay so what is Boltzmann constant

Answer 27

Simply R/ avagadro

Question 28

How can we rearrange the equation to link TEMPERTAURE and mean kinetic energy together

Answer 28

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)

Question 29

Final equation for ke mean and temp in kelvin

Answer 29

1,5KT = mean ke

Question 30

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

Answer 30

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

Question 31

Another equation of PV in particle form

Answer 31

We know PV = nRT
If we sub in n = N/Na
We get PV = NKT

Question 32

All three PV equatuins then and 4 gas

Answer 32

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

Question 33

REMMEBER aLl of these only apply to

Answer 33

Ideal gases nothing else with 5 assumptions

Question 34

How is mass independence of kinetic energy average

Answer 34

Because ke is = 1.5 KT

But having different masses will result in different rms

Question 35

How to find rms using temp and ke

Answer 35

Equator 1/2mc2 = 1.5KT

And rearrange

Question 36

How can you use these ideas of ke being prop to t to explain why such a light atoms like helium has escaped earth

Answer 36

Because yh at same temp same ke but small mass so rms is huge and if enough ti can escape grav pull and wscape

Question 37

Okay finally we said gases have greatest potential energy

However what do we say in an IDEAL GAS

Answer 37

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!

Question 38

Fact no potential energy means what for internal

So what happens to internal energy if I double temperature in an ideal gas final

Answer 38

That all internal is kinetic

So doubling temp doubles kinetic and thus doubles INTERNAL ENERGY TOO But only for an IDEAL GAS!

Question 39

Remember if T is propritnsk mean square speed, then what is t proprtinsl to rms

Answer 39

Rms 2! So if rms doubles then 5 multiply by 4 and volume by 4 too

Question 40

For these factor questions involving differnt pressures, apply laws to BOTH

Answer 40

Sides so both pressures whatever and then add them up

Question 41

Remember with scales you are

Answer 41

DIVIDING, so if 0.5 on top and 0.25 on bottom that becomes 2!

Question 42

Always in factor questions first you. Should

Answer 42

So the thing you are calculating,ting isolate of any variables so squares roots whatever, now you can apply the rules

Question 43

Remember volume of gas and volume of molecules are

Answer 43

Not the same, assumption is volume of gas much bigger compared to volume of molecules, as a lot of space between etc

Question 44

Equation m is mass of what

Answer 44

Mass of INDICUAL PARTICLE