Chapter 14

Question 1

The average thermal energy of a particle is proportional to…

Answer 1

The temperature

Question 2

Equation for average thermal energy

Answer 2

E = kT
where k = boltzmann’s constant 1.38 x10^-23 Jk^-1
and T = temperature in Kelvin.

Question 3

How do you convert energy per particle to electron per volt?

Answer 3

kT / (1.6X10^-19)

Divide by an electron

Question 4

How do you convert energy per particle to energy per mol^-1?

Answer 4

kT x (6 x 10^23)
Multiply by Avogadro's constant.

Question 5

The ratio E/kT

Answer 5

Particles in matter are held together by bonds, the energy needed to break these bonds is E. When kT is big enough compared with E the bonds are broken and the matter comes apart

Question 6

What is activation energy?

Answer 6

• The energy needed to make something happen
• For a change of state to happen particles need to ‘climb’ an energy barrier
• The activation energy, E, is the the energy needed to overcome that barrier.

Question 7

Where does the activation energy come from?

Answer 7

-It comes from the random thermal energy of the particles.

Question 8

Examples of things that involve activation energy

Answer 8

• A change of state (e.g liquid to gas)
• Thermionic emission
• Ionisation in a candle
• Conduction in a semiconductor
• Viscous flow.

Question 9

Gaining energy through random collisions

Answer 9

-Each time particles collide there is a chance that one of them will gain extra energy- above and beyond the average kT. If that happens several times in a row, a particle can gain energies much, much higher than average.

Question 10

Hotter temp =

Answer 10

Higher energy

Question 11

Energy equation with photons

Answer 11

hf = kT

Question 12

Highest temperatures =

Answer 12

Mater comes apart completely

Question 13

Lowest temperatures =

Answer 13

Particles slow down or stop

Question 14

Why do these changes happen?

Answer 14

Because of the different amounts of random jostling energy shared amongst the particles at different temps

Question 15

Graph of energy against temperature

Answer 15

Directly proportional so straight line graph positive gradient

Question 16

At high temperatures

Answer 16

-Bonds break and matter comes apart. Atoms come apart into ions and electrons. The ratio E/kT is small even for large E

Question 17

At low temperatures

Answer 17

-Thermal activity is feasible and E/kT is large except for processes with very small E. Matter condenses to solid or liquid and complex structures form.

Question 18

When do most processes start happening?

Answer 18

-Many processes start happening at an appreciable rate when E/kT is in the range 15-30.

Question 19

Random thermal energy

Answer 19

The random thermal energy of a particle is a small multiple of the energy kT. As the temperature increases more particles can cross the energy gap characteristic of activation processes.

Question 20

Getting extra energy by chance

Answer 20

-By chance, particles may get extra energy from the random thermal motion of particles in the surroundings

Question 21

Why/How do particles change energy levels?

Answer 21

Many processes for instance melting, evaporating, ionising start happening at an appreciable rate when the energy needed is a multiple of the average energy kT per particle.

Question 22

Why is the energy level change random?

Answer 22

-Because it is by chance that a particle will be hit by enough particles or hit by another unusually energetic particle that it will gain the energy.

Question 23

What is a physical example that molecules climb energy states (gravitational hills)?

Answer 23

• The Earths atmosphere
• As you go higher into the atmosphere the air thins and air molecules are pulled towards the Earths surface by gravity but diffuse away from the surface
• Earths surface is a gravitational hill

Question 24

What is the fraction of molecules which by chance have the extra energy to be at a height greater by h?

Answer 24

f = e^(-E/kT)

Where E= average energy of thermal activity
T= Temp in Kelvin

Question 25

Diffusion in terms of random motion

Answer 25

- Molecules diffuse from higher to lower concentration - Random motion takes molecules from where there are fewer. - Diffusion goes down concentration gradients

Question 26

As E/kT increases...

Answer 26

The fraction of particles with that energy rapidly gets smaller

Question 27

Equation for the Boltzmann factor:

Answer 27

Boltzmann factor = e^(-E/kT)

Question 28

The Boltzmann factor when the E/kT ratio is low

Answer 28

- At small ratios the temperature is Hot - The temperature T is high - The ratio E/kT is small - The fraction e^(E/kT) is large and approaches 1

Question 29

The Boltzmann factor when the E/kT ratio is high

Answer 29

- At high ratios the temperature is Cold - The temperature is T is low - The ratio E/kT is large - The fraction e^(E/kT) is small and approaches 0

Question 30

graph: The boltzmann factor e^(E/kT) against the ratio e/kT

Answer 30

Negative straight line graph almost through 0

Question 31

The boltzmann factor against temperature graph: When the ratio T/K is low

Answer 31

- -At low ratios the temperature is Cold - The temperature is T is low - The ratio E/kT is large - The fraction e^(E/kT) is small and approaches 0

Question 32

The boltzmann factor against temperature graph: When the ratio T/K is high

Answer 32

- At high ratios the temperature is Hot - The temperature T is high - The ratio E/kT is small - The fraction e^(E/kT) is large and approaches 1

Question 33

The boltzmann factor against temperature graph

Answer 33

- When E > kT the Boltzmann factor increases very rapidly with temp - Increase exponentially

Question 34

When do important changes happen

Answer 34

-Important changes happen when E/kT is of the order 15-30

Question 35

What is the Boltzmann factor E

Answer 35

-Boltzmann factor is the ratio of numbers of particles in states differing by energy E

Question 36

Activation process

Answer 36

- This is process of a molecule 'climbing' the energy hill - An energy hill has to be climbed before the process can happen - The energy needed has be to acquired by chance from random thermal agitation of the surroundings.

Question 37

What needs to be true for activation processes to occur?

Answer 37

The rate of reaction is proportional to e^(-E/kT)

Question 38

How can the boltzmann factor help explain fevers?

Answer 38

- Reactions in the body increase their rate dramatically is the temperature increases and decrease if it falls. - You can get experimental evidence of the value of the activation energy by observing how much the rate increase for a given increase in temp.

Question 39

What is the origin of the Boltzmann factor?

Answer 39

-The origin of the Boltzmann factor is the small probability of repeatedly gaining extra energy at random from a large collection of other particles

Question 40

Rate of reaction

Answer 40

-To a first approximation the rate of a reaction with activation energy E is proportional to e^(-E/kT), and increases rapidly with temperature if E >> kT

Question 41

Reaction changes

Answer 41

-Reactions can involve changes in the number of spatial or orientational arrangements of particles, as well as of their energies.

Question 42

What does the Boltzmann factor tell you?

Answer 42

- It tells you the ratio of the particles in two energy states - It gives the ratio of the numbers of particles in energy states E joules apart

Question 43

Only about one in 10^13 to one in 10^7 particles have enough energy to overcome the activation energy, this sounds small but why is this not what is seems?

Answer 43

-Because particles are moving so fast, and reactions are happening about 10^9 every second.

Question 44

The boltzmann factor varies with temperature

Answer 44

- You get an s shaped curve if you plot boltzmann factor against temp - At low temps the boltzmann is very low so fe particles have sufficient energy to react and reactions are slow - Whereas at high temps the boltzmann approaches 1 so nearly all particles have enough energy to react and reactions are fast.

Question 45

What is the rate of reaction with activation energy proportional to?

Answer 45

The boltzmann factor.

Question 46

Why/ when is the Boltzmann factor important?

Answer 46

The Boltzmann factor is important in cases where particles require a large amount of energy for a process to occur. The Boltzmann factor gives an approximate estimate of the fraction of particles with an excess of energy of at least ε. Thus the value of the Boltzmann factor plays an important role in determining the rate of many physical processes.

Question 47

Thermionic emission

Answer 47

To escape from a metal surface, a conduction electron must cross an energy barrier: the work function of the surface. The number of electrons with energy in excess of the work function φ is approximately proportional to e^(−φ kT). If the temperature increases, then e^(−φ kT) increases and more electrons per second are emitted from the surface.

Question 48

Evaporation

Answer 48

To escape from a liquid, a molecule must have enough energy to overcome the attraction of the other molecules in the surface. The fraction of molecules on the surface that have sufficient energy to escape is approximately proportional to the Boltzmann factor e^(–ε / kT), where ε is the energy needed by a molecule to escape. Thus at temperature T, the number of molecules in the vapour state is approximately proportional to e^(–ε / kT).

Question 49

What would the graph show of evaporation?

Answer 49

The vapour pressure varies as p = p0 e^(–ε / kT). Thus a graph of ln p against 1/T will be a straight line of gradient -ε / k.

Question 50

Intrinsic semiconductors

Answer 50

Conduction in an intrinsic semiconductor is due to electrons which have broken free from the atoms and move about inside the semiconductor. The higher the temperature, the greater the number of free electrons. At temperature T, the number of free electrons is approximately proportional to the Boltzmann factor e–ε / kT, where ε is the energy needed to free an electron. Hence the conductivity σ e^(–ε / kT).