Chapter 14 Flashcards
The average thermal energy of a particle is proportional to…
The temperature
Equation for average thermal energy
E = kT
where k = boltzmann’s constant 1.38 x10^-23 Jk^-1
and T = temperature in Kelvin.
How do you convert energy per particle to electron per volt?
kT / (1.6X10^-19)
Divide by an electron
How do you convert energy per particle to energy per mol^-1?
kT x (6 x 10^23) Multiply by Avogadro's constant.
The ratio E/kT
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
What is activation energy?
- 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.
Where does the activation energy come from?
-It comes from the random thermal energy of the particles.
Examples of things that involve activation energy
- A change of state (e.g liquid to gas)
- Thermionic emission
- Ionisation in a candle
- Conduction in a semiconductor
- Viscous flow.
Gaining energy through random collisions
-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.
Hotter temp =
Higher energy
Energy equation with photons
hf = kT
Highest temperatures =
Mater comes apart completely
Lowest temperatures =
Particles slow down or stop
Why do these changes happen?
Because of the different amounts of random jostling energy shared amongst the particles at different temps
Graph of energy against temperature
Directly proportional so straight line graph positive gradient
At high temperatures
-Bonds break and matter comes apart. Atoms come apart into ions and electrons. The ratio E/kT is small even for large E
At low temperatures
-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.
When do most processes start happening?
-Many processes start happening at an appreciable rate when E/kT is in the range 15-30.
Random thermal energy
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.
Getting extra energy by chance
-By chance, particles may get extra energy from the random thermal motion of particles in the surroundings
Why/How do particles change energy levels?
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.
Why is the energy level change random?
-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.
What is a physical example that molecules climb energy states (gravitational hills)?
- 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
What is the fraction of molecules which by chance have the extra energy to be at a height greater by h?
f = e^(-E/kT)
Where E= average energy of thermal activity
T= Temp in Kelvin
Diffusion in terms of random motion
- Molecules diffuse from higher to lower concentration
- Random motion takes molecules from where there are fewer.
- Diffusion goes down concentration gradients
As E/kT increases…
The fraction of particles with that energy rapidly gets smaller
Equation for the Boltzmann factor:
Boltzmann factor = e^(-E/kT)
The Boltzmann factor when the E/kT ratio is low
- 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
The Boltzmann factor when the E/kT ratio is high
- 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
graph: The boltzmann factor e^(E/kT) against the ratio e/kT
Negative straight line graph almost through 0
The boltzmann factor against temperature graph: When the ratio T/K is low
- -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
The boltzmann factor against temperature graph: When the ratio T/K is high
- 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
The boltzmann factor against temperature graph
- When E > kT the Boltzmann factor increases very rapidly with temp
- Increase exponentially
When do important changes happen
-Important changes happen when E/kT is of the order 15-30
What is the Boltzmann factor E
-Boltzmann factor is the ratio of numbers of particles in states differing by energy E
Activation process
- 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.
What needs to be true for activation processes to occur?
The rate of reaction is proportional to e^(-E/kT)
How can the boltzmann factor help explain fevers?
- 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.
What is the origin of the Boltzmann factor?
-The origin of the Boltzmann factor is the small probability of repeatedly gaining extra energy at random from a large collection of other particles
Rate of reaction
-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»_space; kT
Reaction changes
-Reactions can involve changes in the number of spatial or orientational arrangements of particles, as well as of their energies.
What does the Boltzmann factor tell you?
- 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
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?
-Because particles are moving so fast, and reactions are happening about 10^9 every second.
The boltzmann factor varies with temperature
- 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.
What is the rate of reaction with activation energy proportional to?
The boltzmann factor.
Why/ when is the Boltzmann factor important?
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.
Thermionic emission
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.
Evaporation
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).
What would the graph show of evaporation?
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.
Intrinsic semiconductors
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).
