Intro to Physical Chemistry Flashcards
There are two types of Mechanical Energy
What are they?
Kinetic and Potential Energy
Molecules possess both of them
What is Kinetic Energy
The energy possessed by molecules because of their motion
If a molecules is moving through space, we say it has
Translational motion
How can we calculate kinetic energy
Where:
m= mass of a molecule
v= speed
Molecule with more than one atom (most) have which types of kinetic energy
Rotational and Vibrational Kinetic energy
Energy of small molecules is quantised (quantum mechanics)
What does this mean in term of the motion of molecules
Each kind of motion is associated with a set of discrete energy levels
Each type of molecular motion is associated with a set of these levels
What is Translational Energy?
The movement of the molecule as a whole through space
i.e., along a place in the coordinate system (x, y and z axis)
What is Rotational Energy?
When the molecules rotate about its axis
What is Vibrational Energy?
When there is a change in the bond lengths and bond angles on molecules
What is Electronic energy?
Rather than motion these are associated with the electrons in the atoms/molecules
Increases in energy level from which types of energy
Lowest: Translational
Rotational
Vibrational
Highest: Electronic
What is the separation between levels in Transitional Energy
The separation between levels is 10¯⁴¹ J
The spacing of the translational energy level is so small that it can be treated as continuous
What is the Seperation between the energy levels in rotational energy
The seperation between levels is 10¯²³ J
Rotational energy levels become further apart as the energy level increases
What is the seperation between energy levels in Vibrational energy
The seperatation between levels is 10¯²⁰
Vibrational energy levels are constantly spaced
What is the energy level seperation for Electronic energy levels
The seperation between level is 10¯¹⁸
Electronic energy levels become closer together as the energy increases
These are usually more widely spaced than the vibrational levels
How can different energies interact based on energy levels
May rotational energies fit between the ground and lowest excited vibration energy state
While many vibrational levels fit between the ground and lowest excited electron states
These features have impacts on the study of molecular energy levels by spectroscopy
How can molecules exchange energy
Molecules which are moving collide with another and exchange energy during these collisions
We do not know the particular energy of each individula molecule
But, what do we know?
We do know the average number of molecules in a given energy level
This quantity is known as the population
At equilibrium, the relative population of molecules in an excited state (ni) compared to that in the ground state (n₀) is shown by what?
The Boltzmann distribution
What is the equation for the Boltzmann distribution
ni = population of molecules in an excited state
n₀ = population of molecules in the ground state
Ei = energy of the excited state
KB = Boltzmann constant = 1.381 x 10¯²³ J K¯¹
T = Temperature (K)
What are the two things the Boltzmann distribution predict
- Higher energy levels are less likely to be populated
- Higher temperatures (more thermal energy) cause the populations of higher energy levels to increase
We can work out how the average molecular energy is divided up or partitioned among the different motions using the equipartition theorem
What does the equipartition theorem state
- That the average energy for each mode of motion or ‘degree of freedom’ for one molecule = ½ kBT
- A molecule with N atoms has 3N degrees of freedom in total
So in a gas, a molecule which can move independently along any of the three dimensions, has three translational degrees of freedom
This means the translation contribution to the average internal energy of molecule is worked out how
3/2 kBT
A linear molecule can rotate independently about any two axes perpendicular to the bonds
So the rotational contribution to the average internal energy is
kBT
A non-linear molecule can rotate about three axes
So the rotational contribution to the average internal energy
3/2 kBT
Vibrational energy level seperations are often very large compared to the thermal energy
So that the molecular populations in the excited states are usually very small
This means what
We can ignore the vibrational degrees of freedom
What is intermolecular Potential Energy
The energy possessed by molecules because of their position relative to one another (a force is acting upon it)
Most molecules are neutral but exert attractive and repulsive forces on one another which are related to the electrostatic forces between two charged particles
When two molecules are widely seperated, how does this affect the potential energy
The attractive contribution to the potential energy dominates
Therefore the overall potential energy is negative (although the sign is just a convention)
When two molecules are close together, how does this affect the potential energy
The repulsive contribution to the potential energy dominated
The overall potential energy is therefore positive
Somewhere between these positive and negative values for potential energy there’s a minimul in the overall potential energy
This corresponds to what
The equilibrium seperation between the molecules
What is an ideal gas
Gases with no forces between molecules
In practice all gases are idea when the pressure is close to zero and the molecules are a long way apart
Because there are no forces between the molecules of an ideal gas, how does this effect the potential energy
The molecules of an ideal gas have no potential energy
This means the molecular energy is soley kinetic
What is the ideal gas equation
p = pressure (Pa or N m¯²)
V = volume (m³)
n = moles of gas
R = gas constant (8.314 J mol¯¹ K¯¹)
T = absolute temperature (K)
The ideal gas equation defines the gas constant
The gas constant is equal to
Avogadro’s number x Boltzmass constant
The ideal gas equation is what is known as
an equation of state
For a given sample of an ideal gas, any two of the quantities of pressure, volume and temperature are sufficient to describe its state
No ideal gas can exist in a state which does not lie on the surface described by the equation
By keeping the amount of gas and one of the 3 variables that define our surface: pressure, volume or temperature constant, we can see that the different gas laws correspond to cross sections through the surface
What are these 3 laws
- Boyle’s law (constant temperature)
- Gay-Lussac’s law (constant volume)
- Charles’s law (constant pressure
What is Boyle’s law
At constant temperature the ideal gas equation reduces to Boyle’s law which states that pressure is inversely proportional to volume
What is Charles’s law
At constant pressure the ideal gas equation reduces to Charles’s law which states that the volume is proportional to temperature
When this a ploted on a graph and extrapolated to zero volume, we find that the volume of an ideal gas reach zero at -273.15°C, regardless of the pressure - absolute zero
This is where all molecular motion ceases
The Kinetic model of gases allows the gas laws to be explained in terms of molecules
It is based on three assumptions, what are they?
- The gas consists of molecules of mass (m) in ceaseless random motion which move in striaght lines between collisions
- The volume of the molecules is negligible - their diameters are negligible compared to the average distance travelled between collisions
- The molecules only interact by elastic collisions with one another and with the walls of the container and the time taken for a collision to occur is negligible compared to the time between collisions
What is an elastic collision
Is one in which the total translational energy of the molecules is conserved
Using the assumptions of the kinetic theory, we can derive a relationship between the macroscopic pressure and volume of an ideal gas and the microscopic properties of it’s molecules (root mean square speed)
What is this equation
p = pressure (Pa)
V = volume (m³)
n = number of moles
M = molar mass of molecules (kg mol¯¹)
c = root mean square speed (√v²)
Substituting the ideal gas equation allows equations to be derived that give the root mean square speed of the gas molecule in terms of either molar or molecular quantities
What are these equations
In addition the kinetic model can tell us how speeds of gas molecules are distributed amongst the possible range of values
This can be shown through what
The Maxwell Speed Distribution
The shape of this speed distribution can vary with temperature or the molecular mass changes
Increasing the temperature will do what to probable speeds and the range
Increase the most probable speed in the distribution and the range of speeds which are observed
Lower peaks, further to the right
Increasing the molecular mass will do what to probable speeds and the range
Descreases the most probable speed and range of speeds which are observed in the distribution
High peak far to the left
