Intro to Physical Chemistry

Question 1

There are two types of Mechanical Energy
What are they?

Answer 1

Kinetic and Potential Energy
Molecules possess both of them

Question 2

What is Kinetic Energy

Answer 2

The energy possessed by molecules because of their motion

Question 3

If a molecules is moving through space, we say it has

Answer 3

Translational motion

Question 4

How can we calculate kinetic energy

Answer 4

Where:
m= mass of a molecule
v= speed

Question 5

Molecule with more than one atom (most) have which types of kinetic energy

Answer 5

Rotational and Vibrational Kinetic energy

Question 6

Energy of small molecules is quantised (quantum mechanics)
What does this mean in term of the motion of molecules

Answer 6

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

Question 7

What is Translational Energy?

Answer 7

The movement of the molecule as a whole through space
i.e., along a place in the coordinate system (x, y and z axis)

Question 8

What is Rotational Energy?

Answer 8

When the molecules rotate about its axis

Question 9

What is Vibrational Energy?

Answer 9

When there is a change in the bond lengths and bond angles on molecules

Question 10

What is Electronic energy?

Answer 10

Rather than motion these are associated with the electrons in the atoms/molecules

Question 11

Increases in energy level from which types of energy

Answer 11

Lowest: Translational
Rotational
Vibrational
Highest: Electronic

Question 12

What is the separation between levels in Transitional Energy

Answer 12

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

Question 13

What is the Seperation between the energy levels in rotational energy

Answer 13

The seperation between levels is 10¯²³ J
Rotational energy levels become further apart as the energy level increases

Question 14

What is the seperation between energy levels in Vibrational energy

Answer 14

The seperatation between levels is 10¯²⁰
Vibrational energy levels are constantly spaced

Question 15

What is the energy level seperation for Electronic energy levels

Answer 15

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

Question 16

How can different energies interact based on energy levels

Answer 16

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

Question 17

How can molecules exchange energy

Answer 17

Molecules which are moving collide with another and exchange energy during these collisions

Question 18

We do not know the particular energy of each individula molecule
But, what do we know?

Answer 18

We do know the average number of molecules in a given energy level
This quantity is known as the population

Question 19

At equilibrium, the relative population of molecules in an excited state (ni) compared to that in the ground state (n₀) is shown by what?

Answer 19

The Boltzmann distribution

Question 20

What is the equation for the Boltzmann distribution

Answer 20

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)

Question 21

What are the two things the Boltzmann distribution predict

Answer 21

• Higher energy levels are less likely to be populated
• Higher temperatures (more thermal energy) cause the populations of higher energy levels to increase

Question 22

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

Answer 22

• 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

Question 23

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

Answer 23

3/2 kBT

Question 24

A linear molecule can rotate independently about any two axes perpendicular to the bonds
So the rotational contribution to the average internal energy is

Answer 24

kBT

Question 25

A non-linear molecule can rotate about three axes So the rotational contribution to the average internal energy

Answer 25

3/2 kBT

Question 26

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

Answer 26

We can ignore the vibrational degrees of freedom

Question 27

What is intermolecular Potential Energy

Answer 27

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

Question 28

When two molecules are widely seperated, how does this affect the potential energy

Answer 28

The attractive contribution to the potential energy dominates Therefore the overall potential energy is negative (although the sign is just a convention)

Question 29

When two molecules are close together, how does this affect the potential energy

Answer 29

The repulsive contribution to the potential energy dominated The overall potential energy is therefore positive

Question 30

Somewhere between these positive and negative values for potential energy there's a minimul in the overall potential energy This corresponds to what

Answer 30

The equilibrium seperation between the molecules

Question 31

What is an ideal gas

Answer 31

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

Question 32

Because there are no forces between the molecules of an ideal gas, how does this effect the potential energy

Answer 32

The molecules of an ideal gas have no potential energy This means the molecular energy is soley kinetic

Question 33

What is the ideal gas equation

Answer 33

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)

Question 34

The ideal gas equation defines the gas constant The gas constant is equal to

Answer 34

Avogadro's number x Boltzmass constant

Question 35

The ideal gas equation is what is known as

Answer 35

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

Question 36

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

Answer 36

* Boyle's law (constant temperature) * Gay-Lussac's law (constant volume) * Charles's law (constant pressure

Question 37

What is Boyle's law

Answer 37

At **constant temperature** the ideal gas equation reduces to Boyle's law which states that **pressure is inversely proportional to volume**

Question 38

What is Charles's law

Answer 38

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

Question 39

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?

Answer 39

* 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

Question 40

What is an elastic collision

Answer 40

Is one in which the total translational energy of the molecules is conserved

Question 41

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

Answer 41

p = pressure (Pa) V = volume (m³) n = number of moles M = molar mass of molecules (kg mol¯¹) c = root mean square speed (√v²)

Question 42

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

Answer 42

Question 43

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

Answer 43

The Maxwell Speed Distribution The shape of this speed distribution can vary with temperature or the molecular mass changes

Question 44

Increasing the temperature will do what to probable speeds and the range

Answer 44

Increase the most probable speed in the distribution and the range of speeds which are observed Lower peaks, further to the right

Question 45

Increasing the molecular mass will do what to probable speeds and the range

Answer 45

Descreases the most probable speed and range of speeds which are observed in the distribution High peak far to the left