GEN CHEMWork, Heat, Heat Capacity

Overview

■ Chemical thermodynamics– work, heat, heat capacity

■ Heat

■ Work

■ Internal Energy

■ The molecular interpretation of heat and work

Review ■ The system is a well defined area of space that is currently being considered

■ We define 3 kinds– Open

Matter and energy can exchange– Closed

Matter cannot but energy can exchange– Isolated

Matter and energy can not exchange

The System

Review ■ Thermodynamics is the focus of the work for the next few weeks

■ This area deals with reaction progression and energies asking questions such as:

– Will this reaction go to completion– If not how far will it progress– How much energy can goes into or out of a

reaction– How much energy is required to start a

reaction

Thermodynamics

Review ■ The energy inside a system is called internal energy

■ This is the sum of kinetic energy and the bonding of the system

■ It is difficult to measure this precisely as often one cannot not all interactions and all movements of molecules (although this is possible for simple systems under approximations)

■ Instead we measure CHANGES in internal energy

Internal Energy

Review ■ When internal energy in a system changesthat energy either comes from or goes to the surroundings

■ There are many ways for energy to interchange with the enviroment

■ For simplicity we break these changes down into two kinds

– Work– Heat

Changes in Energy

Review ■ Work is the ordered motion of molecules

■ More general it is the ability to generate change in something that inherently resists change

■ Common examples includes expansion of a gas, mechanical and electrical work

Work

Review ■ Heat is the other way which internal energy is exchanged

■ This is the random movement of molecules

■ Although we sometimes we discus it as a quantity it is a transfer process that occurs at the boundary

– For this reason boundaries (between system and the universe) need to be well defined

Heat

MOLECULAR INTERPRETATION

Motion

■ A molecule has a certain number of motional degrees of freedom

■ The ability to:– Translate (the motion of its centre

of mass through space)– Rotate around its centre of mass– Vibrate (As its bond lengths and

angles change, leaving its centre of mass unmoved)

Motion Effects

■ Many physical and chemical properties depend on the energy associated with each of these modes of motion

– For example, a chemical bond might break if a lot of energy becomes concentrated in it, for instance as vigorous vibration

Motion and Energy

■ These motions are one means in which the internal energy is stored in the molecule

■ The other being more about the PE of (the charge interactions) and electronic states

■ To understand how these motions correlate to energies we look at simple cases where we can calculate total energy correctly

Total Energy - A perfect case

■ Although total energy is difficult to calculate in general under some approximations it can be done

■ Specifically the energy of a monoatomic perfect gas

■ This lets us examine translational effects on internal energy

■ In the case of a monoatomic perfect gas

– There are no intermolecular interactions (perfect gas)

– There are no vibrations or rotations (monoatomic)

– There is only translation, that’s why we can do it

Total Energy Monoatomic Perfect Gas

■ The total energy of a monatomic perfect gas comes from the equipartition theorem (more of that at a much later date)

■ According to this theorem, the average energy of each degree of (quadratic) freedoms contribution is !" 𝑘𝑇

■ So for 3 dimensions that is32 𝑘𝑇

■ For a monoatomic gas (of N atoms) that only has the translation we

32𝑁𝑘𝑇

■ Since, 𝑁 = 𝑛𝑁* and 𝑅 = 𝑁*𝑘 we can simplify this a bit to

32𝑛𝑅𝑇

Total Energy Monoatomic Perfect Gas

■ Putting that into our internal energy we arrive at the total energy for a monatomic perfect gas

𝑈- 𝑇 = 𝑈- 0 +32𝑅𝑇

■ The key point here is that:– Translations has an energy that increases LINEARLY with 𝑇

■ That at 25°C the energy has a value of about 4kJmol-1

Molecules and Internal Energy

■ When our gas isn’t monoatomic, it’s a molecule and we have extra energy contributions

■ In these cases we need to take into account the effects of rotation and vibrations

Linear Rotation

■ Linear molecules can rotate around two axes

■ If they rotate on the third axes no change is observed

Linear Rotation

■ Each of these rotational degrees of freedom adds another

12 𝑘𝑇

to the energy

■ This gives the energy as

𝑈- 𝑇 = 𝑈- 0 +52𝑅𝑇

3D Rotation

■ For a molecule that can rotate in 3d there is another 12 𝑘𝑇 in the energy to give the energy as

𝑈- 𝑇 = 𝑈- 0 + 3𝑅𝑇

Rotation and Energy

■ The energy of a molecules that can only translate is

𝑈- 𝑇 = 𝑈- 0 +32𝑅𝑇

■ The energy of a molecule that can also rotate is𝑈- 𝑇 = 𝑈- 0 + 3𝑅𝑇

■ The key point is that the energy is now increasing twice as fast with T

Vibrations and Energy

■ These systems also have vibrations

■ For example:– The linear molecule can stretch– The bent OH2 like molecule can

both bend and stretch

Vibrations and Energy

■ Calculating the energy in a vibration is non trivial

■ However the amount of energy contributed by a vibration is also quite small for room temperature of all but the biggest molecules

– By big molecules I mean polymers and proteins

Beyond the Simple

■ The internal energy of anything that has interactions (as in not perfect gas) is difficult

■ There is no simple expression that will cover all cases

■ To do this sort of calculation we use molecular mechanics and quantum mechanics

Internal EnergyMeasure the Change■ For anything that is not simple we

usually stop focusing on this absolute energy and focus on energy differences

■ We still however remain aware of the molecular origins, that energy can be stored in a molecule

■ That this energy can be interpreted as translation, rotations vibrations, (and electronic excitations)

Change Through Work and Heat

■ It has been found experimentally that the internal energy of a system may be changed either

– by doing work on the system – by heating it

■ The internal energy of the system is blind to the mode employed

■ It doesn't care how the energy was transferred just that it was

The Formula for Change in Internal Energy■ If we write 𝑤 for the work done on a

system

■ 𝑞 for the energy transferred as heat to a system,

■ Δ𝑈 for the resulting change in internal energy

■ Then we can write this change asΔ𝑈 = 𝑞 + 𝑤

■ This in fact summarizes the equivalence of heat and work, they are both process to exchange internal energy

Observations Of Conservation

■ If a system is isolated from its surrounding then no change can take place

■ Even if we observe a change form rotations to vibrations the internal energy won’t change if it is isolated

■ Similarly a system that is doing work will loose internal energy and loose its capacity to do more work, while the surroundings will gain it

■ This summary of observations is now known as the:

First Law of thermodynamics

The internal energy of an isolated system is constant.

Workshop

■ Today we will have a workshop

■ This will be assessed

■ Questions will be similar to those in your upcoming exam

■ But today you get to talk and discuses it while doing it

■ Do ask questions

■ Good luck!