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Thermodynamics
Systems:
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Open – both matter and energy exchanged between the system and surroundings
Closed – only energy is exchanged between the system and surroundings
Isolated – neither energy or matter are exchanged

Energy of a system
Internal energy (U): Kinetic or potential
Energy transfer
Heat energy (q) and work energy (w) are exchanged



Heat (q) – disorganised energy
Work (w) – organised energy

First Law
ΔU = q + w
(Change in internal energy of a system = heat added to the system + work done by the
system)
- Positive q: heat added to the system
- Positive w: work done on the system
- Joules (J) = Newton metres (Nm)
- Calorie (cal) – energy to raise 1g of water by 1’C
 Energy is an extensive variable (on a scale) – it’s proportional
- (Intensive: property doesn’t scale – not proportional)
 State variables: properties that describe the system
...
Energy, pressure, volume
(not heat energy, it depends on work)
Enthalpy – describes change in heat energy, ΔH
Systems do work- PΔV
dU = q + w =
dU = q – PdV ( - minus because work is done by the system on the surroundings)
(The magnitude of the work done when a gas expands is equal to the product of the
pressure of the gas times the change in the volume of the gas
...
If we consider what happens
at a constant pressure, P, we can define the enthalpy H:
H = U + PV
dH = dU + PdV (depends on lots of small changes – most biological systems operate at a
constant pressure)

ΔH = ΔU + PΔV
ΔU = ΔH - PΔV
ΔH ≡ q (heat energy in or out) at constant P
(dU = q – PdV; dH = dU + PdV)
Can we measure enthalpies?
Using calorimetry:
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

Positive correlation (straight line) between H and T when q is constant – change in
heat is proportional to temperature change
But it isn’t always a constant/straight slope – taking up heat without an increase in
temperature
...
when a substance changes shape (eg
...

This is the energy required to raise the temperature T by 1 K (heat per temperature change)
...
When molecules are heated, there is a rise in heat capacity,
then a fall
...
So this extra energy is going into breaking bonds
...
Making bonds is endothermic (ΔH<0); this is
favourable
...

The heat capacity after the phase
change is often different to the heat
capacity before the phase change
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Entropy – the tendency (by probability) for things to get disordered
(Working out the multiplicity of different microstates – possible arrangement of molecules)

(W: multiplicities, M: locations, N: Number)
Spontaneous change increases the number of microstates
...

WA + WB = WAB = WA X WB
This can be solved using natural logs, making it an extensive variable
...
38 x 10-23 J K-1)
Entropy (S) is a state variable, also in J K-1

S = kBlnW
If we want to consider entropy per mole of a substance, then we need to use R, the gas
constant, where: R = NA kB (NA is Avogadro’s number)
...

Entropy change is proportional to 1/T because heat input at a lower constant T would
produce a bigger entropy increase (look at equation above) due to a larger proportional
change in volume (the lower the temperature, the lower the initial volume)
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(this concept was developed by Clausius)
At absolute zero, the volume of an ideal gas would be zero, and heat input would give an
infinite dS
...


-TΔStotal = ΔHsystem - TΔSsystem

We can define a new state variable, G, the Gibbs free energy:
G = H – TS
We can then show that, at a constant temperature and pressure:

ΔG = ΔH – TΔS

For a spontaneous process, ΔG must be negative
...

If ΔH is more negative than TΔS, then ΔG will be negative
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Standard Free Energy
We define standard free energy, G°’, under standard conditions: 25°C (298 K), 1 atm
pressure, 1 M concentration, at pH 7, per mole of a substance
...


Free energy and concentration
G represents the amount of energy available in the system that can be used for work
...
At 1M: G = G°’
We know that ΔG = ΔH – TΔS
...
The multiplicity of the substance is inversely proportional to the concentration:
W = 1 / [A]
...
314 J mol-1 k-1))
So, at the new concentration:
G[A] = G°’ + ΔG

G = G°’ + RTln[A]
As entropy gets smaller, G increases
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Equilibria and chemical reactions
ATP + H2O

ADP + Pi

ΔH is negative (exothermic)
...

The reaction exists in equilibrium
...
This would lower the entropy of the
surroundings to the test tube
...
)
Substituting in the equation for the dependence of G on concentration, we get:

When the reaction is at equilibrium, the free energy change is zero
...
Therefore:

ΔG°’ = -RTlnKeq
So, the position of the equilibrium is determined by the standard free energy difference (all
concentrations 1M)
...
So by changing the concentrations, we
can drive the reaction in either direction, and we can also vary the amount of free energy
available from the system to do work
...
Adding ADP and Pi increases the ΔG of the forward reaction,
and decreases the ΔG of the reverse reaction
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