Biochemistry
Thermodynamics
Thermo= heat and dynamics = motion. Thermodynamics is a scientific discipline that was originally developed to better
understand steam-engines which use heat to put things into motion. But it turned out it can be applied much broader, even
in life sciences. Thermodynamics is the reasoning about the forces that allow flow of material, about what makes molecules
move, react with one another, make proteins fold and catalyse reactions, make some molecules bind well and the other
poor, allows kidney cells to take up salts against the concentration gradient, and in general allows life to organise itself in
even more complex structures. Without the ‘force’, there is no flow (dynamics), and without flow, there is no life. The force
can be described in terms of energy, as was traditionally done in the steam-engine time when the theories were invented.
Thermodynamics is always about a system; it has an universal name for the object of investigation → system. The system is
what you investigate. In the steam-engine days, the system referred to the engine, but it can be anything. In life sciences,
the system is often an organism or a cell, or sometimes a molecule. Everything outside of the system (the rest) is called the
environment. thermodynamics provides us tools to investigate the exchange of energy between a system and its
environment.
Variables are parameters that influence the system. A special class of variables are he state variables. The state variables
define the state in which the system is, regardless of how it got there. Examples of state variables are temperature, volume
and pressure. I am the system and I am sitting on the couch. State variables in this case are the temperature, place and
position. However, how much work I did that day or how I moved to that couch are not state variables but process
variables. Heat and work are examples of process variables.
State variables can be classified into two groups of state variables:
1. Intensive variables: average out. → temperature and pressure.
2. Extensive variables: they add up. You are sitting on the couch and someone comes and sits next to you in close
contact. The two of us are now one new system. The mass therefore adds up (increases). Therefore, mass is an
extensive state variable. However, the temperature is still the same, so the temperature is the intensive state
variable. The volume adds up, so it is an extensive variable. The pressure does not add up, so it is an intensive
variable. → you can count them.
There exists pairs of state variables that include one extensive and one intensive state variable. In such pairs, a difference of
one (intensive) leads to exchange of the other (extensive) to reach the equilibrium. Equilibrium is the state in which
opposing forces/influences are balanced. If two objects of different temperatures are in contact, they will exchange heat
until both have the same temperature. Temperature can be recognized as intensive state variable and heat as extensive.
Another pair are pressure and volume. If you combine two balloons filled with gasses, their volume will add up, so that is
the extensive state variable. Their pressure does not add up, so that is the intensive state variable. Their will be an
exchange of volume (one will grow at the expense of the other) that results in a more equal pressure. HEAT IS NOT A STATE
VARIABLE.
- Extensive variables: energy, volume, enthalpy, number of molecules.
- Intensive variables: temperature, pressure, concentration.
The first law
A system has a certain amount of internal energy (symbol U and sometimes E). U has many contributions and it is often
impossible to determine U for a system. Fortunately, that is not a problem, because in thermodynamics we are interested
in changes of ∆U. Delta (∆) is generally used to express a change. If the internal energy of a system DECREASES, so for
example when a chemical bond is broken, that energy is released and can be used to do work or produce heat. Nothing
else. Let’s say that our system does volume work: the system uses internal energy to push and grow. So a decrease of
internal energy leads to positive work. The symbol for work is ω. In addition, some internal energy is released as heat. Heat
(symbol q) flows from system to environment. A flux of heat away from the system is indicated as negative heat flow,
whereas a positive q means that heat is put into the system. If we put this in an equation, we get:
∆U = q – ω
Positive q, heat goes into the system, U increases. Positive ω, system does work, U decreases.
This formula is known as the first law of thermodynamics: energy is conserved. The energy cannot disappear, nor can
energy be produced out of thin air. It can only be transformed. From a macroscopic perspective we already know this:
potential energy from a ball is converted into kinetic energy once it is released from a height, and the kinetic energy will be
converted into heat once the ball lies still on the ground. When dealing with molecules, we talk about internal energy, and
it comprises of many different contributions.
,Biochemistry
Translation energy: rate of movement in space
Rotation energy: molecules can rotate
Vibration energy: movement of atoms within a molecule
Binding energy: energy in chemical bonds between atoms (electrons)
Potential energies caused by intermolecular interactions (H-bonds, Vanderwaals forces)
Electron energies: energies of electrons within an atom
So molecules are balls (atoms) attached via springs that can bend and vibrate. Potential energies arise from ’potential’
forces, in most cases Coulomb based rather than gravitational forces.
Enthalpy
1. Steam engines operate at constant volume (steal barrels) and fluctuating pressures (puffing steam train):
W= V x ∆p → heat is released in the environment
- W= volume work ∆U = q – V x ∆p
V= constant volume
∆p = fluctuating pressure - ∆U = internal energy
q= heat
In other words, the volume stays constant, but the pressure changes.
V= constant volume
∆p = fluctuating pressure
2. Biology generally works at constant temperature, constant pressure and slowly fluctuating volume (growth):
W= p x ∆V
∆U = q - p x ∆V
- W= volume work
p= constant pressure At constant pressure we write:
∆V= fluctuating volume
∆U = qp – p x ∆V
In other words, the pressure stays constant and the volume changes.
- Qp= the heat added to/produced by the
system at a constant pressure
Enthalpy (H) change is the heat added to (+) or produced by (-) the system at a constant pressure. It is not that much used
in steam engines, more in chemistry and biology due to the constant pressure and temperature.
∆H = ∆U + p x ∆V (omschrijven formula ∆U = qp – p x ∆V)
- ∆H= the heat added to or produced by the system at a constant pressure. ∆H = ∆U except for volume changes.
However, in many processes, volume changes are negligible and we can assume ∆H = ∆U.
In many biological processes, volume work is negligible and ∆H = ∆U. However, in some processes volume work cannot be
ignored. For example when gasses are produced the effect is quite striking. Change in energy of the system will be: ∆U = - p
∆V. Since the system will do work if ∆V > 0, and p is also positive, the minus sign ensures that the energy content of the
system drops if it does volume work.
Forces and molecules
Why does a cup of coffee become cold and a cold beer becomes warm? It has all to do with probability.
There are 5 ways to divide the particles over
the two compartments, but there is only
one way to divide the particles such that all
four are in compartment I. Therefore, W
(multiplicity) = 1. The multiplicity is in how
many ways the particles can be distributed.
So if you have 6 particles and 6 boxes, the
multiplicity is 1. Increase in volume leads to
an increase in W and hence, entropy. The
more entropy can be generated, the higher
the probability force,
, Biochemistry
For the first question, you would assume 1.
However, all the particles are different from
each other. Therefore, there are actually 4
different ways in which 1 particle is in
compartment I (W= 4).
- W is the number of microscopic arrangements
that have the same macroscopic appearance. We
can only count/measure how many
molecules/particles are in a compartment. We
cannot tell one molecule from one another, but
we do know that they are different ‘individuals’
that behave independently. There are 5
macroscopic states:
4:0, 0:4, 3:1, 1:3 and 2:2. How many microscopic states are there?
1 + 1 +4 + 4 + 6 = 16.
If we consider state 3:1 (or 1:3), however, there are 4
ways to get to this state: which of the 4 molecules is
alone, does not matter. So the probability to find this
state is 4 x (0.5)4! We say that there are 4 ways, so-called
microscopic states, in which the macroscopic state “3:1”
can be achieved.
there is no force that drives there particles out of the
compartments. It simply due to chance and therefore we
call this the probability force.
From the microscopic perspective, every molecule is
unique and is cruising the spaces it can occupy: every
microscopic state where every molecule is labelled and
traced is equally probable. It is only when we consider
the overall, macroscopic state, that difference in multiplicity and thus probability arise.
When the number of particles increases, the
chance for equal division ratio of (1/2)
increases. The chance to find almost all
particles together decreases to nearly zero.
If all the particles are in the left, they will
move to the right due to the probability
drive/force. They will eventually be equally
distributes and the system has reached the
equilibrium. This is by far the most probable
state of a system. Individual particles will
move but there will not be any displacement.
The most probable state is called the
equilibrium.
Entropy and the second law
From a macroscopic view, we should consider the concentration of molecules (number of molecules per volume) and we
are in equilibrium if the concentrations of the compounds are equal in both compartments. So diffusion is in essence a
process caused by random movement of blind molecules that spontaneously move towards an increase in probability as
differences in concentrations decrease, because a homogenous spread of particles through a space is more probable.
Concentration differences can be considered as driving forces for macroscopic, average, movement of molecules →
probability force/drive. If the concentration gradient (when a solute is more concentrated in one area than the other), is
completely gone, there is no probability force anymore and the system is in (diffusive) equilibrium. Equilibrium is achieved
when there is no thermodynamic driving force anymore.
If we increase the volume, there are many more ways in which the molecules can be arranged in that space (gas). If we
would think of that space (volume) as a collection of pixles (little boxes), and in every pixle a molecule can be present, or
