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Samenvatting Biochemistry
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MATH MODULEExponent rules:
27 x 23 = 210 Logarithmic functions
27/23 = 24 23 = 8 log2 8 = 3
(27)3 = 221 1 1 1
(2 x 7)3 = 23 x 73 Log1/2 = x ( )x = x = 3
8 2 8
91/2 = √ 9 = 3 Logx 27 = 3 x3 = 27 x = 3
93/2 = (91/2)3 = 33 Log100 1 = x 100x = 1 x = 0
1 1/2 1/2 1/2 1 1 1
16-1/2 = ( ) = 1 /16 = Log8 = -2 8-2 =
16 4 64 64
8 27 3 Log2 8 + Log2 32 = Log2 (8 x 32) = Log2
( )-1/3 = ( )1/3 = 271/3/81/3 =
27 8 2 256
1 1 Log3 81 – Log3 9 = Log3 (81/9) = Log3 9
(-8)-1/3 = (- )1/3 = 1/(-8)1/3 = - 3 x Log2 8 = Log2 83
8 2
82/3 = (82)1/3 = 641/3 = 4 or 82/3 = (81/3)2 = 22 3
Log8 64 = Log2 8 / Log2 64 =
=4 5
1/2-3 = 23
THERMODYNAMICS
State variables
State variables describe the state of the system at a given moment. State variables are independent of
how the system ended up in that state. Examples are position, volume, temperature, pressure, etc. Work
and heat are not state variables. They do depend on the process that led to the state.
State variables are again divided in 2: intensive and extensive variables. The distinction between the 2 is
most clear when combining 2 system, extensive variables add up, whereas intensive variables average
out. Often, one can recognize pairs of state variables, where one is intensive and the other extensive. A
difference in intensive variable leads to exchange of extensive variable.
The first law of thermodynamics
Each system has a certain amount of internal energy, U. U has many contributions, such as bond energy,
interaction energy, kinetic energy (vibration, rotation, translation), nuclear energy, etc. It is often not
possible to determine U for a system. Fortunately, thermodynamics deals with changes in U: ΔU. The first
law of thermodynamics is that energy is conserved. Energy can’t disappear, it can only be converted from
one form into another. The internal energy of a system can be used for 2 things:
1. To do work
2. To produce heat
If a system does work (ω), the energy content of the system decreases. If a system produces heat, its
energy content decreases. For example, when a system does volume work, the volume of the system
increases and the internal energy decreases (needed to ‘push’). A positive flux of heat (q) means energy
is added to the system, so, negative q means that the system produced heat and loses internal energy.
So, the first law is: ΔU = q – ω.
,Enthalpy
An example of work done by a system is the expansion of a gas against a constant pressure: the amount
of work done by the system is p ∆V. The 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. Biology generally works at a constant temperature and pressure and
(slowly) varying volume (growth). So, considering only volume work and heat exchange at constant
temperature and pressure, energy will be: ∆U = ∆eU = q - p ∆V. Where the subscript e is used to
emphasize that this is an exchange process: heat is exchanged from one object to another. Energy is
being exchanged between the system and the environment, in the form of heat exchange. So, there is
often interest in this heat, at constant pressure but changing volumes, which is called qp where the
subscript indicates that there is work under constant pressure p. This heat is: qp = ΔU + p ΔV ≡ ΔH. Here, ≡
means ‘by definition’, and ΔH is called the enthalpy. It is defined as: H = U + p V. It is the heat that is
added to or produced by the system at constant pressure. Enthalpy and energy differences are the same
except for the volume work. In many biological processes, volume work (change) is negligible and ΔU =
ΔH.
Forces on molecules
A state in which molecules or energy quanta are spread around many different places turns out to be
more probable than a state in which they are confined in a specific spot. Spontaneous processes move
from an improbable state to a more probable state and this change is drive by an increase in probability.
Suppose there are 4 identical molecules that move in and out of two compartments. The different states
that the system can be in, are 4:0, 3:1, 2:2, 1:3 and 0:4. The chance p for an individual molecule to be in
compartment I is 0.5, and in compartment II also 0.5 (probabilities always add up to 1).
The chance to find the system in state 4:0 is then p(molecule 1 is in compartment I) x
p(molecule 2 is in compartment I) x p(molecule 3 is in compartment I) x p(molecule 4 is
in compartment I) = 0.5 x 0.5 x 0.5 x 0.5 = (0.5)4. There is only one way to achieve this.
Considering state 3:1, however, there are 4 ways to get to this state. So, the probability
to find this state is 4 x (0.5)4. There are 4 ways, so-called microscopic states, in which
the macroscopic state “3:1” can be achieved. This number is the multiplicity (W). So, W
= 4 for the 3:1 and 1:3 states in the example. The number is W = 6 for the 2:2 case.
Microscopic and macroscopic perspective
Every microscopic state where every molecule is labelled and traced, is equally probable. It is only when
considering the overall, macroscopic state, that difference in multiplicity and thus probability arise.
Compare it to throwing two dice: the microscopic state (1,1) is equally likely as (3,4) or any other
combination (the probability of each being 1/36). The macroscopic state “2”, however, is only achieved
by one combination of dice (1,1), whereas the state “7” has multiplicity of 6 {(1,6),
(6,1), (2,5), (5,2), (3,4), (4,3)}. The probability to observe equal number of molecules
in both compartments will approach 1 very quickly with increasing number of
molecules. So, the system will show a strong tendency to spread the molecules
evenly, and once it has done this, the system is at the most probable macroscopic
state and will stay there: there is no other place to go. This most probable state is
called equilibrium.
Entropy and the second law
Thermodynamics calls probability ‘entropy’. Entropy is defined as: S = kB ln(W), in which kB is the
Boltzmann constant (1.38 x 10-23 J K-1). The second law of thermodynamics is: in a spontaneous reaction,
the total entropy needs to increase. Gas will expand into vacuum, because it leads to an increased S,
coffee will cool down, because it leads to an increased S.
There is one important difference between macroscopic objects and
molecules: at the molecular level, energy is quantitized. It comes as
defined packages of fixed energy. These fixed energy packages correspond
to fixed orbits around a nucleus. Let’s consider 3 particles with zero
energy and add one quantum of energy. Now, either of the 3 particles can
, jump to a higher energy state. So, when U = 1, W = 3. When adding 2 quanta of energy, W = 6. This is
because it is possible that 2 particles go one energy level higher, or 1 particle jumps 2 energy levels.
When combining the last system to a system with U = 0 (W = 1), the multiplicity of the combined system
is 1 x 6 = 6.
Exchange of heat
When 2 systems are brought in thermal contact, they will exchange energy (heat) until they have the
same temperature. The driving force for exchange is the ‘probability drive’. There are more ways to
distribute the energy over the 2 systems if they have equal temperature. Temperature (T) is defined
based on the change of entropy upon a change in energy. A temperature difference is therefore again a
probability drive: it indicates how much entropy can be gained if energy (in the form of heat) is
q
exchanged: ΔeS = . A system that is thermally isolated will always develop towards maximal entropy. A
T
system that can exchange heat changes the entropy of the environment. So, a process that increases the
total entropy will occur spontaneously. What matters is the increase of the entropy of the universe due
to the process in the system. The system increases the entropy of the environment via heat exchange.
Gibbs free energy
The link between heat and entropy is: ΔS = q/T. The entropy of the environment increases due to the
heat of the system: ΔSenv = -qsys/T. This gives: ΔStot = ΔSsys -qsys/T. ΔH (enthalpy) is the heat added to or
produced by the system at constant pressure: -qsys = -ΔHsys. So, ΔStot = ΔSsys -ΔHsys /T. This must be higher
than 0 for the process to occur spontaneously. Multiplying by T gives: TΔStot = TΔSsys -ΔHsys. The Gibbs free
energy is defined as: G = H – TS. This is the opposite of the former formula, which results in: G = -TΔStot.
So, ΔG must be lower than 0 for the process to occur spontaneously. The Gibbs free energy is used to
predict if processes will occur spontaneously or not. It is calculated from the system only, but accounts
for the entropy increase of the environment. It is in fact not an energy, but an entropy balance. It
expresses how much work a system can be made to do. The more negative ΔG, the larger the total
entropy increase, the larger the probability drive, the more potential to do work.
ΔH ΔS
- + The reaction is both enthalpically (exothermic) and entropically favoured. It is
spontaneous at all temperatures.
- - The reaction is enthalpically favoured (exothermic) but entropically opposed. It is
spontaneous only at temperatures below T = ΔH/ΔS.
+ + The reaction is enthalpically opposed (endothermic) but entropically favoured. It is
spontaneous only ate temperatures above T = ΔH/ΔS.
+ - The reaction is both enthalpically and entropically opposed. It is non-spontaneous
at all temperatures.
INTERACTIONS
Electrons that are closer to the nucleus feel a stronger attraction. As a result, some atoms have a
stronger tendency to attract electrons. Other atoms only attract their outer electrons weakly. They have a
tendency to loose electrons. This property of an atom is called electronegativity. Strong electronegativity
means a strong attraction of its outer electrons, and therefore a tendency to gain
electrons upon interaction with other atoms. Electronegativity correlates with the
position in the periodic table. There are different types of connections that can occur
between molecules:
Covalent bond In a covalent bond, two atoms of intermediate
electronegativity share a pair of electrons. Carbon is a good example of such an
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