BIOCHEMISTRY - DR. JAKUBOWSKI

04/13/16

You may remember from General Chemistry that the change in the internal energy of a system, ΔE, is given by:

ΔE_{sys} = q + w = q - P_{ext}ΔV

where q is the heat (thermal energy)
transferred to the system (+), from the system (-), w is the work done on
(+) or by (-) the system. If only PV work is done, w = - P_{ext}ΔV, where
P_{ext }is the external pressure resisting a volume change in the system, ΔV.
When pressure is constant, and only PV work is done,

q_{p} = ΔE_{sys}
+ P_{ext}ΔV = ΔH,

where q_{p} is the heat transferred at constant P
(easily measured in a coffee cup calorimeter) which is equal to the change
in enthalpy, ΔH, of the system. For exothermic reactions, the
reactants have more thermal energy than the products, and the heat energy
(measured in kilocalories) released is the difference between the energy of
the products and reactants. When heat energy is used to measure the
difference in energy, we call the energy enthalpy (H) and the heat released
as the change in enthalpy (ΔH), as illustrated below.

For exothermic reactions, ΔH < 0. For endothermic reactions, ΔH > 0.

The equation ΔE_{sys} = q + w =
q - P_{ext}ΔV is one expression of the First Law of Thermodynamics.
Another, a statement of energy conservation, is:

ΔE_{tot} = ΔE_{universe}
= ΔE_{sys} +
ΔE_{surr }= 0.

Clearly, there must be something more that decides whether a reaction
goes to a significant extent other that if heat is released from the system.
That is, the spontaneity of a reaction must depend on more than just ΔH_{sys}.
. Another example of a spontaneous natural reaction is the evaporation of
water (a physical, not chemical process).

Heat is absorbed from the surroundings to break
the intermolecular forces (H bonds) among the water molecules (the system),
allowing the liquid to be turned into a gas. If the surroundings are the
skin, evaporation of water in the form of sweat cools the body. What are
these reactions spontaneous and essentially irreversible even though they
are endothermic? Notice that in both of these endothermic reactions (the
reactions of Ba(OH)_{2}.8H_{2}O(s) and 2NH_{4}SCN(s) and the evaporation of water),
the products are more disorganized (more disordered) than the products. A
solid is more ordered than a liquid or gas, and a liquid is more ordered
than a gas. In nature, ordered things become more disordered with
time. Entropy (S), the other factor (in addition to enthalpy changes) is
often considered to be a measure of the disorder of a system. The
greater the entropy, the greater the disorder. For
reactions that go from order (low S) to disorder (high S), the changed in S,
ΔS > 0. For reaction that goes from low order to high order, ΔS < 0.

However, this common description of entropy is quite misleading. Macroscopic examples describing order/disordered states (such as the cleanliness of your room or the shuffling of a deck of card) are inappropriate since entropy deals with microscopic states.

The driving force for spontaneous reactions is the dispersion
of energy and matter. Increases in entropy for
reactions that involve matter occur when gases or solutes in
solution are dispersed, leading to increases in
positional entropy. For reactions involving energy changes, entropy
increases when energy is dispersed
as random, undirected thermal motion, leading to increases
in thermal entropy. In this sense, entropy, S (a measure of
("spreadedness") is a measure of number of different ways
(microstates) that particles or energy can be arranged (W), not a
measure of disorder! W is an abbreviation for the German word,
Wahrscheinlichkeith, which means probability. It can be shown that
for a solute dissolving in a solvent, W_{sys} = W_{solute} x
W_{solvent}. Note that this is a multiplicative function.
Entropy is a logarithmic function of W which allows additivity of
solute and solvent W values, a feature found in other thermodynamic
state functions like ΔE, ΔH, and ΔS. Hence ln W_{sys} = ln
W_{solute} + ln W_{solvent}. Boltzman showed that

S = k ln W where k is the Boltzman constant (1.68 x
10-23 J/K), S units: J/K

for molecules, or

S = kN_{A} ln W = RlnW
(J/K.mol) for moles of molecules.

Boltzman realized the connection between the macroscopic entropy of a system and the microscopic order/disorder of a system through the equation S = klnW, Increasing S (macroscopic property) occurs with increasing numbers of possible microscopic states for the atoms and molecules of a system.

The dissolution of a solute in water and the
expansion of a gas into a vacuum, both which proceed spontaneously toward an
increase in matter dispersal, are examples of familiar processes
characterized by a ΔS_{sys} > 0.

The spontaneity of exothermic and endothermic processes
will depend on the ΔS_{tot} =
ΔS_{surr} +
ΔS_{sys}. ΔS_{sys} often
depends on matter dispersal (positional entropy). ΔS_{surr} depends
on energy changes in the surroundings, ΔH_{surr }=
-ΔH_{sys
}
(thermal entropy).

It is more convenient to express thermodynamic properties based
on the system which is being studied, not on the surrounding.
This can be readily done for the ΔS_{surr}
which depends both on ΔH_{sys} and the temperature. First
consider the dependency on ΔH_{sys}. thermal energy flow
into or out of the system, and since ΔH_{sys} = - ΔH_{surr},

ΔS_{surr }is
proportional to
-ΔH_{sys}

For an exothermic reaction, ΔS_{surr} >
0 (since ΔH_{sys}
< 0) and the reaction is favored;

For an endothermic reaction, ΔS_{surr} <
0, (since ΔH_{sys}
> 0), and the reaction is disfavored;

ΔS_{surr} also depends on the
temperature T of the surroundings:

ΔS_{surr }is
proportional to
1/T

If the T_{surr} is high, a given
heat transfer to or from the surroundings will have a smaller
effect on the ΔS_{surr};
conversely, if the T_{surr} is low, the effect on ΔS_{surr}
will be greater. (Atkins, in a recent General Chemistry,
uses the analogy of the effect of a sneeze in library compared to in
a crowded street; An American Chemistry General
Chemistry text uses the analogy of giving $5 to a friend with $1000
compared to one who has just $10.) Hence,

ΔS_{surr} = -ΔH_{sys}/T (Note: from
a more rigorous thermodynamic approach, entropy can be determined
from dS = dq_{rev}/T.)

ΔS_{tot} = ΔS_{surr}
+ Δ S_{sys}

ΔS_{tot}
depends on both enthalpy changes in the system and entropy changes
in the surroundings.

ΔS_{tot } = - ΔH_{sys}/T + ΔS_{sys} Multiplying both
sides by -T gives

-TΔS_{tot} = ΔH_{sys}
+ TΔS_{sys}

The thermodynamic function Gibb's Free Energy, G, can
be defined as: G = H - TS;

At constant T and P, ΔG = ΔH - TΔS

Hence

ΔG_{sys} = ΔH_{sys} -
TΔS_{sys } = - TΔS_{tot}

Spontaneity is determined by ΔS_{tot }OR ΔG_{sys} since ΔS_{tot} = -ΔG_{sys}/T .
ΔG_{sys} is widely use in discussing spontaneity since it
is a state function, depends only on the enthalpy and entropy
changes in the system, and is negative (as is the potential energy
change for a falling object) for all spontaneous processes.

The second law of thermodynamics can be succinctly stated:
For any spontaneous process, the ΔS_{tot} >
0. Unlike energy (from the First Law), entropy is not
conserved.

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