Thursday, January 2, 2014

Thermodynamics & Gibbs Free Energy


Free Energy, Enthalpy & Entropy 
By Curtis Bustos


Equation and key terms: 

∆G = ∆H – T∆S used to determine whether a chemical-reaction process is spontaneous or not.
Gibbs free energy (G) = an amount of free energy that is capable of doing work during a chemical reaction at a constant temperature and pressure.
∆G = change in free energy (J/mol)
Enthalpy (H) = the heat content of the reacting system.  
∆H = change in enthalpy (heat in J/mol)
T = temperature in Kelvin (˚C + 273 = Kelvin (K)). Temperature affects ∆S.
Entropy (S) = a quantitative expression for the randomness or disorder of a system.
∆S = change in entropy (disorder or randomness in J/mol)
∆G standard (ΔG°) = the standard free energy change is simply an alternative mathematical calculation used to express its equilibrium constant. ΔG° = -RT ln Keq.  
Spontaneous = favorable (-∆G) reaction.
Non-spontaneous = non-favorable (+∆G) reaction.
Exergonic = -∆G
Endergonic = +∆G
Favorable = ê∆H and ­é∆S. If ∆H is low and ∆S is high, then ∆G will be negative or favorable.
Non-favorable ­é∆H and ê∆S. If ∆H is high and ∆S is low, then ∆G will be positive or non-favorable.
Equilibrium = when ∆G = 0. At this point, the rate of the forward reaction equals the rate the the reverse reaction. This is aka DEATH from a biological perspective.
Reactants = the starting substances of a chemical reaction.
Products = the substances produced in a chemical reaction.
Activation Energy (Ea) = the free energy of the highest transition-state (if more than one) relative to the free energy of the reactants in a chemical-reaction.
Transition State (TS) = the point of highest free energy (there may be more than one TS) for a chemical-reaction. Represented by ∆G double-dagger.
SN1 (unimolecular) = rate of reaction depends on one species (substrate). A stepwise reaction.
SN2 (bimolecular) = rate of reaction depends on two species (substrate & nucleophile). A concerted reaction.
Rate Determining Step (RDS) = the transition state of highest free-energy.  
Intermediate = a state at which a chemical process undergoes a specific molecular-conformation in order to reach an end product.  

Note - thermodynamics DOES NOT provide a reaction-rate or the speed at which a chemical reaction takes place. Kinetics will provide this information. 



Laws of thermodynamics:

First law (biochemist’s version) – in any physical or chemical change, the total amount of energy in the universe remains constant, although the form of energy may change.

Second law (biochemist’s version) – in all natural processes, the entropy of the universe increases (this definition has several versions). Spontaneous processes are characterized by the conversion from order to disorder (­entropy). From the illustration below, you can see a spontaneous process and how entropy (disorder or randomness) will naturally increase with time. Notice how molecules naturally move from a high concentration to a low concentration and achieve a higher level of disorder:



From this, we can also see that chemical reactions tend toward disorder and equilibrium.

Example of an entropically favorable reaction in the gas phase:
2NH3 à N2 + 3H2


We can see from the reaction above that we start with one molecule (2NH3) and end with two molecules (N2 + 3H2). Whenever we go from 1 molecule to 2 molecules or more, a higher level of disorder is achieved and is thus entropically favorable. Entropy is therefore a function of concentration!



Furthermore, when describing thermodynamics, words such as system and surroundings are used a lot. To avoid confusion, let’s start by defining a system and its surroundings. A system can be defined as a specific part of the universe that is of interest.  Surroundings can be defined as the universe or environment that holds or contains these systems of interest. For example, atmospheric pressure of the earth surrounds different systems of molecules and has an affect on their boiling points (contingent upon different levels of elevation). The boiling point of a molecule represents a specific system while the atmospheric pressure represents the surroundings.

When a system changes, such as by a molecular conformational change, some of its energy (G) may be used to carry out this chemical process. Where does this energy come from? It comes from enthalpy, temperature and entropy as described below:

Gibbs free energy (G):
G = H – TS or free energy equals enthalpy (heat) minus the multiplication of temperature (in Kelvin) by entropy (disorder). Change (∆ = change) in G can also be represented as ∆G.  ∆G can be calculated by ∆G = ∆H – T∆S (fundamental equation for all of chemistry).





Thermodynamics is a useful concept that helps determine if a reaction is spontaneous or non-spontaneous.  For example, a change in free energy (G) can be represented as ∆G. ∆G can tell us whether a reaction is spontaneous or not by simply referring to + or -∆G. -∆G = spontaneous (a process that is driven by the output of free energy) and +∆G = non-spontaneous (a process that is driven by the input of free energy).

∆G = ∆H – T∆S
Enthalpy (∆H)
Entropy (∆S)
Spontaneous (-∆G)
ê  - 
favorable contribution
é+
favorable contribution
Non-spontaneous (+∆G)
é+
unfavorable contribution
ê -
unfavorable contribution
Contingent upon relative magnitudes of ∆H, ∆S and temperature. Note – reaction is spontaneous when T < ∆H/∆S
é+
unfavorable contribution
é+
favorable contribution
Contingent upon relative magnitudes of ∆H, ∆S and temperature. Note – reaction is spontaneous when T > ∆H/∆S
ê -
favorable contribution
ê -
unfavorable contribution





By the way, there is a relationship between ∆G standard (ΔG°)
  and the equilibrium constant (ΔG° = -RT ln Keq).

For example,

When molar concentrations are greater in the products than they are in the reactants, products will be favored. A+B C+D. These double-arrows imply products are favored at equilibrium.

When molar concentrations are greater in the reactants than they are in the products, reactants will be favored. A+B ⥃ C+D. These double-arrows imply reactants are favored at equilibrium.



Quantitatively:


K ≈ 1 neither products nor reactants in a chemical process are favored at equilibrium.

K >> 1 the products are favored in a chemical process at equilibrium. The molar concentration of products (numerator) outweigh the molar concentration of reactants (denominator).

K << 1 the reactants are favored in a chemical process at equilibrium. The molar concentration of reactants (denominator) outweigh the molar concentration of products (numerator).


We now can apply Keq to our equation ΔG° = -RT ln Keq. After a few calculations, it should become apparent that ΔG° is affected by the concentrations of both the reactants and products of a chemical-reaction. 
Keq or K (units are canceled out)
ΔG° (kJ/mol)
Products or Reactants are favored at equilibrium
10-3
17.1
Reactants
10-2
11.4
Reactants
10-1
5.7
Reactants
1
0.0
Neutral
101
-5.7
Products
102
-11.4
Products
103
-17.1
Products



What does it mean when ΔG or ΔG°  = 0?
When ΔG = 0 in a chemical reaction, the net-change in free energy is zero. Therefore, there is no spontaneity as a net result. A graphical representation may help:



The graphical representation above shows I as a forward reaction (A à B+C exergonic) and II as a reverse reaction (B+C à A endergonic). If the forward reaction has a ΔG = -50kJ/mol (spontaneous) and the reverse reaction has a ΔG = +50kJ/mol (non-spontaneous), then -50kJ/mol and +50kJ/mol will cancel out and result in a net ΔG = 0… this is called equilibrium from a thermodynamic standpoint. Additionally, the ratio of molar concentrations of products to reactants












and the rate of forward and reverse reactions will remain unchanged over time.










Note - equilibrium does not suggest that molar concentrations of products and reactants are equal to each other (unless K = 1)!




Moreover, -∆G = spontaneous.  Products will be favored at equilibrium. Whereas +∆G = non-spontaneous. Reactants will be favored at equilibrium. This makes sense because chemical reactions are inclined to move toward a lower energy-state for stability. Products on the -∆G graph and reactants on the +∆G graph are both in lower energy-states than their reverse reactions:





Connecting the dots:
a.     First law of thermodynamics states that in any physical or chemical change, the total amount of energy in the universe remains constant, although the form of the energy may change.
b.     Second law of thermodynamics states that in all natural processes, the entropy of the universe increases.
c.      Spontaneous processes are characterized by the conversion from order to disorder (­entropy).
d.     Thermodynamic equilibrium is established when ∆G = O (net ∆G from spontaneous to non-spontaneous).
e.     Equilibrium = death from a biological perspective.

Is it possible for a living organism to cheat death? To cheat death would be to cheat spontaneity and entropy. Perhaps the key to longevity is manipulation of entropy?


Gibbs free-energy diagram explained:



1 = reactants

2 = 1st transition state. This is an extremely unstable conformation. The bonds are transitioning in a phase where they are not completely broken nor are they completely formed. Major growing pains! The 1st transition state is also the highest-in-energy transition-state; therefore, the rate-determining step can be viewed in comparison to the 1st transition state. The rate of the overall reaction is equal to the rate of the highest transition state hence the rate determining step).

3 = intermediate. A molecular-conformation is produced between 2 & 4 as part of a chemical conversion. Reactions with intermediates are considered to be multistep.
4 = 2nd transition state. Lowest transition-state; This transition state cannot be the rate-determining step because the 1st transition state is higher in free energy.

5 = products

Activation energy or energy barrier is the energy required for the reactants at 1 to reach the highest transition state (if more than one) at 2.  ∆Gdouble-dagger

∆G can be measured by the free energy difference from 1 to 5 (spontaneous) or 5 to 1 (non-spontaneous). An additional diagram with one transition-state may prove to be helpful:





In the spontaneous reaction, the products are lower in energy than the reactants; this will result with a -∆G.

In the non-spontaneous reaction, the products are higher in energy than the reactants; this will result with a +∆G.


Relative stability can also be seen on a Gibbs free energy diagram:


1 is relatively more stable than 2,3,4.
2 is MOST UNSTABLE.
3 is relatively more stable than 2,4.
4 is relatively more stable than 2
5 is relatively more stable than 1,2,3,4 (MOST STABLE). 

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