1. Describe the thermodynamic changes of the chemical reaction in Figure 1.
Assume that the changes of pure reactant to pure product is a thermodynamically favourable process.
(20 marks)
The Gibbs free energy, G of a system is defined as the energy of a system that is free to do work at constant temperature and pressure. Gibbs free energy, G, gives us another way of determining spontaneity. A change in
Gibbs energy, ΔG, arises from changes in enthalpy and entropy where ΔH is negative for exothermic and positive for endothermic reactions. We define a new quantity ΔG such that
ΔG = -T ΔS total
∆𝑆 total
= ∆𝑆 −
∆𝐻
𝑇
Where
It follows that
ΔG = -T (ΔS
-
∆𝐻
𝑇
)
ΔG = ΔH - TΔS
G is the change in Gibbs free energy (kJ/mol)
H is the change in enthalpy (kJ/mol)
T is absolute temperature in K
S is the change in entropy (kJ/mol K)
We can also calculate the change in G in this way
ΔG = G(products) - G(reactants)
For the overall change in entropy of the system and surrounding, the spontaneous change of a system must take into account. At constant temperature and pressure, the direction of any spontaneous change is toward a lower Gibbs free energy. The dif ference in sign between ΔG and ΔStotal implies that the condition for a process being spontaneous changes from
ΔStotal >0 in terms of the total entropy to ΔG < 0. In a spontaneous change at

constant temperature and pressure the Gibb’s energy decreases where ΔG greater than 0 or negative). At constant T and P,
Total entropy ∆𝑆
Gibbs energy ∆𝐺
This show the inverse relationship between ∆𝑆 and ∆𝐺.
At constant T and P, a reaction mixture tends to adjust its composition until its Gibbs energy is a minimum.
Gibbs energy, G
equilibrium
Pure reactant Pure products
When ∆𝐺 is minimum, the reaction is at equilibrium.
The diagram below shows that during a reaction, the amount of free energy decreases until the reaction is at equilibrium. If the reaction goes towards completion, the free energy minimum occurs very close to the pure products part of the curve. In other words, the curve moves depending on the conditions of the reaction.

𝐺 𝑜
is the standard free energy. It is a constant value at constant temperature.
It is the free energy of 1 mol L-1 of a compound in solution at 1 atm and any constant temperature. Consider the reaction
X + Y Z
Hence, the reaction free energy
ΔG = G 0 z
– (G 0 x
+ G 0 y
)
Conversion of pure reactant to pure product is a thermodynamically favourable process. At equilibrium, ΔG = 0.
ΔG = G 0 p
– G 0 r
If G 0 p
< G 0 r
,
ΔG -ve
If G 0 p
> G 0 r
, ΔG +ve
So G 0 p
= G 0 r
, ΔG =0

Gibbs energy, 𝐺 0
G 0 r
∆𝐺 < 0 ∆𝐺 > 0
G 0 p
Pure Reactant
∆𝐺 = 𝑜
Pure Product
Table below show the properties about enthalpy change, entropy change, and change in free energy. If ∆G is negative, the forward reaction is spontaneous.
If ∆G is 0, the system is at equilibrium. If ∆G is positive, the reaction is spontaneous in the reverse direction
Enthalpy Change Entropy Change Spontaneous Reaction?
Exothermic (Δ H < 0) Increase (Δ S > 0) Yes, Δ G < 0
Exothermic (Δ H < 0) Decrease (Δ S <
Endothermic (Δ
H >
0)
Increase (Δ
S > 0)
Only at low temps, if |T Δ S | <
|Δ H |
Only at high temps, if T Δ S > Δ H
0)
Endothermic (Δ
H >
Decrease (Δ
S <
No, Δ
G > 0
0) 0)
2. When 300 mL of oil and 900 mL of water are agitated in a container, emulsification occurs. However, the system quickly reverts back into two separate phases as agitation stops. Explain, in terms of entropy and surface free energy, a. the occurrence of phase separation. (10 marks) b. the mechanism of surfactants in promoting emulsification. (10 marks)

a) Most pharmaceutical dispersions are lyophobic disperse systems. The two phases do not mix readily. High interfacial tension,
γ, is high. Hence requires third component to stabilised the system that is stabilising components for example surfactant, suspending agent, solubilising agent.The internal phase (referred to as disperse phase) is present as present as particles dispersed throughout an external, continuous phase.
The interface
between internal
and external phase
Internal
(disperse)phase
External
(continuous) phase
Mixing of 300ml (25%) of oil and 900ml (75%) of water then oil will becomes disperse phase and water becomes continuous phase.
Water
Agitation Stop mixing
Oil
Water
Lowest A Higher A Lower A Lowest A

Phase separation occurs because interfacial surface tension (
γ) if high. Input of work (agitation) is required to mix the two phases. When agitation occurs, the entropy, S which is the measure of the extend of disorder and randomness of the system is increasing, consequently causing increase in G* since ΔG = ΔH - TΔS. Surface free energy (G*) of the system depends on the total surface area (A) and interfacial tension ( γ) between droplets and continuous medium ΔG* = γΔA
When a small quantity of oil is layered on water, oil will not disperse as droplets through the water unless we start mixing:
Oil
Water
W
Mix
ΔG* = γΔA
Where
ΔG* is Gibbs free energy
γ is surface tension
ΔA is surface area
From going left to right we know that A increase. I ncrease surface area (ΔA
+ve) cause the increase of
ΔG* and thermodynamically unfavourable (ΔG*
+ve).
ΔA -ve ΔA -ve
Oil
Water
Lower A
Higher A
Lowest A

Merging of droplets is a desire to reduce interfacial area, thereby decreasing the Gibbs free energy, G* since ΔG* =  ΔA. And then, phase separation occur. b) mechanism of surfactants in promoting emulsification
Oil and water do not mix so we need to do some work to create an emulsion.
It require input of work, w, in order to disperse the oil as we are increasing the size of the interface between the two phases. Dispersed oil droplets coalesce until phases separate with the decreasing interfacial area and minimized surface free energy. Nature will attempt to minimize G* and the emulsion will coalesce. Because the minimize interfacial area and surface free energy are unstable, so in order to make use of emulsions in pharmaceutical formulations, we need to add surfactants at oil/water interface. Surfactant molecules have the same basic molecular structure that are a hydrophile attached to a lipophile and it is this nature that makes them adsorb at surfaces. Added surfactant molecules adsorb at the oil-water interface, where they orient themselves such that the hydrophile is in the water and the lipophile is in the oil. After adding surfactants into the solutions, due to its poor aqueous solubility there is weak interaction between hydrocarbon chain of surfactant and water. But, non-polar hydrocarbon chains induce order in neighbouring water molecules. Water molecules cluster surrounding hydrocarbon tails restrict movement of the tails ( Δ S –ve). After water molecules return to disordered state ( Δ S +ve), tail groups free to move, because they are no longer hindered by H
2
O clusters ( Δ S +ve). The tail groups escape from water by positioning themselves in the hydrophobic area of oil droplets. The head groups face outside to the water molecules.
After that, it will decrease surface tension, the tendency for interface to contract also decrease, then the possibility that collisions between droplets will lead to coalescence will decrease and lastly increase the kinetic stability of the dispersion and less thermodynamically unstable and promote emulsification.

Add surfactant
Pure H
2
O, molecules Surfactant molecule anchored at favour bulk over interface interface + water molecule