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Gibbs Free Energy Formula can be used to determine the spontaneity of a process. Gibbs Free Energy tells us whether a process will be spontaneous or not. Josiah Williard Gibbs introduced this equation in 1873, in his paper "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surface". He outlined the principles of his new equation which was able to predict or estimate the tendencies of the numerous natural or chemical processes to start when bodies or systems are brought into close contact with each other.
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Keyterms: Energy, Spontaneity, Thermodynamics, Entropy, Spontaneous processes, Enthalpy, Entropy, Temperature
Introduction to Gibbs Free Energy
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Gibbs Free Energy can either be emphatically or enthalpically or both. However, it can be neither of these. It is related to the Second Law of Thermodynamics which states that the sum of the entropy of the system and its surroundings must always increase.
Entropy is the measure of the displacement of the energy of the system if it can contain energy. Therefore, Gibbs Free Energy is integral to the understanding of various equations as it makes it quite clear and easy to understand all the spontaneous processes in the universe.
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Gibbs Free Energy Formula
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The change in Gibbs Free Energy is given by the following equation which includes the change in Enthalpy, change in Entropy and Temperature.
ΔG = ΔH - TΔS
ΔG = Gibbs free energy
ΔH = Change in enthalpy
ΔS = Change in entropy
T = Temperature in K
Gibbs Free Energy Formula
Breaking down this equation
ΔG stands for Overall Energy Change within a System
ΔH stands for Enthalpy or Heat Content. It is generally defined as the change in bond strength and molecular stability. The Process will be Enthalpically favourable.
TΔS stands for Entropy. It is generally defined as the change in the order of the reaction. The Process will be Entropically favourable.
Results
- If ΔG is negative, that means that the process is Spontaneous
- If ΔG is Positive, that means that the process is NonSpontaneous
Calculation of Gibbs Free Energy
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Before understanding the details of solving the equation, there are certain energy conditions that you should be familiar with, such as:
To understand the various conditions of calculating Gibbs Free Energy.
- If ΔH is negative or Exothermic and Energetically Favourable
And ΔS is positive which signifies Entropically Favourable.
Thus, ΔG will be Negative and Always Spontaneous.
ΔG = ΔH - TΔS
(-) (-) (+)
- If ΔH is positive or Endothermic and Energetically Unfavourable
And ΔS is negative which signifies Entropically Unfavourable.
Thus, ΔG will be Positive and Never Spontaneous.
ΔG = ΔH - TΔS
(+) (+) (-)
- If ΔH is positive or Endothermic, that energetic unfavorability could be outweighed by the other term if the process is Entropically favourable.
The factor will increase with a High Temperature, it will be more like to be Spontaneous.
ΔG = ΔH - TΔS
(+/-) (+) (+)
- If ΔH is negative or Exothermic and Energetically Favourable,
And ΔS is negative which signifies Entropically Unfavourable.
Thus, the Entropically unfavorability will be minimized at Lower Temperatures, it will be Spontaneous.
ΔG = ΔH - TΔS
(+/-) (-) (-)
- However, in the case of a chemical equilibrium which happens when the free energy reaches its minimum possible value.
Then, If ΔG<0 and K>Q, then the reaction will occur to the right.
If ΔG>0 and K If ΔG=0 and K=Q, then the reaction will be at equilibrium and will not proceed in either direction.
Equilibrium Constant of Gibbs Free Energy
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The Equilibrium constant of Gibbs Free energy (K) is a component by which one can define whether the reaction is spontaneous or not. It can also be defined as the ratio of the concentration of products to the reactants in the case of chemical reactions.
When a system is in the state of equilibrium, the value of K will be equal to Q and ΔG=0.
However, when ΔG=0, the value of equilibrium constant K=1 and neither the reactants nor products are favoured at equilibrium.
With regards to temperature, the value of K decreases during an exothermic reaction and increases during an endothermic reaction.
Things to Remember
- Gibbs Free Energy is the measurement of useful work obtained in the form of energy by a thermodynamic system.
- It is denoted by ΔG.
- In order to calculate, the value of Gibbs free energy or ΔG, enthalpy and entropy are important.
- Enthalpy is the amount of heat content of a chemical or physical system.
- Entropy is the amount of thermal energy produced in the system with every given unit temperature which was unavailable for doing the useful work.
- The formula for calculation Gibbs Free Energy is, ΔG = ΔH - TΔS
- It works under the standard state of a substance which refers to standard conditions such as 1 atm pressure, 1 molar effective concentration and a temperature of 298 Kelvin.
- If the free energy of the reactants in a chemical reaction is more than the free energy of the products, the entropy will increase and the reaction will be spontaneous in nature.
Sample Questions
Ques. If the temperature is 127 degrees centigrade, ΔH is 92.22 kJ/mol and ΔS is -198.75 J/k-mol. What will be the nature of the reaction? (2 Marks)
Ans. We know that, ΔG = ΔH - TΔS
Keeping all the values in the equation, we will get ΔG as 92.22.
Thus, ΔG is positive and the reaction is Nonspontaneous.
Ques. Calculate the Gibbs Free Energy, if at the temperature of 293 Kelvin, the change in Enthalpy is 19.07 Kcal and the change in entropy is 90 cal/K. (2 Marks)
Ans. ΔG = ΔH - TΔS
ΔG = 19.07 Kcal - 293(90 cal/K) = -7.3 Kcal
Thus, the Gibbs Free energy is -7.3 Kcal.
Ques. The relationship between the Free Energy change (ΔG) and Entropy change (ΔS) at constant temperature (T) is which of the following: (2 Marks)
a) ΔG = ΔH + TΔS
b) ΔH = ΔG + TΔS
c) ΔG = -ΔH + -TΔS
d) ΔG = ΔH - TΔS
Ans. We are well aware by now that Gibbs Energy is formulated by ΔG = ΔH - TΔS.
So, ΔH = ΔG + TΔS
Ques. Which of the following changes in states represent the smallest value of ΔS and which one has the largest value of ΔS? (3 Marks)
a) freezing of water to ice
b) melting of ice to liquid water
c) sublimation of ice to gas
d) none
i) a & b
ii) b & c
iii) a & c
iv) d
Ans. The freezing of water is a decrease in entropy thus it will have the smallest value of ΔS. It happens because solids have less entropy than liquids. However, the other two options represent an increase in Entropy. The sublimation of ice to gas is more of an increase than the melting of ice to water as gas possesses more entropy than liquid. Thus, it would have the largest value of ΔS.
This is the reaction of diamond converting to Graphite
2C (diamond solid) → 2C (graphite s)
Ques. Find out the Gibbs Free energy (ΔG) and determine if the aforementioned reaction is spontaneous or nonspontaneous. The values required for the calculation are given below: (2 Marks)
ΔH (diamond solid)= 1.9 kJ/mol
Sº (diamond)= 2.38 J/(mol K)
Sº (graphite)= 5.74 J/(mol K)
Ans. ΔH = (2 mol of graphite)x (entropy change of graphite) - (2 mol of diamond)x (entropy change of diamond)
ΔH= 2 (0) - 2 (1.9 kJ/mol) = -3.8 kJ
ΔS = (2 mol of graphite)x (entropy change of graphite) - (2 mol of diamond)x (entropy change of diamond)
ΔS = 2x(5.74 J/(mol K)) - 2(3.38 J/mol K) = +6.72 J/mol
ΔG= ΔH - TΔS
ΔG= (-3.8x10^3) - (298.15 x 6.72 J/mol K) = -5.51 kJ
This reaction is spontaneous.
Ques. Determine if the statement is True or False:
"Spontaneous reactions are faster than non-spontaneous reactions." (2 Marks)
Ans. The Spontaneity does not determine the speed or velocity. Moreover, there are many spontaneous reactions that range very slowly such as the melting of an ice cube in cold water. Also, there are other reactions that are very fast such as melting an ice cube in hot water.
Ques. Calculate the temperature of the reaction: (2 Marks)
CaCl2 (s) → Ca ² (aq) + 2Cl¯ (aq)
if ΔG fo a solid= -748.1 kJ/mol, ΔH = -53.1 J/K and
ΔS for
Ca² = -53.1 J/Kmol
CaCl = 104.6 J/Kmol
Cl- = 56.5
Ans. ΔG= ΔH - TΔS
Changing the equation to, T= (ΔH - ΔG) ÷ S
T = (0- [-795.8]) – (-748.1)) [2(56.50 + (-53.1)] – [104.6]
Thus T = -34.539 K
Ques. How can the entropy change for a reaction be positive if the enthalpy change is negative? (3 Marks)
Ans. We can define entropy as Q/T where Q is heat associated with a reversible process.
ΔH is only equal to Q when P is constant.
For Spontaneous and thus irreversible reactions, the ΔS is the same as for a reversible reaction because S is a state variable; it does not depend on how one gets from one condition to another. In contrast, ΔH is not equal to Q as this is not a reversible reaction.
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