Entropy and Gibbs free Energy

Question 1

The second law of thermodynamics

Answer 1

The second law of thermodynamics states that the total entropy increases in all processes that take place by themselves
(spontaneous changes). In other words, reactions go in the direction of more disorder.

Question 2

Define Entropy

Answer 2

Entropy is the number of possible arrangements of the particles and their energy in a given system. It can also be thought of as a dispersal of energy, either from the system to the surroundings or from the surroundings to the system. The system becomes energetically more stable when it becomes more disordered.

Question 3

Real life examples of Entropy

Answer 3

1. A polymer chain with freely rotating bonds, i.e. single bonds, can be coiled into thousands of different shapes all having similar energy. The natural shape of the chain (random unstretched coils) has the highest entropy. The most unlikely shape is a perfectly ordered straight chain.
2. The stretched form of a rubber band has lower entropy because the polymer chains are more ordered (less random). So when the stretching force is removed, the rubber goes back to the form with greater entropy (more randomness).

Question 4

Diffusion

Answer 4

The process of random movement and
random collisions of molecules is called diffusion. The reason molecules in a vapour diffuse is because of the laws of chance and probability.

Question 5

Standard molar entropy

Answer 5

Standard molar entropy is the entropy of one mole of substance in its standard state. The symbol ⦵ indicates that the entropy is at standard conditions.
The values of all standard molar entropies are positive. Remember that elements have positive standard molar entropy values. Do not mix entropies up with enthalpies: the elements in their standard states have enthalpy values of zero.
(The entropy values are compared to a theoretically perfect crystal. The third law of thermodynamics states that ‘All perfect crystals have the same entropy at a temperature of absolute zero’. The nearest we can get to this is a perfect diamond weighing 12 g cooled to as low a temperature as possible)

Question 6

Generalisations regarding entropy values

Answer 6

• Gases generally have much higher entropy values than liquids, and liquids have higher entropy values than solids (an exception would be CaCO3 ‘solid’ as it has greater entropy than mercury which is a ‘liquid’).
• Simpler substances with fewer atoms have lower entropy values than more complex substances with a greater number of atoms.
• For similar types of substances, harder substances have a lower entropy value. For example, diamond has a lower entropy value than graphite and calcium has a lower entropy value than lead.
• When a solid dissolves in a solvent, the entropy generally increases. In the solid, the particles are ordered and can only vibrate. Not only are the particles spread out more but also the number of ways of arranging the energy is greater.

Question 7

Kinetics behind the entropy change as state changes

Answer 7

There is a gradual increase in entropy as the temperature of a substance is increased. Increasing the temperature of a solid makes the molecules, atoms or ions vibrate more. Increasing the temperature of a liquid or gas increases the entropy because it increases the disorder of the particles. When a substance melts or vaporises, there is a large increase in entropy because there is a very large increase in the disorder of the particles.

Question 8

Total entropy change equation

Answer 8

ΔS⦵total = ΔS⦵system + ΔS⦵surroundings
(If the total entropy change increases, the entropy change is positive. The reaction will then occur spontaneously. We say that the reaction is feasible. If the total entropy change decreases, the entropy change is negative)

Question 9

Entropy changes in exothermic and endothermic reactions (detail)

Answer 9

(The surroundings are so large that when energy exchange takes place there is such a small change in temperature or pressure that we can ignore this)
For an exothermic reaction, the energy released to the surroundings increases the number of ways of arranging the energy. This is because the energy goes into rotation and translation (movement from place to place) of molecules in the surroundings. So there is likely to be an increase in entropy and an increased probability of the chemical change occurring spontaneously. In other words, the reaction becomes more feasible.
For an endothermic reaction, the energy absorbed from the surroundings decreases the number of ways of arranging the energy. So there is likely to be a decrease in entropy and a decreased probability of the chemical change occurring spontaneously.

Question 10

Entropy change of system equation

Answer 10

ΔS⦵system = ΣS⦵products − ΣS⦵reactants

Question 11

Entropy change of surroundings equation (not required)

Answer 11

ΔS⦵surroundings = − ΔH⦵reaction / T

Question 12

Entropy in equilibrium reactions

Answer 12

At the position of equilibrium, the total entropy change of the forward reaction equals the total entropy change of the backward reaction, and under standard conditions the overall entropy change is zero.

Question 13

Entropy and temperature

Answer 13

If we carry out reactions at temperatures above standard temperature, an increase in temperature makes the entropy change of the surroundings less negative or more positive. If we carry out reactions at temperatures below standard temperature, a decrease in temperature makes the entropy change of the surroundings more negative or less positive.
We assume that neither the standard molar entropies nor the enthalpy change of formation changes with temperature.

Question 14

Q4 b ii - (from book pg 504) : Explain, in terms of entropy changes, what happens when the pressure on this system is increased.

Answer 14

The pressure on the system increases, a negative contribution is made to the change in entropy (It is a measure of how much the energy of atoms and molecules become more spread out in a process). If we increase the pressure on the system, the volume decreases. The energies of the particles are in a smaller space, so they are less spread out.

Question 15

Entropy, enthalpy change and Gibbs free energy

Answer 15

• For an exothermic reaction the entropy change of the system is negative. But the large negative value of the enthalpy change more than compensates for the negative entropy change of the system. This is because it causes the term − ΔH⦵reaction / T to have a high positive value. So the total energy change is positive and the reaction, once started, is spontaneous. In highly exothermic reactions, where the value of ΔH⦵reaction is large and negative, the enthalpy change is the driving force of the reaction.
• In endothermic reactions, the entropy term tends to be more important. The term − H⦵reaction / T has a negative value. If the value of ΔS⦵system and ΔS⦵surroundings are both negative, then the reaction will not be spontaneous. However, if the value of ΔS⦵system is positive and large enough, it can compensate for the negative value of the ΔS⦵surroundings so that ΔS⦵total becomes positive. The reaction is spontaneous.

Question 16

Define Gibbs free energy + equation

Answer 16

The energy change that takes into account post the entropy change of a reaction and the enthalpy change.
ΔG⦵ = ΔH⦵reaction − TΔS⦵system
p.s. don’t forget to multiply the value of ΔH⦵ by 1000 if ΔH⦵ is in kJ. This is because the units of ΔS⦵ are in joules per kelvin per mole.

Question 17

Standard molar Gibbs free energy of formation

Answer 17

The standard molar Gibbs free energy of formation is the free energy change that accompanies the formation of one mole of a compound from its elements in their standard state.
(The Gibbs free energy change we will be using will usually be the Gibbs free energy change of formation)

Question 18

Spontaneous vs Feasible

Answer 18

The words spontaneous and feasible both have meanings of ‘likely to happen’. We use the word feasible for chemical reactions. The word spontaneous is a more general term and applies to physical processes such as diffusion and dissolving as well.
(For a reaction to be feasible (spontaneous), ΔS⦵total must be positive. The value of T is always positive on the absolute (kelvin) temperature scale. So applying these signs to the relationship ΔG⦵=−TS⦵total, the value of ΔG must be negative for a reaction to be spontaneous. If the value of ΔG is positive, the reaction is not feasible.

Question 19

Temperature change and reaction spontaneity in case of Exothermic reactions

Answer 19

For an exothermic reaction, the first term (ΔHreaction) has a negative value.

• If the value of ΔSsystem is positive, the
  second term (−TΔSsystem) is negative and the reaction will be spontaneous because both ΔHreaction and −TΔSsystem are negative. So ΔG is negative.
• If the value of ΔSsystem is negative, the second term is positive to overcome the negative value of ΔHreaction and make ΔG positive. So the reaction is less likely to be spontaneous at a higher temperature. This mirrors what we know about the effect of temperature on equilibrium: for an exothermic reaction, a higher temperature shifts the position of the equilibrium in favour of the reactants. The reaction is likely to be spontaneous if the temperature is low because ΔHreaction is more likely to have a greater negative value than the positive value of the second term. So ΔG is negative. If the temperature is very high, the second term may be positive enough to shift the position of equilibrium in favour of the reactants.

Question 20

Temperature change and reaction spontaneity in case of Endothermic reactions

Answer 20

For an endothermic reaction, the first term (ΔHreaction) has a positive value.

• If the value of ΔSsystem is negative, the second term is positive. The reaction will not occur because both terms are positive, making the value of ΔG positive.
• If the value of ΔSsystem is positive, the second term is negative. The reaction is unlikely to be spontaneous if the temperature is low because ΔHreaction is more likely to have a greater positive value than the negative value of the second term. So ΔG is positive. If the temperature is very high, the second term may be negative enough to overcome the positive value of ΔHreaction and make ΔG negative. So the reaction is more likely to be spontaneous at a higher temperature. This mirrors what we know about the effect of temperature on equilibrium: for an endothermic reaction, a higher temperature shifts the position of equilibrium in favour of the products.

Question 21

General comparison of Gibbs free energy values (pg 508, Table 23.2)

Answer 21

The standard enthalpy change of an element is zero. Similarly, the standard Gibbs free energy change of formation of an element is zero. Many compounds in the solid state have high negative values of Gibbs free energy change of formation. Many gases and liquids have standard Gibbs free energy change values that are negative but many others, such as ethene, have positive values. The standard Gibbs free energy change of formation also depends on the state.

Question 22

Define Standard Gibbs free energy change of reaction + equation

Answer 22

The standard Gibbs free energy change of reaction is the Gibbs free energy change when the amounts of the reactants shown in the stoichiometric equation react under standard conditions to give products. The reactants and products must be in their standard states.
ΔG⦵reaction = ΣΔG⦵products − ΣΔG⦵reactants
( or using the same idea as Hess’s law, a free energy cycle can be drawn and the equation;
ΔG⦵2 = ΔG⦵1 + ΔG⦵reaction
so, ΔG⦵reaction = ΔG⦵2 − ΔG⦵1
can be made)
(Units : KJ )

Question 23

Steps to calculate the Gibbs free energy change of reaction from an energy cycle
(Worked example 9 &10 pg 508, 509)

Answer 23

• write the balanced equation at the top
• draw the cycle with the elements at the bottom
• draw in all arrows making sure that they go in the correct directions
• calculate ΔG⦵reaction = ΔG⦵2 − ΔG⦵1 taking into account the number of moles of reactants and products

Question 24

Gibbs free energy and Work

Answer 24

Gibbs free energy change can be thought of as part of the enthalpy change that is needed to do work. If we rearrange the equation ΔG = ΔH − TΔS as ΔH = ΔG + TΔS, we can regard the +TΔS part as being the energy unavailable to do work because it is involved with the disorder of the system. The ΔG part is free energy that is available to do work, e.g. driving the charge in electrochemical cells.

Question 25

What do values of both Gibbs free energy of formation and reaction determine?

Answer 25

Gibbs free energy of formation is a measure of the stability of a compound. The more negative the value of ΔG⦵f , the greater the stability of the compound. It is unlikely to decompose. If ΔG⦵f is positive, the compound is likely to be unstable with respect to its elements.
The Gibbs free energy change of reaction is also a measure of the feasibility of a reaction. Reactions with negative values of ΔG⦵reaction are likely to be feasible (spontaneous), whereas those with positive values are less likely to be spontaneous.

Question 26

What do the electrode potential values indicate regarding feasibility of reaction and conc. of reactants and products? (A Preview on Electrochemistry)

Answer 26

• If the value of E⦵cell is zero then the reaction is in an equilibrium where the products and reactants are balanced. The position of equilibrium is neither to the right nor to the left.
• If the value of E⦵cell is about +0.1 V, there are more products than reactants.
• If the value of E⦵cell is about −0.1 V, there are more reactants than products.
• If the value of E⦵cell is more positive than about +0.6 V the reaction goes to completion.
• If the value of E⦵cell is more negative than about −0.6 V there is no reaction or minimal reaction.

Question 27

What do values of Gibbs free energy change indicate in equilibrium reaction

Answer 27

• When a system is in chemical equilibrium and the amounts of products and reactants balance, the value of ΔG⦵reaction is zero (ΔG⦵reaction = 0).
• The products predominate if the value of ΔG⦵reaction has a fairly low negative value, e.g. −10 kJ mol−1.
• The reactants predominate if the value of ΔG⦵reaction has a slightly positive value, e.g. +10 kJ mol−1.
• The reaction can be regarded as complete if the value of ΔG⦵reaction is high and negative, e.g. −60 kJ mol−1.
• The reaction can be regarded as not being feasible (spontaneous) at all if the value of ΔG⦵reaction is high and positive, e.g. +60 kJ mol−1.

Question 28

Equation relating Gibbs free energy change and standard electrode potential
(Worked example 11 pg 510)

Answer 28

ΔG⦵ = −nFE⦵cell
where:
ΔG⦵ is the standard Gibbs free energy in J mol−1
n is the number of moles of electrons transferred in the cell reaction
F is the charge on a mole of electrons in C mol−1
(this is the Faraday, 96 500 C mol−1)
E⦵cell is the standard cell potential

Question 29

Exam style Q Ch 23

Answer 29

Q 8 a) and d)