Chap 5D - Entropy

Define spontaneous processes and entropy (and unit)

• Spontaneous process (Def.) : One that takes place naturally in the direction stated. The change occurs without a need for continuous input of energy from outside the system

• Entropy (definition) : Entropy ‘S’ is a measure of the randomness or disorder in a system, reflected in the number of ways that the energy of a system can be distributed through the motion of its particles. 

• Unit : J mol–1 K –1

Describe S > 0

• If ∆S > 0  Entropy of system increases after change -> thermodynamically favourable (spontaneous) 

  • Takes place without outside interference 

  • Takes place in definite direction

  • Decreases free energy of a system 

Explain how change in temperature affects entropy

• When temperature is increased, the disorder of the system generally increases

• The kinetic energy of the molecules increases and so there will more ways of arranging the energy quanta in hotter species -> there are more ways to arrange the particles over a wider range of speeds -> entropy increases

• Increase in the spread of kinetic energy of gaseous particles at a higher temperature can be seen from the broadening of the Maxwell-Boltzmann energy distribution curve

• Increase in temperature -> entropy change is positive 

Heating causes: 

1. Particles in solids vibrate more vigorously, which makes the arrangement of their particles slightly less orderly

2. Particles in liquids and gases move faster leading to greater disorder

Explain how state affects entropy

• For the same amount of substance , entropy of solid < liquid < gas (disorderliness of particles increase from solid to liquid to gas) 

• ∆S > 0 for change in phase from solid to liquid/gas, and also for liquid to gas

1. Solid  

• The particles in the solid state vibrate about their fixed positions

• The energy is thus the least dispersed and the solid has the lowest entropy

• When temperature increases, entropy increases gradually as the kinetic energy of the particles increases

2. Liquid 

• When the solid melts, the particles move more freely in the liquid state and become more disordered

• When a solid changes into a liquid, the orderly arrangement of particles in the solid is destroyed, hence there is an increase in entropy

• As the liquid is heated, its entropy increases as the particles gain kinetic energy

3. Gas 

• During vaporisation, the liquid converts to a gas where the particles are able to move even more freely

• Hence there is a larger increase in entropy (S >> 0) as there are more ways to distribute the particles and their energy in the gaseous state

• The gaseous state has greatest entropy because its particles possess the highest energy and are also moving randomly in all directions

Explain how number of particles affect entropy

• When a chemical reaction results in an increase in the number of gas particles, the particles in gas are the most disordered so the number of ways that the particles and the energy can be arranged increase greatly

• There is a large increase in entropy

Explain how mixing into a larger container affects entropy

• Before mixing, each gas has the same volume and pressure

• After the barrier is removed, each gas expands to occupy the whole container and hence the volume of each gas doubles

• The partial pressure of each gas is reduced by half but total pressure remains constant

• As the volume available for each gas (H2 and N2) is increased, there are more ways to distribute the particles and hence their energy -> entropy increases

• If the two sets of particles have different energies before mixing, the energy distribution of the system will increase due to collisions upon mixing -> thermal chaos increases

Explain how mixing into one container and no container affects entropy

1. Mixing in one container

• When gases are mixed at constant volume, the volume available to distribute each gas particle is the same. Hence the entropy does not change

2. No container 

• When liquids with similar polarities (Eg. Benzene and hexane) are mixed together, entropy increases

• This is because total volume increases and hence there are more ways to distribute the particles and hence their energy

OR

• When a gas expands, the volume available for distribution of the particles increases

• Entropy increases as there are more ways that the particles and the energy can be distributed

Explain why dissolution of an ionic solid affects entropy

• Dissolving an ionic solid in water (dissolution) involves the disruption of the crystal structure of solid NaCl and hydration of the Na+ and Cl- ions.

• Disruption of the crystal lattice increases disorder, since the Na+ and Cl− ions were previously rigidly held in the solid state but are now free to move about in the solvent.

• Hydration decreases disorder about the Na+ and Cl− ions because water molecules are now arranged in an orderly manner about the Na+ and Cl− ions

• Generally, the overall dissolution process results in a net increase in disorderliness and S > 0

  • For dissolution of ionic solids containing ions with large radii such as HgCl2

  • Compounds containing ions of low ionic charge such as +1 cations and −1 anions (since their charge densities are low and they do not result in a very orderly arrangement of water molecules) 

• For some ionic solids such as CaSO4 with more highly charged ions, the water molecules are more strongly ordered about the ions, and the hydration process greatly decreases disorder

• This outweighs the increase in disorder caused by the disruption of the crystal lattice, and the dissolution process leads to decrease in entropy

Compare G < 0 , G = 0, G > 0

ΔG < 0	ΔG = 0	ΔG > 0
The reaction takes place spontaneously (thermodynamically favourable) The reaction is exergonic	The system is at equilibrium There is no net reaction in the forward or backward direction	The reaction cannot take place spontaneously (not thermodynamically favourable) It is spontaneous in the reverse direction The reaction is endergonic

Explain why combustion of diamond doesn’t occur

• Combustion of diamond does not involve a significant change in entropy since conversion of reactants to products does not involve a change in the total number of gaseous particles -> ∆S⦵ ≈ 0

• ∆G⦵ = ∆H⦵ − T∆S⦵< 0, since ∆H⦵ < 0 ->  reaction is expected to be thermodynamically spontaneous

• But diamonds do not undergo combustion in air as activation energy for the reaction is too high due to the strong extensive network of covalent bonds in diamond

Describe G when H < 0 and S > 0 + examples

ΔH	ΔS	ΔG = ΔH - TΔS	Reaction	Explanation
Negative	Positive	Always negative	Spontaneous at all temperatures Continuous input of energy from outside the system is not needed for such reactions	H⦵< 0, Since S⦵> 0 then −TS⦵< 0, Both H⦵ and –TS⦵ < 0 -> G⦵ = H⦵− TS⦵< 0 Eg. Combustion of organic compounds and explosives, decomposition of ozone and dinitrogen monoxide

Explain G when H > 0 and S < 0 + examples

Positive

Negative

Always positive

Not spontaneous at all temperatures Energy must be continuously supplied for the process to take place (external assistance)

Explain G when H and S is negative + examples

Negative

Negative

Negative at low temperature if |ΔH| > |TΔS|

Spontaneous at low temperatures  Reaction is enthalpy driven Exo

Explain G when H and S is positive + examples

Positive

Positive

Negative at high temperature if ΔH < TΔS

Spontaneous at high temperatures  Reaction is entropy driven Endo

Explain whether the reaction is spontaneous. 2N2O(g) + O2(g) → 4NO(g) ΔH = +197.1 kJ mol−1

ΔS is positive since there is an increase in the number of moles of gas. Hence there are more ways to distribute the particles and their energies. Since ΔG = ΔH − TΔS, ΔG is negative when TΔS > ΔH. The reaction is spontaneous when the temperature is high. When temperature increases, TΔS becomes more positive. ΔG = ΔH − TΔS Hence ΔG becomes more negative

Describe limitations of use of G

1. Non-standard condition

• G can only be used to predict spontaneity of a reaction under standard conditions

• Under nonstandard conditions, G must be calculated

2. Kinetics consideration

• While the Gibbs free energy change can be used to determine the spontaneity of a reaction, it does not take into account the kinetics of the reaction (ROR) 

• The reacting species may have to overcome a large Ea before reaction can occur 

• Some reactions are thermodynamically (or energetically) favourable (G<0) but kinetically not favourable (occur very slowly) (Eg. Rusting : kinetically stable)