Chemical Thermodynamics: Spontaneous Processes & Entropy lecture 2 mod 2

• Chemical Thermodynamics Part 2 is the second lecture in module 2
• Chapter 19 is the textbook chapter to read

Learning Objectives

• The goal is to understand the number of possible arrangements of particles in a system in relation to entropy
• Qualitatively predict entropy changes
• Carry out calculations using S°

Spontaneous Processes

• These, once started, will continue without any help
• They were originally thought to be only exothermic processes, which would lead to a lowering in energy

Entropy

• Entropy (S) must also be considered
• Entropy is a measure of the number of possible arrangements of particles in a system
• Entropy is a measure of the distribution of energy over available states in a system
• Entropy is the number of available microstates
• Entropy is a measure of randomness and disorder

Entropy - Gas Molecules in Flasks

• Higher entropy occurs when two molecules are in each flask because particles have more possible arrangements, or the system is more disordered/random
• An ordered system is very unlikely; there's a 1 in 4 chance of both molecules being in the left flask
• 4 molecules have just 0.54 = 6.25% - a 1 in 16 chance of being both in the left flask
• 1 mole of molecules has just 0.56.023 x 1023 chance – less than 1 in 10100
• There is a very small chance of an ordered system, and systems spontaneously becomes more disordered, increasing entropy

Second Law of Thermodynamics

• Whenever a spontaneous event takes place in the universe, the total entropy of the universe increases
• In thermodynamics, the universe consists of the system of interest, plus the surroundings
• The entropy of a system can decrease during a spontaneous process, as long as the entropy of the surroundings increases by a larger amount
• The enthalpy of the universe is constant, the entropy of the universe is increasing, and the available energy is constantly being dispersed throughout the universe

Measuring Entropy

• Unlike enthalpy, it is possible to measure absolute values of entropy for a substance
• The third law of thermodynamics states that at absolute zero, the entropy of a perfectly ordered pure crystalline substance is zero
• A value measured at 1 bar is called a standard entropy (S°), and units are J mol-1 K-1.

Entropy Values

• Solids have the lowest entropies, followed by liquids, with gases having the highest
• S° (H₂O, s) = 41 J mol-1 K-1
• S° (H₂O, I) = 70 J mol-1 K-1
• S° (H₂O, g) = 189 J mol-1 K-1
• Small values are S° measured in J, not kJ and unit is K-1
• In contrast to ∆H°, S° for an element in its standard state is not zero
• S° (H2, g, 298 K) = 130.6 J mol-1 K-1
• S° (O2, g, 298 K) = 205.0 J mol-1 K-1
• The reference point is the pure crystalline solid at 0 K

Standard Entropy of Reaction

• AS° can be written just like for ∆Η°
• AS° = sum of entropy of products - sum of entropy of reactants
• △S° = ∑[S° (products)] - ∑[S° (reactants)], while taking into account of stoichiometry
• Generally, AS can be qualitatively predicted for a chemical reaction based on the states of the substances involved
• A reaction which results in the formation of a gas from a solid or liquid will very likely have AS +ve
• A reaction having fewer moles of products than reactants (all in the same phase) will very likely have ∆S –ve

Effect of Phase/Number of Particles

• Entropy Increase: ice -> liquid water -> water vapour
• Entropy Decrease: 2NO(g) + O2(g) -> 2NO2(g)

Qualitative Example

• The sign of ∆ꝰS can be predicted if the following reactions are known:

1. N2(1) → N2(g)
2. N2(g) + 3H2(g) → 2NH3(g)

• For (1), 1 mole of liquid is converted to 1 mole of gas, and molecules of gaseous N2 are less constrained than liquid molecules, therefore have more possible arrangements, so AS will be +ve
• For (2), 4 moles of gas react to give 2 moles of gas, meaning fewer possible arrangements of the product molecules, so AS will be -ve

Quantitative Example

• To calculate AS° for the hydrolysis of urea, use the following equation: CO(NH2)2(s) + H2O(l) → CO2(g) + 2NH3(g)
• The following values are given:
  • S° [CO(NH2)2(s)] = 173.8 J mol-1 K-1
  • S° [H2O(I)] = 69.96 J mol-1 K-1
  • S° [CO2(g)] = 213.6 J mol-1 K-1
  • S° [NH3(g)] = 192.5 J mol-1 K-1
• ∆S° = [213.6 + (2×192.5)] – [173.8 + 69.96] J mol-1 K-1 = 354.8 J mol-1 K-1
• The large positive value is consistent with the formation of 3 moles of gas from an aqueous solution

Spontaneity

• A positive value of AS for a particular process is no guarantee that the process will be spontaneous
• The melting of ice at -10 °C is nonspontaneous despite AS being positive
• Spontaneity is determined by a combination of ∆H and AS, and is thus Gibbs energy

Gibbs Energy

• Gibbs energy (G) is defined as follows: G = H - TS
  • H is the enthalpy of the system
  • S is the entropy of the system
  • T is the temperature in Kelvin (0 °C = 273 K)
• Absolute values of G cannot be measured, so we always talk about the change in G for a process, ∆G
• ∆G = ∆H – TAS
• The usual terminology is used when referring to a chemical reaction (rather than a physical change)
• ∆rG = ∆rH – T∆rS