Entropy & Gibb’s Free Energy

Entropy

Entropy is a measure of the dispersal or distribution of matter and/or energy in a system.

What does entropy measure?

Entropy measures how disordered or chaotic a system is.

Entropy

Entropy is a measure of the dispersal or distribution of matter and/or energy in a system.

What does entropy measure?

Entropy measures how disordered or chaotic a system is.

True or False: An increase in entropy means a system becomes energetically less stable.

False.

What does an increase in entropy mean?

An increase in entropy means a system becomes energetically more stable.

What happens to entropy during the thermal decomposition of calcium carbonate?

During the thermal decomposition of calcium carbonate, the entropy of the system increases.

Why does the entropy increase when a solid melts?

The entropy increases when a solid melts because the particles become more disordered in the liquid state.

Standard molar entropy

Standard molar entropy (S°) is the entropy value of one mole of a pure substance under standard conditions of temperature and pressure.

What are the units of entropy?

The units of entropy are joules per Kelvin per mole, J K⁻¹ mol⁻¹.

True or False: The entropy of a substance is the same in all states of matter.

False.

How does the entropy of water vapor compare to liquid water?

The entropy of water vapor is higher than that of liquid water.

What is the symbol for standard molar entropy?

The symbol for standard molar entropy is S°.

Explain why there is an increase in entropy when copper carbonate undergoes thermal decomposition.

There is an increase in entropy when copper carbonate undergoes thermal decomposition because one mole of reactant is forming two moles of product, and the solid reactant is forming a solid product and a gaseous product which is higher entropy.

True or False: There is an increase in entropy when water vapour is cooled to form water.

False.

What happens to entropy when water vapour is cooled to form water?

There is a decrease in entropy when water vapour is cooled to form water.

Does the following reaction show an increase or decrease in entropy? 2NaHCO3 (s) → Na2CO3 (s) + CO2 (g) + H2O (g)

The reaction shows an increase in entropy.

Explain whether the following reaction shows an increase or decrease in entropy: C3H8 (g) + 5O2 (g) → 3CO2 (g) + 4H2O (g)

The reaction shows an increase in entropy because 6 moles of gaseous reactant form 7 moles of gaseous product.

For the following reaction, explain whether the forward or reverse reaction shows a decrease in entropy: CH4 (g) + H2O (g) → CO (g) + 3H2 (g)

The reverse reaction shows a decrease in entropy because 4 moles of gas form 2 moles of gas.

Explain why the entropy change of the following precipitation reaction is negative: AgNO3 (aq) + NaBr (aq) → NaNO3 (aq) + AgBr (s)

The entropy change of the following precipitation reaction is negative because 2 moles of aqueous reactants form 1 mole of aqueous product and 1 mole of solid.

State the equation for calculating standard entropy change.

The equation for calculating standard entropy change is: ΔS°(reaction) = ΣS°(products) - ΣS°(reactants).

What does ΔS° represent?

ΔS° represents the standard entropy change of a reaction.

True or False: When calculating ΔS°, the coefficients from the balanced equation must be applied.

True.

Define standard conditions.

Standard conditions are 298 K (25°C) and 1 atm pressure.

True or False: The entropy of a system increases during a chemical reaction.

False.

ΔS°

A positive ΔS° value indicates an increase in the disorder of the system / entropy.

Negative ΔS° value

A negative ΔS° value indicates a decrease in the disorder of the system / entropy.

Entropy and temperature relationship

As temperature increases, the entropy of a substance generally increases due to increased particle motion and disorder.

Standard entropy change for water vapour condensing

The standard entropy change for water vapour condensing is -119 J K-1 mol-1.

ΔS° (H2O (g))

ΔS° (H2O (g)) = + 189 J K-1 mol-1

ΔS° (H2O (l))

ΔS° (H2O (l)) = + 70 J K-1 mol-1

ΔS°(reaction)

ΔS°(reaction) = ΣS°(products) - ΣS°(reactants)

Entropy change for hydrogenation of propene

The standard entropy change for the hydrogenation of propene is -128 J K-1 mol-1.

Gibbs free energy

Gibbs free energy is a thermodynamic concept that combines enthalpy change and entropy change to determine the feasibility of a reaction.

Gibbs free energy equation (enthalpy and entropy)

The Gibbs free energy equation, in terms of enthalpy and entropy, is: ΔGo = ΔHo - TΔSo.

Gibbs free energy equation (ΔGo values)

The Gibbs free energy equation, in terms of ΔGo values, is: ΔGo = ΣΔGproductso - ΣΔGreactantso.

Units of ΔG

The units of ΔG are kilojoules per mole, kJ mol⁻¹.

Negative ΔG value significance

A negative ΔG value indicates that a reaction is spontaneous or feasible.

Positive ΔG value significance

A positive ΔG value indicates that a reaction is not spontaneous or feasible.

Relationship between ΔG and temperature

The relationship between ΔG and temperature is inverse, as shown in the equation ΔG = ΔH - TΔS.

Units of ΔS conversion for ΔG

The units of ΔS must be converted from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ when calculating ΔG.

Units of ΔH and ΔS

The units of ΔH and ΔG are kJ mol-1. The units of ΔS are J K-1 mol-1.

Free energy change for NaHCO3 decomposition

The free energy change for the decomposition of sodium hydrogen carbonate, NaHCO3 (s), at 500 K is -32 kJ mol-1.

Spontaneous reaction

A spontaneous reaction is a reaction that occurs without external influence and has a negative Gibbs free energy change (ΔG < 0).

Condition for spontaneous reaction

For a reaction to be spontaneous, the Gibbs free energy change (ΔG) must be negative or equal to zero.

Exothermic reactions spontaneity

Not all exothermic reactions are spontaneous. The spontaneity of a chemical reaction also depends on the entropy change.

Factors determining spontaneity of a reaction

The factors that determine the spontaneity of a reaction are: Enthalpy change (ΔH), Entropy change (ΔS), Temperature (T).

Temperature effect on endothermic reactions

For endothermic reactions with positive ΔS, increasing temperature makes the reaction more likely to be spontaneous.

Endothermic reactions with negative ΔS

Endothermic reactions with negative ΔS are never spontaneous, regardless of temperature.

Equation for spontaneity temperature

The equation to determine the temperature at which a reaction becomes spontaneous is: T = ΔHꝋ / ΔSꝋ.

Exothermic reactions with positive ΔS

Exothermic reactions with positive ΔS are always spontaneous, regardless of temperature.

Feasibility of exothermic reaction with negative ΔS

As temperature increases, an exothermic reaction with negative ΔS becomes less feasible and may become non-spontaneous at very high temperatures.

Spontaneity of NaHCO3 reaction

The reaction is spontaneous because ΔG is negative.

Temperature for CO and H2O reaction spontaneity

The temperature at which the reaction of carbon monoxide with water becomes spontaneous is: T = -41.4 / -0.135 = 307 K.

Equilibrium constant (K)

The equilibrium constant (K) is a value that indicates the ratio of products to reactants at equilibrium for a given reaction.

Reaction quotient (Q)

The reaction quotient, Q, represents the ratio of product concentrations to reactant concentrations at any point in a reaction, not necessarily at equilibrium.

Q at equilibrium

At equilibrium, Q is equal to K.

Gibbs free energy and reaction progress

As a reaction progresses towards equilibrium, the Gibbs free energy decreases until it reaches its minimum value at equilibrium.

ΔG at equilibrium

When a reaction reaches equilibrium, ΔG becomes zero.

Large positive value of K

A large positive value of K indicates that products are favored at equilibrium.

Predicting reaction direction with K

If Q < K, the reaction will proceed forward; if Q > K, the reaction will proceed in reverse; if Q = K, the reaction is at equilibrium.

Significance of ΔG° in relation to K

ΔG° determines the value of K: A negative ΔG° results in K > 1 (products favored), A positive ΔG° results in K < 1 (reactants favored).

Standard Gibbs free energy change for Haber Process

The standard Gibbs free energy change, ΔG°, for the Haber Process at 298 K is: ΔG° = -31.8 kJ mol-1.

Equilibrium constant for Haber process

K = e to the power of negative (ΔG° / RT) = 3.77 x 10^5.

Change in Gibbs free energy for Haber process

The change in Gibbs free energy, ΔG, for the Haber process at 298 K is: ΔG = 2412 J mol-1 = 2.412 kJ mol-1.

Spontaneity of Haber process

This means that the reaction is not spontaneous as ΔG is positive.