Entropy & Spontaneity (DP IB Chemistry)

CuCO₃ (s) → CuO (s) + CO₂ (g)

There is an increase in entropy when copper carbonate undergoes thermal decomposition because:

• One mole of reactant is forming two moles of product,

• The solid reactant is forming a solid product and a gaseous product which is higher entropy.

False.

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

2NaHCO₃ (s) → Na₂CO₃ (s) + CO₂ (g) + H₂O (g)

The reaction shows an increase 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.

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.

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.

The equation for calculating standard entropy change is:

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

ΔS° represents the standard entropy change of a reaction.

True.

When calculating ΔS°, the coefficients from the balanced equation must be applied.

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

False.

The entropy of a system can increase or decrease during a chemical reaction, depending on the nature of the reactants and products.

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

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

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

False.

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

H₂O (g) → H₂O (l)

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

• ΔS°(reaction) = (+ 70) - (+ 189) = - 119 J K^-1 mol^-1

The standard entropy change for the hydrogenation of propene is:

C₃H₆ (g) + H₂ (g) → C₃H₈ (g)

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

• ΔS°(reaction) = (+ 270) - (+ 267 + 131) = - 128 J K^-1 mol^-1

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

The Gibbs free energy equation, in terms of enthalpy and entropy, is:

ΔG^o = ΔH^o – TΔS^o

The Gibbs free energy equation, in terms of ΔG^o values, is:

ΔG^o = ΣΔG_products^o – ΣΔG_reactants^o

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

False.

ΔG can be calculated using ΔH and ΔS values, along with the temperature.

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

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

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

True.

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

False.

The units of ΔH and ΔG are kJ mol^–1.

The units of ΔS J K^-1 mol^–1.

The free energy change for the decomposition of sodium hydrogen carbonate, NaHCO₃ (s), at 500 K is:

• ΔG = ΔH – TΔS

• ΔS = 334 / 1000 = 0.334

• ΔG = 135 – (500 x 0.334) = -32 kJ mol^-1.

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

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

False.

Not all exothermic reactions are spontaneous.

The spontaneity of a chemical reaction also depends on the entropy change.

The factors that determine the spontaneity of a reaction are:

• Enthalpy change (ΔH),

• Entropy change (ΔS),

• Temperature (T).

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

False.

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

The equation to determine the temperature at which a reaction becomes spontaneous is:

T = ΔH^ꝋ / ΔS^ꝋ

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

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

The reaction is spontaneous because is ΔG negative.

Reactions become spontaneous when ΔH^ꝋ = 0, which means that T = ΔH^ꝋ / ΔS^ꝋ.

The temperature at which the reaction of carbon monoxide with water becomes spontaneous is:

• T = ΔH^ꝋ / ΔS^ꝋ

• T = -41.4 / -0.135 = 307 K

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

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

True.

At equilibrium, Q is equal to K.

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

When a reaction reaches equilibrium, ΔG becomes zero.

True.

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

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.

ΔG° determines the value of K:

• A negative ΔG° results in K > 1 (products favored)

• A positive ΔG° results in K < 1 (reactants favored).

The standard Gibbs free energy change, ΔG°, for the Haber Process at 298 K is:

• ΔG° = ΔH° - TΔS°

• ΔS° = -202 / 1000 = 0.202

• ΔG° = -92 - (298 x 0.202) = -31.8 kJ mol^-1

The equation constant is:

• K =

• K = = 3.77 x 10⁵

The change in Gibbs free energy, ΔG, for the Haber process at 298 K is:

• ΔG = ΔG° + RT ln Q

• ΔG = -31 800 + (8.31 x 298 x ln(1 x 10⁶) )

• ΔG = 2412 J mol^-1 = 2.412 kJ mol^-1

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