Entropy & Spontaneity

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Apuntes de la lección

Entropy and Dispersal of Energy

Entropy, S, is a measure of the distribution of matter and/or energy in a system.
It tells us how many possible ways the particles and their energy can be arranged.
A more disordered system has higher entropy and is usually more energetically stable.
The driving force behind reactions cannot be explained by enthalpy changes alone; entropy explains why endothermic reactions occur.
Under the same conditions, entropy increases in the order: solid < liquid < gas.

Predicting Entropy Changes

Entropy increases when a gas is formed or when a solid becomes a liquid or gas.
Entropy decreases when a gas is used up or when a gas becomes a liquid or solid.
Particles becoming more mobile or disordered leads to an increase in entropy.
For example, in CaCO₃(s) → CaO(s) + CO₂(g), a gas is formed, so entropy increases.
Melting ice: H₂O(s) → H₂O(l) increases entropy because molecules become more disordered.

Calculating Standard Entropy Changes

The standard molar entropy, S⦵, refers to substances in their standard states at 298.15 K and 100 kPa.
The entropy change of a reaction is calculated using: ΔS⦵ = ΣS⦵(products) – ΣS⦵(reactants).
The units of ΔS⦵ are J K⁻¹ mol⁻¹.
Coefficients from the balanced equation must be applied when calculating ΔS⦵.
Standard entropy values are found in Section 13 of the IB Chemistry data booklet.
A negative ΔS⦵ means the system becomes more ordered.

Gibbs Free Energy

The feasibility of a reaction is determined by both enthalpy change and entropy change.
These combine in the Gibbs equation: ΔG = ΔH – TΔS.
ΔG is in kJ mol⁻¹, ΔH in kJ mol⁻¹, T in K, and ΔS must be converted to kJ K⁻¹ mol⁻¹ by dividing by 1000.
ΔG can be calculated from ΔH and ΔS values or from standard Gibbs free energies of formation: ΔG⦵ = ΣΔG⦵f(products) – ΣΔG⦵f(reactants).
A negative ΔG means the reaction is spontaneous under standard conditions.

Spontaneous Reactions

For a reaction to be spontaneous, ΔG must be negative (ΔG ≤ 0).
When ΔG is positive, the reaction is not spontaneous and unlikely to occur.
Spontaneity depends on the signs of ΔH and ΔS and on temperature.
Exothermic (ΔH < 0) with positive ΔS: always spontaneous regardless of temperature.
Endothermic (ΔH > 0) with negative ΔS: never spontaneous regardless of temperature.
Exothermic with negative ΔS: spontaneous only at low temperatures (TΔS < ΔH).
Endothermic with positive ΔS: spontaneous only at high temperatures (TΔS > ΔH).

Temperature and Spontaneity

The temperature at which a non-spontaneous reaction becomes feasible can be found by setting ΔG = 0.
Rearranging the Gibbs equation gives T = ΔH⦵ / ΔS⦵.
At this temperature, the reaction is at the boundary between spontaneous and non-spontaneous.
For example, the reduction of Al₂O₃ with carbon becomes spontaneous at about 2299 K.

Gibbs Free Energy and Equilibrium

When a reversible reaction reaches equilibrium, Gibbs free energy is at its lowest.
As products increase, Gibbs free energy decreases until equilibrium is reached.
At equilibrium, ΔG = 0 and the reaction is spontaneous in the direction that decreases free energy.
The standard Gibbs free energy change is related to the equilibrium constant by ΔG⦵ = –RT ln K.
R = 8.31 J K⁻¹ mol⁻¹, T in K, and ΔG⦵ in J mol⁻¹ when using this equation.
If K > 1, products are favoured; if K < 1, reactants are favoured.

Reaction Quotient and Gibbs Free Energy

The reaction quotient, Q, is calculated like the equilibrium constant but with non-equilibrium concentrations.
The relationship between ΔG and Q is ΔG = ΔG⦵ + RT ln Q.
At equilibrium, Q = K and ΔG = 0, so ΔG⦵ = –RT ln K.
The size of Q indicates how far a reaction is from equilibrium and in which direction it proceeds.
These equations are given in Section 1 of the IB Chemistry data booklet.

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Preguntas de práctica

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1.Which statement best defines entropy?
Easy
- AA measure of the distribution of matter and/or energy in a system
- BThe total heat content of a system at constant pressure
- CThe energy available to do useful work
- DThe minimum energy required for a reaction to occur
2.For a given substance, entropy increases when its solid form melts into a liquid.
Easy
True or false?
3.Under the same conditions, in which order does entropy increase?
Easy
- Asolid < liquid < gas
- Bgas < liquid < solid
- Cliquid < solid < gas
- Dsolid < gas < liquid
4.Which of the following changes results in a decrease in entropy?
Easy
- AH2O(l) → H2O(g)
- BCl2(g) → Cl2(l)
- CCaCO3(s) → CaO(s) + CO2(g)
- DMelting ice to form liquid water
5.Which of the following changes are accompanied by an increase in entropy? (select all that apply)
Medium
- AH2O(l) → H2O(g)
- BCl2(g) → Cl2(l)
- CCaCO3(s) → CaO(s) + CO2(g)
- DN2(g) + 3H2(g) ⇌ 2NH3(g)
- EH2O(s) → H2O(l)
6.Which equation links Gibbs free energy, enthalpy and entropy?
Medium
- AΔG = ΔH − TΔS
- BΔG = ΔH + TΔS
- CΔG = ΔS − TΔH
- DΔG = TΔH − ΔS
7.A reaction has ΔH = +135 kJ mol−1 and ΔS = +344 J K−1 mol−1. What is the free energy change at 298 K?
Medium
- A+32.5 kJ mol−1
- B−32.5 kJ mol−1
- C+237 kJ mol−1
- D−102 kJ mol−1
8.For the reaction CO(g) + H2O(g) → CO2(g) + H2(g), ΔH = −41.4 kJ mol−1 and ΔS = −135 J K−1 mol−1. What is ΔG at 700 K?
Medium
- A+53.1 kJ mol−1
- B−53.1 kJ mol−1
- C+94.5 kJ mol−1
- D−94.5 kJ mol−1

Más preguntas

9.Which statements about entropy are correct? (select all that apply)
Medium
- AEntropy is a measure of the dispersal of energy and matter.
- BA system with higher entropy is always more energetically stable.
- CFor a given substance, entropy increases when its solid form melts.
- DThe entropy of a perfect crystal at 0 K is zero.
- EEntropy decreases when a gas is formed from a solid.
10.Match each change with the sign of its entropy change, ΔS.
Medium
- H2O(l) → H2O(g)
- Cl2(g) → Cl2(l)
- CaCO3(s) → CaO(s) + CO2(g)
- N2(g) + 3H2(g) → 2NH3(g)
- ΔS positive
- ΔS negative
11.Place the following states of a substance in order of increasing entropy under the same conditions.
Easy
- solid
- liquid
- gas
12.The reaction CO(g) + H2O(g) → CO2(g) + H2(g) has ΔH = −41.4 kJ mol−1 and ΔS = −135 J K−1 mol−1. What is ΔG for this reaction at 700 K?
Medium
- A+53.1 kJ mol−1
- B−53.1 kJ mol−1
- C+94.5 kJ mol−1
- D−94.5 kJ mol−1
13.For the reaction N2O4(g) → 2NO2(g), ΔS is positive. Which statement about the spontaneity of this reaction is correct?
Medium
- AIt is spontaneous at all temperatures.
- BIt is never spontaneous.
- CIt is spontaneous only at low temperatures.
- DIt is spontaneous only at high temperatures.
14.Which of the following statements about the Gibbs free energy equation are correct? (select all that apply)
Medium
- AΔG = ΔH − TΔS
- BA negative ΔG indicates a spontaneous reaction.
- CΔS must be converted to kJ K−1 mol−1 when using the equation.
- DA positive ΔG means the reaction is spontaneous.
- EThe units of ΔG are J mol−1.
15.For a reversible reaction at equilibrium, the Gibbs free energy is at its lowest value.
Easy
True or false?
16.For a reaction, ΔH is negative and ΔS is negative. Which statement is correct?
Medium
- AThe reaction is spontaneous at all temperatures.
- BThe reaction is never spontaneous.
- CThe reaction is spontaneous at low temperatures.
- DThe reaction is spontaneous at high temperatures.
17.For the reaction N₂(g) + 3H₂(g) ⇌ 2NH₃(g), the standard molar entropies are S⦵(N₂) = 192 J K⁻¹ mol⁻¹, S⦵(H₂) = 131 J K⁻¹ mol⁻¹ and S⦵(NH₃) = 192 J K⁻¹ mol⁻¹. What is the standard entropy change, ΔS⦵, for this reaction?
Easy
- A−201 J K⁻¹ mol⁻¹
- B+201 J K⁻¹ mol⁻¹
- C−585 J K⁻¹ mol⁻¹
- D−393 J K⁻¹ mol⁻¹
18.The standard molar entropies are S⦵(CaCO₃(s)) = 93 J K⁻¹ mol⁻¹, S⦵(CaO(s)) = 40 J K⁻¹ mol⁻¹ and S⦵(CO₂(g)) = 214 J K⁻¹ mol⁻¹. What is the standard entropy change, ΔS⦵, for CaCO₃(s) → CaO(s) + CO₂(g)?
Medium
- A+161 J K⁻¹ mol⁻¹
- B−161 J K⁻¹ mol⁻¹
- C+254 J K⁻¹ mol⁻¹
- D+347 J K⁻¹ mol⁻¹
19.For 2Ca(s) + O₂(g) → 2CaO(s), ΔH⦵ = −635.5 kJ mol⁻¹ and the standard molar entropies are S⦵(Ca(s)) = 41.00 J K⁻¹ mol⁻¹, S⦵(O₂(g)) = 205.0 J K⁻¹ mol⁻¹ and S⦵(CaO(s)) = 40.00 J K⁻¹ mol⁻¹. What is the standard Gibbs free energy change, ΔG⦵, at 298 K?
Medium
- A−573.8 kJ mol⁻¹
- B−697.2 kJ mol⁻¹
- C−635.5 kJ mol⁻¹
- D−761.0 kJ mol⁻¹
20.For the reaction 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(g), ΔH⦵ = +135 kJ mol⁻¹ and ΔS⦵ = +344 J K⁻¹ mol⁻¹. What is ΔG⦵ at 298 K?
Medium
- A+32.5 kJ mol⁻¹
- B−32.5 kJ mol⁻¹
- C+102.5 kJ mol⁻¹
- D+237.5 kJ mol⁻¹
21.For the combustion of ethanol, C₂H₅OH(l) + 3O₂(g) → 2CO₂(g) + 3H₂O(g), the standard free energies of formation are ΔG⦵f(C₂H₅OH(l)) = −175 kJ mol⁻¹, ΔG⦵f(O₂(g)) = 0 kJ mol⁻¹, ΔG⦵f(CO₂(g)) = −394 kJ mol⁻¹ and ΔG⦵f(H₂O(g)) = −229 kJ mol⁻¹. What is ΔG⦵ for the reaction?
Medium
- A−1300 kJ mol⁻¹
- B−1475 kJ mol⁻¹
- C−1125 kJ mol⁻¹
- D+1300 kJ mol⁻¹
22.The reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g) has ΔG⦵ = −142 kJ mol⁻¹. At 1455 K the concentrations are [SO₂] = 0.100 mol dm⁻³, [O₂] = 0.200 mol dm⁻³ and [SO₃] = 0.950 mol dm⁻³. What is ΔG at this temperature? (R = 8.31 J K⁻¹ mol⁻¹)
Medium
- A−68.1 kJ mol⁻¹
- B−142 kJ mol⁻¹
- C+73.9 kJ mol⁻¹
- D−215.9 kJ mol⁻¹
23.Ethanoic acid and ethanol react to form ethyl ethanoate and water. At 25 °C, ΔG⦵ = −4.38 kJ mol⁻¹. What is the value of the equilibrium constant, K, for this reaction? (R = 8.31 J K⁻¹ mol⁻¹)
Medium
- A5.87
- B1.77
- C0.170
- D34.4
24.For a reaction, ΔH⦵ = +1336 kJ mol⁻¹ and ΔS⦵ = +581 J K⁻¹ mol⁻¹. At what temperature does the reaction become spontaneous?
Hard
- A2299 K
- B2.30 K
- C1336 K
- D581 K
25.The dissolution of KCl in water is endothermic with ΔH⦵ = +16 kJ mol⁻¹. Use the entropy data to determine ΔS⦵ and decide whether the process is spontaneous at 298 K.
Medium
- AΔS⦵ = +77 J K⁻¹ mol⁻¹; spontaneous because ΔG⦵ = −6.9 kJ mol⁻¹
- BΔS⦵ = −77 J K⁻¹ mol⁻¹; not spontaneous because ΔG⦵ = +39 kJ mol⁻¹
- CΔS⦵ = +77 J K⁻¹ mol⁻¹; not spontaneous because ΔG⦵ = +6.9 kJ mol⁻¹
- DΔS⦵ = +143 J K⁻¹ mol⁻¹; spontaneous because ΔG⦵ = −26.6 kJ mol⁻¹
26.Which changes of state are accompanied by an increase in entropy? (select all that apply)
Medium
- AMelting ice to form liquid water
- BBoiling water to form steam
- CFreezing water to form ice
- DCondensing steam to form liquid water
- ESubliming iodine solid to form iodine vapour
27.Which statements about the Gibbs equation, ΔG = ΔH − TΔS, are correct? (select all that apply)
Medium
- AA reaction is spontaneous when ΔG is negative or zero.
- BFor an endothermic reaction with positive ΔS, the reaction becomes spontaneous at high temperature.
- CFor an exothermic reaction with negative ΔS, the reaction becomes spontaneous at high temperature.
- DAn exothermic reaction with positive ΔS is spontaneous at all temperatures.
- EIf ΔG is positive, the forward reaction is spontaneous.
28.For a reversible reaction at equilibrium, the Gibbs free energy is at its lowest value and ΔG = 0.
Easy
True or false?
29.An endothermic reaction with a negative entropy change can become spontaneous at high temperature.
Medium
True or false?
30.A student determines the standard entropy change for the decomposition CaCO₃(s) → CaO(s) + CO₂(g) using S⦵(CaCO₃(s)) = 93, S⦵(CaO(s)) = 40 and S⦵(CO₂(g)) = 214 J K⁻¹ mol⁻¹. Which expression gives the correct calculation?
Medium
- A(93) − (40 + 214)
- B(40 + 214) − (93)
- C(93 + 40) − (214)
- D(214) − (93 + 40)
31.Which of the following statements about the standard molar entropy, S⦵, are correct? (select all that apply)
Medium
- AS⦵ values refer to substances in their standard states at 298.15 K and 100 kPa.
- BS⦵ values are always positive for any substance above 0 K.
- CS⦵ values are listed in Section 13 of the IB Chemistry data booklet.
- DS⦵ values have units of kJ K⁻¹ mol⁻¹.
- ES⦵ values are zero for elements in their standard states.
32.When using the equation ΔS⦵ = ΣS⦵(products) − ΣS⦵(reactants), the coefficients from the balanced equation must be applied to each S⦵ value.
Easy
True or false?
33.Match each thermodynamic term with its correct description.
Medium
- ΔG < 0
- ΔG = 0
- ΔG > 0
- K > 1
- Reaction is spontaneous in the forward direction
- System is at equilibrium
- Reaction is not spontaneous in the forward direction
- Products are favoured at equilibrium
34.Place the steps for calculating ΔG from standard Gibbs free energies of formation in the correct order.
Medium
- Multiply each ΔG⦵f by its coefficient in the balanced equation.
- Sum the values for the products and for the reactants separately.
- Subtract the sum for the reactants from the sum for the products.
- State whether the reaction is spontaneous based on the sign of ΔG⦵.
35.Which statement about the spontaneity of this reaction is correct?
Hard
- AIt is spontaneous at all temperatures.
- BIt is never spontaneous.
- CIt becomes spontaneous above a certain temperature.
- DIt becomes spontaneous below a certain temperature.
36.Which quantity is a measure of the distribution of matter and/or energy in a system?
Easy
- AEnthalpy
- BEntropy
- CGibbs free energy
- DActivation energy
37.For a given substance, which change of state is accompanied by a decrease in entropy?
Easy
- AMelting
- BBoiling
- CCondensation
- DSublimation
38.Under the same conditions, which arrangement of a substance has the lowest entropy?
Medium
- AAqueous solution
- BSolid
- CLiquid
- DGas
39.Which statement about a spontaneous reaction at constant temperature and pressure is correct?
Medium
- AΔG is positive
- BΔG is zero or negative
- CΔH is always positive
- DΔS is always positive
40.The standard molar entropy of O₂(g) is 205 J K⁻¹ mol⁻¹. What does the superscript ⦵ in S⦵ indicate?
Medium
- AThe substance is in its standard state at 298.15 K and 100 kPa
- BThe value applies only at 0 K
- CThe value is measured in kJ K⁻¹ mol⁻¹
- DThe substance is a gas
41.Complete the equation used to calculate the standard entropy change of a reaction.
Easy
ΔS⦵(reaction) = ΣS⦵(____) − ΣS⦵(____)
42.Calculate the standard entropy change, in J K−1 mol−1, for the decomposition CaCO3(s) → CaO(s) + CO2(g) using S⦵(CaCO3(s)) = 93, S⦵(CaO(s)) = 40 and S⦵(CO2(g)) = 214 J K−1 mol−1.
Medium
43.Give the term for the point of a reversible reaction at which the Gibbs free energy is at its lowest.
Easy
44.For the reaction CaCO3(s) → CaO(s) + CO2(g), ΔH = +178 kJ mol−1 and ΔS = +161 J K−1 mol−1. Calculate the minimum temperature, in K, at which this decomposition becomes spontaneous.
Medium
45.The reduction of aluminium oxide with carbon: Al2O3(s) + 3C(s) → 2Al(s) + 3CO(g) has ΔH = +1336 kJ mol−1 and ΔS = +581 J K−1 mol−1. Calculate the temperature, in K, at which this reaction becomes spontaneous.
Hard
46.Give the equation that links Gibbs free energy change, enthalpy change and entropy change, using the symbol T for temperature.
Easy
47.For the decomposition CaCO₃(s) → CaO(s) + CO₂(g), ΔH⦵ = +178 kJ mol⁻¹ and ΔS⦵ = +161 J K⁻¹ mol⁻¹. Calculate the minimum temperature, in K, at which this decomposition becomes spontaneous.
Medium
48.For the steam reforming of methane, CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g), ΔH⦵ = +206 kJ mol⁻¹ and ΔS⦵ = +216 J K⁻¹ mol⁻¹. Calculate the temperature, in K, at which the reaction becomes spontaneous.
Medium
49.Complete the equation that links Gibbs free energy change, temperature and the equilibrium constant.
Medium
ΔG⦵ = −R T ____ K
50.Calculate the standard entropy change, ΔS⦵, in J K⁻¹ mol⁻¹, for the boiling of water: H₂O(l) → H₂O(g), given S⦵(H₂O(l)) = 70 J K⁻¹ mol⁻¹ and S⦵(H₂O(g)) = 189 J K⁻¹ mol⁻¹.
Medium
51.Complete the equation for the standard entropy change of a reaction.
Easy
ΔS⦵(reaction) = ΣS⦵(____) – ΣS⦵(____)
52.For the decomposition 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(g), calculate the standard entropy change, ΔS⦵, in J K⁻¹ mol⁻¹. Use S⦵(NaHCO₃(s)) = 102, S⦵(Na₂CO₃(s)) = 135, S⦵(CO₂(g)) = 214, S⦵(H₂O(g)) = 189 J K⁻¹ mol⁻¹.
Medium
53.Explain why the entropy change of the precipitation reaction AgNO3(aq) + NaCl(aq) → NaNO3(aq) + AgCl(s) is negative.
Hard
54.Explain, with reference to the arrangement of molecules, why the standard entropy is zero at 0 K.
Hard
55.Give the equation that links Gibbs free energy change, enthalpy change and entropy change.
Medium
56.Explain why the free energy change for dissolving sodium chloride in water is negative, despite the enthalpy change being positive (+4 kJ mol−1).
Hard
57.Explain why the entropy change of the precipitation reaction AgNO₃(aq) + NaCl(aq) → NaNO₃(aq) + AgCl(s) is negative.
Hard
58.Calculate the standard entropy change, in J K−1 mol−1, for the decomposition CaCO3(s) → CaO(s) + CO2(g) using S⦵(CaCO3(s)) = 93, S⦵(CaO(s)) = 40 and S⦵(CO2(g)) = 214 J K−1 mol−1.
Medium
- A161 J K−1 mol−1
- B177 J K−1 mol−1
- C193 J K−1 mol−1
- D145 J K−1 mol−1
59.For the reaction CaCO3(s) → CaO(s) + CO2(g), ΔH = +178 kJ mol−1 and ΔS = +161 J K−1 mol−1. Calculate the minimum temperature, in K, at which this decomposition becomes spontaneous.
Medium
- A1217 K
- B1328 K
- C1106 K
- D995 K
60.The reduction of aluminium oxide with carbon: Al2O3(s) + 3C(s) → 2Al(s) + 3CO(g) has ΔH = +1336 kJ mol−1 and ΔS = +581 J K−1 mol−1. Calculate the temperature, in K, at which this reaction becomes spontaneous.
Hard
- A2069 K
- B2529 K
- C2759 K
- D2299 K
61.For the decomposition CaCO₃(s) → CaO(s) + CO₂(g), ΔH⦵ = +178 kJ mol⁻¹ and ΔS⦵ = +161 J K⁻¹ mol⁻¹. Calculate the minimum temperature, in K, at which this decomposition becomes spontaneous.
Medium
- A995 K
- B1106 K
- C1217 K
- D1328 K
62.For the steam reforming of methane, CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g), ΔH⦵ = +206 kJ mol⁻¹ and ΔS⦵ = +216 J K⁻¹ mol⁻¹. Calculate the temperature, in K, at which the reaction becomes spontaneous.
Medium
- A1049 K
- B1144 K
- C954 K
- D859 K
63.Calculate the standard entropy change, ΔS⦵, in J K⁻¹ mol⁻¹, for the boiling of water: H₂O(l) → H₂O(g), given S⦵(H₂O(l)) = 70 J K⁻¹ mol⁻¹ and S⦵(H₂O(g)) = 189 J K⁻¹ mol⁻¹.
Medium
- A107 J K⁻¹ mol⁻¹
- B119 J K⁻¹ mol⁻¹
- C131 J K⁻¹ mol⁻¹
- D143 J K⁻¹ mol⁻¹
64.For the decomposition 2NaHCO₃(s) → Na₂CO₃(s) + CO₂(g) + H₂O(g), calculate the standard entropy change, ΔS⦵, in J K⁻¹ mol⁻¹. Use S⦵(NaHCO₃(s)) = 102, S⦵(Na₂CO₃(s)) = 135, S⦵(CO₂(g)) = 214, S⦵(H₂O(g)) = 189 J K⁻¹ mol⁻¹.
Medium
- A400 J K⁻¹ mol⁻¹
- B334 J K⁻¹ mol⁻¹
- C301 J K⁻¹ mol⁻¹
- D367 J K⁻¹ mol⁻¹

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