DP IB Chemistry: HL

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IBChemistry: HLDPTopic Questions15. Energetics/Thermochemistry (HL only)15.2 Entropy & Spontaneity

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First teaching 2014

Last exams 2024

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15.2 Entropy & Spontaneity

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1a3 marks

State whether there is an increase or decrease in entropy for the following reactions.

i)
H2O (l) → H2O (g)
[1]
ii)
Cl2 (g) → Cl2 (l) 
[1]
iii)
CaCO3 (s) → CaO (s) + CO2 (g) 
[1]

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1b1 mark

State the equation to determine the entropy change, ΔS , of a reaction.

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1c
Sme Calculator1 mark

Use your answer to part b) and section 12 of the data booklet to determine the standard entropy change, in J K-1 mol-1 , for water boiling. 

H2O (l) → H2O (g) 

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1d
Sme Calculator1 mark

Explain why the entropy change of the following precipitation reaction is negative.

AgNO3 (aq) + NaCl (aq) → NaNO3 (aq) + AgCl (s) 

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1e1 mark

State the point of a reversible reaction in which the Gibbs free energy is at its lowest. 

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2a
Sme Calculator4 marks

Use section 12 of the data booklet and the information below to determine the following:

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

Compound  ΔHf  (kJ mol-1)
NaHCO3 (s)  -951
Na2CO3 (s) -1131

i)
The sum of the enthalpies of formation, ΔHf , of the products in kJ mol-1.
[1]

ii)
The sum of the enthalpies of formation, ΔHf , of the reactants in kJ mol-1.
[1]

iii)
Use your answers to part i) and ii) to determine the enthalpy change of reaction, ΔHr , for the decomposition of sodium hydrogen carbonate, NaHCO3 (s) in kJ mol-1.
[2]

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2b4 marks

Use section 12 in the data booklet and the information below to determine the following: 

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

Compound  S (J K-1 mol-1) 
NaHCO3 (s)  +102
Na2CO3 (s) +135

i)
The sum of the entropies, S , of the products in J K-1 mol-1
[1]

ii)
The sum of the entropies, S , of the reactants in J K-1 mol-1.

[1]

iii)
Use your answers to part i) and part ii) to determine the standard entropy change for the decomposition of sodium hydrogen carbonate, NaHCO3 (s), in J K-1 mol-1. 
[2]

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2c2 marks

Use your answers to part a) and b) as well as section 1 in the data booklet to determine the free energy change, in kJ mol-1 ,  for the decomposition of sodium hydrogen carbonate, NaHCO3 (s), at 500 K. 

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2d1 mark

Use your answer to part c) to state whether the decomposition of sodium hydrogen carbonate is spontaneous at 500K.

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3a1 mark

State the equation which can be used to determine the standard free energy for a reaction change, ΔG, using ΔG formation data.

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3b
Sme Calculator3 marks

Use section 12 of the data booklet and the equation below to determine the following. 

C3H8 (g) + 5O2 (g) → 3CO2 (g) + 4H2O (g) 

i)

The sum of the Gibbs free enthalpy of formation, ΔGf , of the products in kJ mol-1. 

[1]

ii)
The sum of the Gibbs free enthalpy of formation, ΔGf , of the reactants, kJ mol-1.
[1]

iii)
The Gibbs free energy change, ΔG , for the combustion of propane, kJ mol-1.
[1]

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3c
Sme Calculator2 marks

The reaction of carbon monoxide with water is as follows:

CO (g) + H2O (g) → CO2 (g) + H2 (g) 

The entropy change, ΔS , for this reaction is -135 J K-1 mol-1 and the enthalpy change, ΔH , for the reaction is -41.4 kJ mol-1. 

Determine the free energy change, ΔG , for the reaction at 700 K in kJ mol-1. 

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3d1 mark

Use your answer to part b) state whether the reaction of carbon monoxide and water is spontaneous at 700 K.

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4a2 marks

The image below shows how the entropy of compound Y varies with temperature

2-1

State the changes occurring at T1 and T2.

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4b
Sme Calculator4 marks

 Study the reaction of methane, CH4 , with water shown. 

CH4 (g) + H2O (g) rightwards harpoon over leftwards harpoonCO (g) + 3H2 (g) 

Use sections 12 and 13 of the data booklet to determine the following.

i)
The sum of the enthalpies of formation, ΔHf , of the products in kJ mol-1.
[1]

ii)
The sum of the enthalpies of formation, ΔHf , of the reactants in kJ mol-1.
[1]

iii)
Use your answers to part i) and ii) to determine the enthalpy change of reaction, ΔHr , for the reaction kJ mol-1.
[2]

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4c
Sme Calculator4 marks

The standard entropy of hydrogen gas is 131.0 J K-1 mol-1.

Use section 12 in the data booklet to determine the following for the reaction in part a). 

i)
The sum of the entropies, S , of the products in J K-1 mol-1
[1]

ii)
The sum of the entropies, S , of the reactants in J K-1 mol-1.

[1]

iii)
Use your answers to part i) and part ii) to determine the reaction given in part a) in J K-1 mol-1.

[2]

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4d
Sme Calculator3 marks

We can use the equation ΔG = ΔH - TΔS  to determine the temperature, in K, at which a reaction becomes feasible.

Use your answers to part b) and c) as well as section 1 of the data booklet to determine the following.

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


..........................................................................................................................................................................

The temperature at which the reaction of methane, CH4 , and water becomes spontaneous


..........................................................................................................................................................................

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1a
Sme Calculator2 marks

The equations for two separate reversible reactions are as follows:

 

Reaction A 2SO2 (g) + O2 (g) ⇌ 2SO3 (g)


Reaction B CO (g) + H2O (g) ⇌ CO2 (g) + H2 (g)

Use the information in the following table to determine the enthalpy change, ΔHr , for reaction A. 

  SO2 O2 SO3 H2
ΔHӨf  / kJ mol-1 -296.8 0 -395.7 0
SӨ / J K-1 mol-1 248.2 205.1 256.8 130.6

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1b
Sme Calculator2 marks
Using the information from the table in part a), calculate the standard entropy change, ΔS, of reaction A.

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1c2 marks

Use your answer to parts a) and b) to determine the temperature at which reaction A becomes feasible. 

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1d
Sme Calculator4 marks

By using the data from part a) and section 12 of the data booklet, deduce if reaction B is feasible at a low temperature.

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2a
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Magnesium carbonate decomposes at a relatively high temperature. 

  MgCO3 MgO

ΔHӨf / kJ mol-1

 -1095.8 -601.7

ΔSӨ / J mol-1

 65.7 26.9

 

i)
Write an equation for the decomposition and use section 12 of the data booklet and the information given to determine the enthalpy change for the decomposition of magnesium carbonate.
[3]

ii)
Use section 12 of the data booklet and the information given to determine the standard entropy change for the decomposition of magnesium carbonate.
[2]

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2b
Sme Calculator1 mark

Using your answer to part a) to determine if the decomposition of magnesium carbonate is feasible at 280 ℃. 

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2c
Sme Calculator3 marks

Using your answer to part b) to determine the temperature, in ℃, at which the decomposition of magnesium carbonate becomes feasible.

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3a3 marks

Used in the production of polymers, methanol is manufactured in large quantities.

i)
State the equation for the combustion of methanol. 
[1]
ii)
Comment on the entropy change of the reaction. 
[2]

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3b
Sme Calculator3 marks

Use section 12 of the data booklet to determine the enthalpy change, ΔHr , for the production of methanol from carbon monoxide and hydrogen. 

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3c
Sme Calculator3 marks
Use your answer to part b) and section 12 of the data booklet to calculate the free energy change, ΔG , for the formation of methanol from carbon monoxide and hydrogen at 300 K. 

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3d4 marks

A student states that if the temperature is lowered for the formation of methanol, the reaction will become non-spontaneous. Comment on the student’s statement.

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4a
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The Ostwald process to produce nitric acid involves the oxidation of ammonia. The equation is shown below:


4NH3 (g) + 5O2 (g) → 4NO (g) + 6H2O (g)    ΔHr = -905.2 kJ mol-1

  NH3 (g) O2 (g)
SΘ (J K-1 mol-1) 192.5 205

The free energy change, ΔGΘ , for the oxidation of ammonia at 298 K is -959 kJ mol-1.
Use section 12 of the data booklet, to calculate the entropy change for the oxidation of ammonia in J K-1 mol-1.

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4b
Sme Calculator3 marks

Use your answer to part a) and section 12 of the data booklet to determine the standard entropy of nitric oxide gas. 

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4c
Sme Calculator1 mark

A 1.00 mol sample of NOCl was placed in reactor and heated to 227°C until the system reached equilibrium. The value for the equilibrium constant at this temperature is Kc is 4.5 x 10-4 mol dm-3.  

2NOCl (g) rightwards harpoon over leftwards harpoon 2NO (g) + Cl2 (g)

Write an expression for Kc. 

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4d
Sme Calculator2 marks

Using section 1 and 2 in the data booklet determine the value for the free energy change, ΔGΘ , in kJ mol-1 for the reaction in part c).

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1a5 marks

This question looks at how the entropy change of water varies with temperature.

q1a_15-2_ib_hl_medium_sq

i)
The entropy of water is zero when the temperature is zero Kelvin. Explain why, with reference to the water molecules in your answer.

ii)
Explain why the entropy change, ΔS, is larger at temperature T2 than at temperature T1

iii)
On the figure, draw the boiling point (Tb) of water on the appropriate axis.
.

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1b2 marks

Standard entropies can be used to calculate the entropy change of a reaction, ΔS.
For example, for the formation of nitrogen monoxide from nitrogen and oxygen. 

NO (g) + O3 (g) → NO2 (g) + O2 (g)

Substance

Entropy value (J K-1 mol-1)

NO (g)

210.8

O2 (g)

205.2

NO2 (g)

240.0

O3 (g)

238.9

   

Use the data given to calculate the entropy change of the reaction between nitric oxide and ozone at 298K.

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1c6 marks

The contact process is a method used industrially to form sulfur trioxide, by reacting sulfur dioxide and oxygen together over a vanadium(V) oxide catalyst.
           

The equation for this reaction is shown below:

2SO2 (g) + O2 (g) ⇌ 2SO3 (g)

Substance

Formation enthalpy values (kJ mol-1)

SO2 (g)

-297

SO3 (g)

-395

i)
Calculate the standard enthalpy change of the contact process reaction using the data provided.

ii)
The standard entropy change of this reaction is –189 J K-1 mol-1. Use this value and your enthalpy value from part (i) calculate a value for the free energy change for this reaction at 298K.

iii)
Use your answer to part (ii) to explain whether the reaction is feasible at 298 K.

 

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1d2 marks

The value for the free energy change is an indication whether the forward or backwardreaction is favoured.

The curve that we would expect to see for the reaction between sulfur dioxide and oxygen is shown below.

 Explain why the curve for this reaction is shifted to the right hand side.

q1d_15-2_sq_ib_hl_medium 

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2a3 marks

The enthalpy of solution of sodium chloride is +4 kJ mol-1. Explain why the free energy change for dissolving sodium chloride in water is negative, despite the enthalpy change being a positive value.

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2b3 marks

Calcium carbonate thermally decomposes to form calcium oxide and carbon dioxide, as shown below:

CaCO3 (s) → CaO (s) + CO2 (g)

The enthalpy change of the above reaction is ΔHΘ = +178 kJ mol-1and the entropy change is ΔSΘ = +161 J K-1 mol-1 

Calculate the temperature at which the free-energy change, ΔGΘ, for this process is zero. 

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2c6 marks

Some ionic compounds such as potassium chloride, KCl, will dissolve in water at room temperature in an endothermic process. 

KCl (s) → K+ (aq) + Cl- (aq)                ΔH = +16 kJ mol-1

Substance

Entropy value J K-1 mol-1

KCl (s)

+83

K+ (aq)

+103

Cl- (aq)

+57

i)
Using the data provided, prove that this process is feasible at 298 K.

ii)
Use your knowledge of structure and bonding to explain why ΔHΘ is positive for this process.

 

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2d3 marks

Diamond and graphite are both allotropes of carbon.

The conversion of graphite into diamond is represented as follows

 Carbon (graphite) → Carbon (diamond)

Use this data below to calculate values for ΔH and ΔS for the reaction. Use these values to explain why this reaction is not feasible under standard pressure at any temperature.

 

C (graphite)

C (diamond)

ΔH (kJ mol-1)

0

+1.9

ΔS (J K-1 mol-1)

+5.7

+2.4

 

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3a3 marks

Ethanol is used in large quantities in the production of alcoholic beverages and as a fuel.

The combustion of ethanol is represented by the equation           

            CH3CH2OH (l) + 3O2 (g) → 2CO2 (g) + 3H2O (g) 

The standard entropy, SΘ, of O2 (g) is 205.2 J K-1 mol-1
Using the data given and Section 12 in the Data Booklet, determine the entropy change, ΔSΘ, for the combustion of  ethanol at 298K. 

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3b3 marks

Using the enthalpy of combustion for ethanol from Section 13 in the Data Booklet and the ΔSϴ determined in part (a), calculate the standard free energy for the combustion of ethanol.

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3c3 marks

Explain whether changing the temperature for the combustion of ethanol will alter the spontaneity of the reaction. 

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3d1 mark

Using Section 12 of the Data Booklet, explain the difference in the standard entropy values between methanol, CH3OH and ethanol, CH3CH2OH. 

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4a5 marks

Ammonia, NH3, is produced by the Haber process and is an important chemical in the manufacture of fertilisers and clearing products. 

Ammonia gas can react with oxygen to produce nitrogen monoxide and steam, and is the first step in the Ostwald process which produces nitric acid. 

i)
Write an equation for the reaction of ammonia with oxygen to produce nitrogen monoxide and steam. 

ii)
Using the given values determine the entropy for change for this reaction at 298 K.

Substance

Entropy values (J K-1 mol-1)

NH3 (g)

192.8

O2 (g)

205.2

H2O (g)

188.8

NO (g)

210.8

 

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4b1 mark

Explain why the standard entropy change for the reaction is positive.

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4c6 marks

The second step in the Ostwald process produces nitrogen dioxide as shown in the equation 

2NO (g) + O2 (g) → 2NO2 (g)             ΔHϴ = -112 kJ mol-1   

The standard entropy for NO2 (g) is 240.0 J K-1 mol-1

Determine the value for the free energy change for this reaction at 298 K using the information given

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4d2 marks

Explain whether changing the temperature for the production of nitrogen dioxide will alter the spontaneity of the reaction 

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5a4 marks

The boiling point of a liquid is the temperature at which its solid and liquid phases are in equilibrium as shown in the equation for the vaporisation of water. 

            H2O (l) → H2O (g) 

Use Section 12 of the Data Booklet to determine values for the enthalpy change, ΔHϴ, and entropy change, ΔSϴ, for the reaction at 298 K. 

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5b3 marks

Use your answer to part (a) to estimate a temperature, in K, that the reaction becomes feasible.

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5c1 mark

Explain how your answer to part (b) could be made more accurate. 

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5d2 marks

Explain why the reaction is spontaneous above the boiling point of water.

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