Entropy & Spontaneity (DP IB Chemistry: HL): Exam Questions

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

Explain, with reference to the arrangement of molecules, why the standard entropy is zero at 0 K.

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

Identify the change of state occurring at T₂ and label the boiling point (T_b) on the temperature axis of the graph.

The dissolution and decomposition of ionic compounds are governed by thermodynamic principles.

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.

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 ΔH^Θ = +178 kJ mol^-1and the entropy change is ΔS^Θ = +161 J K^-1 mol^-1 

Calculate the minimum temperature, in K, at which this decomposition becomes spontaneous.

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

i) Using the standard entropy data in the table, show that the dissolution of KCl is spontaneous at 298 K.

[4]

ii) Explain, in terms of lattice and hydration enthalpies, why the enthalpy of solution for KCl is positive.

[2]

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, S^Θ, of O₂ (g) is 205 J K^-1 mol^-1.

Using the data given and section 13 of the data booklet, determine the entropy change, ΔS^Θ, for the combustion of ethanol at 298K. 

Using the enthalpy of combustion for ethanol from section 14 of the data booklet and the ΔS^ϴ determined in part (a), calculate the standard free energy for the combustion of ethanol.

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

Using section 13 of the data booklet, explain the difference in the standard entropy values between methanol, CH₃OH and ethanol, CH₃CH₂OH. 

The Ostwald process for producing nitric acid begins with the catalytic oxidation of ammonia.

The first step of the process involves the reaction of ammonia with oxygen to produce nitrogen monoxide and steam.

i) Write the balanced chemical equation for this reaction.

[2]

ii) Using the data in the table, calculate the standard entropy change, ΔS^ᶿ, for this reaction at 298 K.

[3]

Explain why the standard entropy change for the reaction in (a) is positive.

The second step of the Ostwald process is the oxidation of nitrogen monoxide to nitrogen dioxide:

2NO (g) + O₂ (g) → 2NO₂ (g)             ΔH^ϴ = -112 kJ mol^-1   

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

Calculate the standard Gibbs free energy change, ΔG^ᶿ, for this reaction at 298 K.

Explain how a change in temperature will affect the spontaneity of the reaction in part (c).

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

            H₂O (l) → H₂O (g) 

Using section 13 of the data booklet, determine values for the enthalpy change, ΔH^ϴ, and entropy change, ΔS^ϴ, for the reaction at 298 K. 

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

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

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

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, ΔH_r, for reaction A. 

Using the information from the table in part a), calculate the standard entropy change, ΔS, of reaction A.

Determine the maximum temperature at which reaction A is spontaneous.

By using the data from part a) and section 13 of the data booklet, deduce if reaction B is feasible at a low temperature.

Magnesium carbonate decomposes upon heating to form magnesium oxide and carbon dioxide.

i) Write the balanced chemical equation for this decomposition.

[1]

ii) Using the data provided and values from section 13 of the data booklet, calculate the standard enthalpy change (ΔH^ᶿ_r) and standard entropy change (ΔS^ᶿ) for this reaction.

[4]

Calculate the Gibbs free energy change, ΔG^ᶿ, at 280 °C and state whether the reaction is spontaneous at this temperature.

Calculate the minimum temperature, in °C, at which the decomposition becomes spontaneous.

Methanol is manufactured on a large scale via the reaction of carbon monoxide and hydrogen.

CO (g) + 2H₂ (g) ⇌ CH₃OH (l)

Using data from section 13 of the data booklet, calculate the standard enthalpy change, ΔHᵣᶿ, for this reaction.

Using data from section 13 of the data booklet, calculate the standard entropy change, ΔSᶿ, for this reaction.

Calculate the standard Gibbs free energy change, ΔGᶿ, for the reaction at 298 K.

A student claims, "Since this reaction becomes non-spontaneous at high temperatures, it must be spontaneous at low temperatures."

Comment on the student's statement, explaining why the reaction has a limited temperature range for spontaneity.

The first step in the Ostwald process is the catalytic oxidation of ammonia.

4NH₃ (g) + 5O₂ (g) → 4NO (g) + 6H₂O (g)

At 298 K, the standard enthalpy change, ΔHᶿ_r , for this reaction is -905.2 kJ mol^-1 and the standard Gibbs free energy change, ΔGᶿ, is -959 kJ mol^-1.

Calculate the standard entropy change, ΔS^ᶿ, in J K^-1 mol^-1, for this reaction at 298 K.

The standard entropy, S^ᶿ, for some species in the reaction are given below.

Using your answer to part a) and section 13 of the data booklet, determine the standard entropy of nitric oxide gas. 

Nitrosyl chloride, NOCl, decomposes into nitric oxide and chlorine at high temperatures.

2NOCl (g)  2NO (g) + Cl₂ (g)

A 1.00 mol sample of NOCl was heated to 227°C in a sealed reactor. At equilibrium, the value of the equilibrium constant, K_c, is 4.5 x 10^-4 mol dm^-3.

Write an expression for the equilibrium constant,K_c. 

Using section 1 and 2 in the data booklet determine the value for the free energy change, ΔG^Θ , in kJ mol^-1 for this reaction at 227 °C.