17.1 The Equilibrium Law

A mixture of 1.32 moles of E, 1.49 moles of F and 0.752 moles of G were placed into a 5.0 dm³ container at temperature, T, and allowed to reach equilibrium. At equilibrium, the number of moles of E was 1.86.

Calculate the value of the equilibrium constant, K_c , to 3 significant figures. 

2 E (g) ⇌ 2 F (g) + G (g)        ΔH = -143 kJ mol^-1

Reactants G and H react together to form products J and K according to the equation

3G + H ⇌ 4J + K

A beaker contained 35 cm³ of 0.18 mol dm^-3 of an aqueous solution of G. 

8.41 x 10^-3 moles of H and 3.1 x 10^-3 moles of J were also added to the beaker. The equilibrium mixture contained 4.1 x 10^-3 moles of G. 

Calculate the number of moles of H, J and K at equilibrium.

Using sections 1 and 2 of the data booklet, calculate the equilibrium constant at 300 K for the oxidation of iron: 

2Fe(s) + O₂ (g) → Fe₂O₃ (s) 
ΔH^Θ = -824.2 kJ mol^{- 1} 
ΔS^Θ = -270.5 J mol^-1

Suggest what the value for K_c calculated in part (c) suggests about the equilibrium position for the oxidation of iron.

Diesters are compounds often used as synthetic lubricants for machinery such as compressors. The reaction below shows the formation of a diester from propanoic acid and propane-1,3-diol. 

2CH₃CH₂COOH + HOCH₂CH₂CH₂OH  ⇌  C₉H₁₆O₄ + 2H₂O

At equilibrium, the reaction mixture contained 3.25 moles of CH₃CH₂COOH, 1.15 moles of HOCH₂CH₂CH₂OH, and 1.18 moles of C₉H₁₆O₄.

The value for K_c at temperature, T, is 1.29.

Calculate the concentration of water in the reaction mixture at equilibrium. Give your answer to 3 significant figures. 

A student deduced that in order to calculate the value of K_c for the reaction in part (a) you must work out the concentrations using the overall volume. 

Is the student correct? Justify your answer.

Using sections 1 and 2 of the data booklet, determine the value for ΔG for the reverse reaction in part(a) given that temperature T= 30°C. Give your answer, in kJ, to 2 significant figures.

The reverse reaction in part (a) is slightly endothermic. At a different temperature, T₂, the value for ΔG decreases to -0.52 kJ mol^-1. 

State whether the new temperature, T₂, is higher or lower than the original temperature.
Justify your answer.

The following reaction is used to manufacture sulfuric acid. 

2SO₂ (g) + O₂ (g) ⇌ 2SO₃ (g) 

A mixture of 2.00 mol SO₂ (g) and 1.40 mol O₂ (g) is placed inside a 1.00 dm³ flask and allowed to reach equilibrium at a temperature, T₁. At equilibrium, 0.30 mol of SO₃ (g) was present. Determine the equilibrium concentration of SO₂ (g) and O₂ (g), and hence calculate the value of K_C, including units, at this temperature.

Using Sections 1 and 2 of the Data Booklet and your answer to (a), calculate the standard Gibbs free energy change, ΔG^Ө, in kJ mol^-1, for this reaction at a temperature of 700K.

Experimental data can be used to calculate the reaction quotient, Q, and the equilibrium constant, K_C. 
Distinguish between these two terms.

1.20 mol SO₂ (g), 1.60 mol O₂ (g) and 0.85 mol SO₃ (g) were mixed in a 1.00 dm³ container at temperature, T₂. 

2SO₂ (g) + O₂ (g) ⇌ 2SO₃ (g) 

Use your answer to (a) to deduce the direction of this reaction, showing your working.

Carbon monoxide and chlorine react to form phosgene, COCl₂, according to the following equation. 

CO (g) + Cl₂ (g) ⇌ COCl₂ (g)

Deduce the equilibrium constant expression, K_C, including units for this reaction.

0.50 mol CO (g) and 0.30 mol Cl₂ (g) were mixed in a 10.0 dm³ container. At equilibrium, 0.10 mol of COCl₂ (g) was present. Determine the equilibrium concentration of CO (g) and Cl₂ (g), and hence calculate the value of K_C.

Use Sections 1 and 2 of the Data Booklet with your answer to (b) to deduce, showing your working, the temperature of the reaction at which the standard Gibbs free energy change, ΔG^Ө, is -8.40 kJ.

At 873 K, the standard Gibbs free energy change, ΔG^Ө, was found to be +11.7 kJ.

Deduce, giving your reasons, whether the forward reaction is endothermic or exothermic. Use your answer to (c).

The following thermochemical data is for the oxidation of iron to produce iron(III) oxide at 300 K.

                   ΔH^Ө = -824.2 kJ mol^-1

2Fe (s) + O₂ (g) ⇌ Fe₂O₃ (s)

                        ΔS^Ө = -270.5 J K^-1 mol^-1

Explain why the enthalpy value given is the enthalpy of formation, ΔH^Ө_f, of iron(III) oxide.

Using Section 1 of the Data Booklet, calculate the standard Gibbs free energy change, ΔG^Ө, for the oxidation of iron to iron(III) oxide at 300 K.

Use you answer to (b) and Sections 1 and 2 of the Data Booklet to calculate a value, in terms of e, for K_C for this reaction at 300 K.

Use your answer to (c) to explain why the following oxidation of iron to iron(III) oxide at 300 K can be considered to be irreversible. 

2Fe (s) + O₂ (g) ⇌ Fe₂O₃ (s)

Ethanol and ethanoic acid react to form ethyl ethanoate according to the following equation. 

C₂H₅OH + CH₃COOH ⇌ CH₃COOC₂H₅ + H₂O 

0.47 mol of ethanol and 0.25 mol of ethanoic acid were mixed in a 5.0 dm³ container and left to reach equilibrium. At equilibrium, there was found to be 0.28 mol of ethanol. Calculate the number of moles of the remaining chemicals at equilibrium.

The reaction is performed in a 5.0 dm³ container. 

Deduce the equilibrium constant expression, K_C, for the reaction of ethanol and ethanoic acid and explain why the number of moles can be used directly in your expression.

Using your answer to part (b), calculate, showing your working, a value for the equilibrium constant expression, K_C, for the reaction of ethanol and ethanoic acid.

A second experiment reacting ethanol and ethanoic acid was performed. Analysis showed the equilibrium mixture to contain 0.16 mol ethanoic acid, 0.11 mol ethyl ethanoate and 0.12 mol water. Calculate the number of moles of ethanol in the equilibrium mixture.