5.2 Hess's Law

The compound diborane, B₂H₆, is used as a rocket fuel. The equation for the combustion of diborane is shown below.

B₂H₆ (g) + 3O₂ (g) → B₂O₃ (s) + 3H₂O (l)

Calculate the standard enthalpy change of this reaction using the following data

I. 2B (s) + 3H₂ (g) → B₂H₆ (g)          ΔH = 36 kJ mol^-1
II. H₂ (g) + ½O₂ (g) → H₂O (l)          ΔH = -286 kJ mol^-1

III. 2B (s) + 1½O₂ (g) → B₂O₃ (s)       ΔH = -1274 kJ mol^-1

Ethyne, C₂H₂, is a useful gas as it gives a high temperature flame when burnt with oxygen. State the equation for the combustion of ethyne gas.

Use your answer to part b) to construct a Hess's Law cycle for the combustion of ethyne gas.

Use sections 12 and 13 in the data booklet to determine the enthalpy of formation, ΔH_f, of ethyne gas. 

Coal gasification converts coal into a combustible mixture of carbon monoxide and hydrogen known as coal gas, in a gasifier. 

H₂O (l) + C (s) → CO (g) + H₂ (g) 

Using the following equations, calculate the enthalpy change of reaction, ΔH_r, in kJ for cola gasification. 

I. 2C (s) + O₂ (g) → 2CO (g)            ΔH = -222 kJ

II. 2H₂ (g) + O₂ (g) → 2H₂O (g)        ΔH = -484 kJ

III. H₂O (l) → H₂O (g)                       ΔH = +44 kJ

This coal gas can be used as a fuel as the following equation shows.

CO (g) + H₂ (g) + O₂ (g) → CO₂ (g) + H₂O (g) 

Calculation the enthalpy change of reaction, ΔH_r, in kJ for this combustion reaction from the following equations.

I. 2C (s) + O₂ (g) → 2CO (g)       ΔH = -222 kJ

II. C (s) + O₂ (g) → CO₂ (g)         ΔH = -394 kJ

III. 2H₂ (g) + O₂ (g) → 2H₂O (g) ΔH = -484 kJ

Blending amounts of alternative fuel with conventional fuel is one way to replace petroleum. A fuel blend of 51% to 83% ethanol and the remaining being gasoline is known as E85.

If the fuel blend is vaporised before combustion, predict whether the amount of energy released would be greater, less or the same. Explain your answer.

Use sections 6 and 13 of the Data booklet to calculate the following.

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Strontium salts have a number of applications such as fireworks, flares, glow in the dark paint and toothpaste for sensitive teeth. The strontium required for these salts can be extracted from the ore strontia, SrO, by displacement with powdered aluminium in a vacuum.

The standard enthalpy change for this extraction of strontium is 99.3 kJ mol^-1 and the standard enthalpy of formation of aluminium oxide is -1676.7 kJ mol^-1

Use this information to calculate the standard enthalpy of formation, ΔH_f, in kJ mol^-1 of strontia.

Manganese is too brittle for use as a pure metal, so it is often alloyed with other metals. Manganese is used in steel to increase the strength and resistance to wear. Manganese steel (13% Mn) is extremely strong and used for railway tracks, safes and prison bars. Alloys of 1.5% manganese with aluminium are used to make drinks cans due to the improved corrosion resistance of the alloy.

Manganese is extracted from different ores by reduction with carbon monoxide.

Mn₂O₃ (s) + 3CO (g) → 2Mn (s) + 3CO₂ (g)

The enthalpy of formation, ΔH_f, of Mn₂O₃ (s) is −971 kJ mol^-1. Use this information and section 12 of the data booklet to calculate the enthalpy change of reaction, ΔH_r, in kJ mol^-1. 

The reaction in part c) reaches equilibrium at high temperatures.

Use your answer to part c) to explain how temperature can be altered to increase the yield of the reaction and explain the effect that this would have on the rate of reaction.

Define the term standard enthalpy of combustion, ΔH^ϴ_c.

Write an equation for the complete combustion of propanol, CH₃CH₂CH₂OH (l).

Construct a Hess’s Law cycle for the complete combustion of propanol.

Table 1

Use the data given in Table 1 in part (d) to calculate the enthalpy change of the reaction, ΔH^ϴ_r.

Urea can be used as a fertiliser and is manufactured by the reaction of ammonia and carbon dioxide via the following equation. 

2NH₃ (g) + CO₂ (g) → NH₂CONH₂ (s) + H₂O (l)

Using the data in Table 1 calculate the enthalpy change for the formation of urea, ΔH_r^ө.

Table 1

Ammonia reacts with oxygen to produce steam and nitrogen(II) oxide. Draw a Hess’s Law cycle which could be used to calculate the enthalpy change of the reaction using formation data.

Use Hess’s Law and the information below to calculate the enthalpy change, ΔH^ϴ_r, for the conversion of one mole of ethene and one mole of hydrogen to one mole of ethane. 

C₂H₄ (g) + 3O₂ (g) → 2CO₂ (g) + 2H₂O (l)                  ΔH^ϴ_r = -1411 kJ mol^-1

C₂H₆ (g) + 3.5O₂ (g) → 2CO₂ (g) + 3H₂O (l)               ΔH^ϴ_r = -1560 kJ mol^-1

H₂ (g) + 0.5O₂ (g) → H₂O (l)                                       ΔH^ϴ_r = –286 kJ mol^-1

Use Hess’s Law and the information below to calculate the enthalpy change for the conversion of one mole of solid carbon into carbon monoxide.

C (s) + O₂ (g) → CO₂  (g)                    ΔH^ϴ_r = - 393.5 kJ mol^-1

CO (g) + ½O₂ (g)  → CO₂  (g)            ΔH^ϴ_r = - 283.5 kJ mol^-1

Define the term standard enthalpy of reaction, ΔH^ϴ_r.

Use Hess’s Law and the information below to calculate the enthalpy change, ΔH^ϴ_r, for the conversion of methane and ammonia to form hydrogen cyanide and hydrogen.

N₂ (g) + 3H₂ (g) → 2NH₃ (g)                           ΔH^ϴ_r = -91.8 kJ

C (s) + 2H₂ (g) → CH₄ (g)                                        ΔH^ϴ_r = -74.9 kJ

H₂ (g) + 2C (g) + N₂ (g) → 2HCN (g)              ΔH^ϴ_r = 270.3 kJ

Using your answer to part (b) draw a reaction profile diagram for the reaction outlined.

Draw the Lewis structure for hydrogen cyanide, HCN.

Butane, C₄H₁₀,  is typically used as fuel for cigarette lighters and portable stoves, a propellant in aerosols, a heating fuel, a refrigerant, and in the manufacture of a wide range of products.

Write an equation for the complete combustion of butane.

Determine the enthalpy of formation of butane, C₄H₁₀ , using the enthalpy of combustion data below.

C (s) + O₂ (g) → CO₂ (g)                                            ΔH^ϴ_f = -394 kJ           

H₂ (g) + 0.5O₂ (g) → H₂O (l)                                       ΔH^ϴ_f = -286 kJ

C₄H₁₀ (g) + 6.5O₂ (g) → 4CO₂ (g) + 5H₂O (l)             ΔH^ϴ_f = -2878 kJ

Butane can be formed from the hydrogenation of butene. Using the data in Table 1, determine a value for the enthalpy of formation.

Table 1

The data book value for the hydrogenation of butene is -126 kJ mol-1. Suggest why your answer to part (c) may be different to this value.