5.3 Equilibrium constant (Kp) for Homogeneous Systems (A Level only)

Methanol can be produced by a multi-step process using methane and water as the starting materials.

Step 1 is the production of synthesis gas, which is a mixture of carbon monoxide and hydrogen that is used to synthesise many chemicals including methanol.

Step 1: CH₄ (g) + H₂O (g) ⇋ CO (g) + 3H₂ (g)         ∆H = +206 kJ mol^-1

The general  industrial conditions for synthesis gas production are pressures of between 1000 - 2000 kPa, at temperatures of 1080 K and a nickel catalyst.

Figures 1 and 2 show the percentage conversion of methane into carbon monoxide and hydrogen under different conditions.

Use the information, to discuss the industrial conditions used to form synthesis gas as an intermediate step in the production of methanol.

Explain the effects of the general industrial conditions used for temperature and pressure, as stated in part (a), on the value of K_P.

Step 2 is the production of methanol from the synthesis gas mixture.

Step 2: CO (g) + 2H₂ (g) → CH₃OH (g)         ∆H = -90 kJ mol^-1

A 57.4 mol sample of carbon monoxide was reacted with 98.6 mol of hydrogen. When equilibrium was reached at a given temperature, the total pressure of the mixture was 7.80 MPa and contained 21.1 mol of methanol.

Calculate a value for K_p. Give your answer to the appropriate number of significant figures. Give units with your answer.

The total pressure of the following equilibrium mixture is 7.4 MPa.

2SO₃ (g) ⇋ 2SO₂ (g) + O₂ (g)

Calculate the value of K_P when 65% of sulfur trioxide dissociates at a given temperature.

In the reverse reaction, as shown, 3.5 moles of sulfur dioxide are mixed with 2.5 moles of oxygen.

2SO₂ (g) + O₂ (g) ⇋ 2SO₃ (g)

The total amount of the three gases at equilibrium is 4.8 moles.

Calculate the mole fraction of each gas in the equilibrium mixture.

The total pressure of the equilibrium mixture, shown in part (b), is 12.0 kPa.

Use your answers, from part (b), to calculate K_P for this reaction.

(If you did not get answers for (b), you may assume the following mole fractions: SO₂ (g) = 0.4, O₂ (g) = 0.3, SO₃ (g) = 0.3. These are not the correct answers)

Sulfur trioxide used to be made using the Chamber process involving a lead catalyst. This process had issues producing higher acid concentrations. The Contact Process using platinum or vanadium catalysts was developed to remove this issue.

State the effect of a platinum catalyst on the value of K_P.

Ammonia can react in different ways with oxygen.

Reaction 1: In the presence of a platinum catalyst, ammonia is oxidised to nitric oxide and oxygen is reduced.

Reaction 2: Ammonia is heated with oxygen in the absence of a catalyst producing nitrogen and one other gaseous product.

Write balanced chemical equations, with whole number coefficients, for these reactions.

Give an expression for the equilibrium constant, K_P, when Reaction 1, from part (a) occurs at 320 K.

Reaction 1 used 2.0 moles of ammonia and 6.0 moles of oxygen. They were reacted at 750 K and 500 kPa. At equilibrium, 1.0 moles of nitric oxide were formed.

Calculate a value for the equilibrium constant, K_P, including units, for this equilibrium.

Give your answer to an appropriate number of significant figures.

Reaction 2 used the same conditions of 2.00 moles of ammonia and 6.00 moles of oxygen at 750 K and 500 kPa. At equilibrium, 0.99 mole of nitrogen gas was formed.

At high temperatures,  gaseous phosphorus (V) chloride dissociates according to the following equation.

PCl₅ (g) ⇋ PCl₃ (g) + Cl₂ (g)

At 500K, the equilibrium amount of each gas is shown in Table 1.

Table 1

Calculate the total pressure of the reaction, if K_P = 597 kPa.

Give your answers to an appropriate number of significant figures.

Nitrogen dioxide decomposes according to the following equation.

2NO₂ (g) ⇋ 2NO (g) + O₂ (g)

At 700 K, the equilibrium amount of each gas is shown in Table 2.

Table 2

Calculate the total pressure of the reaction, if K_P = 6.8 x 10^-3 kPa.

Hydrogen iodide can undergo thermal decomposition according to the following equilibrium.

2HI (g) ⇋ H₂ (g) + I₂ (g)

The value of K_P for this reaction at 700K is 0.0185.

Calculate the total pressure when the partial pressure of hydrogen iodide, at equilibrium, is 133 kPa. Give your answer to the appropriate number of significant figures.

Dinitrogen tetroxide decomposes according to the following equilibrium.

N₂O₄ (g) ⇋ 2NO₂ (g)

The value of K_P for this reaction at 350 K is 395 kPa.

The equilibrium mixture contained 1.20 moles of nitrogen dioxide when an initial 2.00 moles of dinitrogen tetroxide were heated at 350 K.

Calculate the partial pressures of dinitrogen tetroxide and nitrogen dioxide.

Give your answer to the appropriate number of significant figures.

In a reaction vessel a mixture of three different gases are at equilibrium. The partial pressure of each gas is as follows:

      H₂                     = 12400 kPa

      CO                    = 7350 kPa

      CH₃OH             = 2620 kPa

The reaction taking place in the reaction vessel is shown below:

2H₂ (g) + CO (g)  ⇌ CH₃OH (g)

Table 1 below shows the partial pressures of an equilibrium mixture containing hydrogen, nitrogen and ammonia.

N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g)

Calculate the value of the equilibrium constant, K_p, in this reaction and state its units.

Table 1

In a reaction vessel a mixture of gases were heated until they reached equilibrium.

Cl₂ (g) +  PCl₃ (g)  ⇌ PCl₅ (g)         ΔH = +124 kJ mol^-1

State how you would alter the temperature and pressure to increase the yield of the products in the equilibrium reaction above.

The equation below shows hydrogen and nitrogen reacting together to form ammonia in equilibrium, as part of the Haber process. The enthalpy value for this reaction is -91 kJ mol^-1.

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Explain the effect, if any, of an increase in temperature on the value of K_p for this reaction if the volume remains constant and justify your answer.

Hydrogen is required for the synthesis of ammonia in the Haber process. The below equation shows how the hydrogen is produced by reacting methane and water vapour to form carbon monoxide and hydrogen.

CH₄(g) + H₂O(g) ⇌ CO(g) + 3H₂(g)          ΔH = +206 kJ mol^-1

State the effect, if any, of an increase in temperature on the equilibrium constant, K_p and on the yield of hydrogen produced.

Explain your answer.

In the Contact Process for the production of sulfuric acid, purified sulfur dioxide and oxygen react together to form sulfur trioxide. The partial pressure of SO₂ was 24 kPa and the total pressure in the vessel was 118 kPa.

2SO₂(g) + O₂(g) ⇌  2SO₃ (g)      ΔH = -190 kJ mol^-1

Calculate the value of K_p, including units.

An equilibrium mixture of the three gases below is prepared in a container of fixed volume.

CO(g)   +   Cl₂(g)   ⇌   COCl₂(g)          ΔH = −108 kJ mol^-1

The reaction was repeated at a different temperature and the value of K_p increased.

State whether the temperature had been increased or decreased for the second reaction. Explain your answer.

An equilibrium mixture of the three gases below is prepared in a container of fixed volume.

CO(g)   +   Cl₂(g)   ⇌   COCl₂(g)          ΔH = −108 kJ mol^-1

State and explain the effect, if any, on the value of K_p in each of the following situations:

Methanol can be synthesised along with water when carbon dioxide and hydrogen gas are reacted together in a sealed container. In an experiment below, 1.0 mol of carbon dioxide and 3.0 mol of hydrogen were reacted together. After the mixture had reached equilibrium, at a pressure of 550 kPa, the yield of methanol was 0.91 mol.

CO₂(g) + 3H₂(g)  ⇌ CH₃OH(g) + H₂O(g)

Calculate a value for K_p. Give your answer to the appropriate number of significant figures. Give units with your answer.

The equilibrium below shows carbon dioxide and hydrogen being produced from water vapour and carbon monoxide reacting together in a reaction vessel.

H₂O(g) + CO(g)  ⇌ H₂(g) + CO₂(g)         ΔH = - 41.2 kJ mol^-1

Methanol can be synthesised by reacting carbon monoxide and hydrogen at a temperature of 69℃ and a pressure of 1.75 MPa, as shown in the equation below.

CO(g) + 2H₂(g) ⇌ CH₃OH(g)

State what the units for K_p would be in kPa for this reaction.

Producing methanol by an industrial process involves several stages and optimum conditions in order to convert the starting reactants, methane and steam, into gaseous products. Figure 1 below, shows the percentage of methane conversion into gaseous products at equilibrium under different conditions.

Using the two graphs in Figure 1, deduce the optimum conditions needed for the conversion of methane and steam into gaseous products. Explain your ideas.

Figure 1

A lab technician added two gases to a flask and then sealed it, allowing equilibrium to be reached. The reaction which took place inside the flask is shown below:

3A(g)  +  2B(g)   ⇌ 2C(g)  +  D(g)        ΔH = –180 kJ mol^-1

In the gas phase equilibrium below, state the change, if any, that would occur to the value of K_p, if the pressure was increased inside the reaction vessel. Explain your answer.

A + B₂ + C ⇌ ABC + B        ΔH = −60 kJ mol^-1

During the synthesis of methanol, the final stage involves the reaction between carbon monoxide and hydrogen gas as shown below. During this stage, an equilibrium was established at 590 K.

CO (g) + 2H₂ (g) ⇌ CH₃OH (g)

The mixture contained a partial pressure of 370kPa of H₂ and 27.4 kPa of CH₃OH. The total pressure was 620 kPa.