1.8 Chemical Equilibria, Le Chatelier's Principle & Kc

A 0.680 mol sample of SO₃ is introduced into a 3.04 dm³ reaction container and allowed to reach equilibrium at temperature T. 32% of the SO₃ had decomposed. 

Calculate the value for K_c in this reaction, giving your answer to 2 significant figures. 

2 SO₃ (g)  2 SO₂ (g) + O₂ (g)     ΔH = + 196 kJ mol^-1

The size of the container for the reaction in part (a) is increased. State the effect if any on the equilibrium constant, K_c, and the position of equilibrium. Justify your answer.

The temperature of the reaction in part (a) is increased. State the effect, if any, on the equilibrium constant, K_c, and the position of equilibrium. Justify your answer.

If the value of the equilibrium constant, K_c, is 2.7 x 10^-2 at temperature T1 for the reaction:

2 SO₃ (g)  2 SO₂ (g) + O₂ (g)
          

Calculate the equilibrium constant, K_c, for the reaction:
4 SO₂ (g) + 2 O₂ (g)  4 SO₃ (g)
Give your answer to 2 decimal places.

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

The value of K_c for the reaction in part (a) at a different temperature, T1, is 2.98 mol dm^-3. Comment on the relationship between the concentration of the reactant E and products F and G with regards to K_c.

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.

For the reaction in part (c) write the expression for the equilibrium constant, K_c, and state the units.

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.

2 CH₃CH₂COOH + HOCH₂CH₂CH₂OH  C₉H₁₆O₄ + 2 H₂O

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

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

Give the units for K_c.

Calculate the concentration of water in the reaction mixture in part (a) 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.

The forward reaction in part (a) is slightly exothermic. At a different temperature, T1, the value for K_c increases to 22.78. 

State whether the new temperature, T1, is higher or lower than the original temperature. Justify your answer.

The graph in Figure 1 shows the effect on pressure and temperature on the equilibrium yield of gaseous molecules.

Figure 1

Use Figure 1 to fully explain whether the forward reaction is exothermic or endothermic

Use Figure 1 to fully explain whether the forward reaction will involve either an increase or decrease in the number of moles of a gas.

The graph to show the relationship between temperature and Kc for a different dynamic equilibrium to produce a gaseous product is shown in Figure 2.

Figure 2

Use the information in Figure 2 to establish whether the forward reaction is exothermic or endothermic. Justify your answer.

Gaseous products can be manufactured by the direct combination of reactants.

Explain why it is important for a chemist to know the value of K_c, at a given temperature, for such a reaction. 

Methanol is the first member of the alcohol homologous series. It is an essential industrial chemical, and can be manufactured according to the following reaction: 

CO₂ (g)  +  3H₂ (g)    CH₃OH (g)  +  H₂O (g)    ?H = -91 kJ mol^-1

The conditions used are called compromise conditions, used to find a balance between producing a high yield of product and having manageable and safe conditions.

Give the K_c expression for this equilibrium reaction and deduce the units. 

The reaction in part (a) often uses a copper-based catalyst, meaning that the usual temperature and pressure of the reaction can be reduced. 

State and explain the effect, if any, that using a catalyst for this reaction will have on the yield of methanol which is produced.

State and explain why lowering the temperature of the reaction will contribute to a higher yield of methanol being produced, but why lowering the pressure would contribute to a lower yield of product. 

Excluding any reasons regarding the yield of the product, give a reason why scientists in industry much prefer to use a lower pressure and temperature where possible. 

Some industrial processes involve reversible reactions. If done under the correct conditions, then these reactions will reach a dynamic equilibrium, producing equilibrium mixtures of reactants and products. The conditions of the reaction can be altered and controlled to maximise the product yield. 

Le Chatelier’s principle is a rule which is used to determine how to move the equilibrium position to the left or right, by altering specific conditions of the reaction. 

State Le Chatelier’s principle. 

An example of an equilibrium reaction can be seen between oxygen and nitrogen.

When heated to a high enough temperature, nitrogen will react with oxygen to form nitrogen monoxide, as shown below:

N₂ (g)  +  O₂ (g)      2NO (g)

When the temperature of the system is increased, the yield of NO increases. 

State whether the forward reaction in this system is exothermic or endothermic.

Explain your answer.

State and explain the effect, if any, on the yield of NO produced if the pressure was increased, but the temperature was kept the same. 

A chemist set up a different reaction, shown below:

W (aq)  +  2X (aq)     3Y (aq)  +  Z (aq)

They started with a flask containing 1.75 x 10^-2 mol of an aqueous solution W. They then added 0.050 mol of solution X to the flask, ensured a closed system, and allowed the reaction to reach equilibrium.

Once equilibrium was reached, the reaction mixture contained 0.012 mol of Z.

The overall volume of the reaction mixture was 105 cm³.

A reaction mixture was set up in a syringe between dinitrogen tetraoxide gas and nitrogen dioxide gas as shown in the equation below:

N₂O₄ (g)    2NO₂ (g)               ?H = +58 kJ mol^-1

The appearance of the gases is very different; dinitrogen tetraoxide is a colourless gas, whereas nitrogen dioxide is dark brown in colour.

Give the K_c expression for this reaction and deduce the units.

Explain why the reaction mixture turns darker in colour when it is heated.

The reaction which takes place in part (a) has a K_c value of 3.21. A student claims that increasing the temperature of this reaction will increase the value of K_c. 

Is the student correct? Justify your answer.

Using Le Chatelier’s principle, explain what would be seen initially if the plunger of the syringe was pressed and the gases within the syringe were compressed.

During an esterification reaction, methanol and ethanoic acid react together to form the ester, methyl ethanoate, and water as shown below:

CH₃OH (l)  +  CH₃COOH (l)    CH₃COOCH₃ (l)  +  H₂O (l)

A chemist sets up the reaction and allows it to reach dynamic equilibrium at a constant temperature. 

Once the reaction in part (a) is set up, the students leave it for 24 hours to make sure that it has reached equilibrium.

State how the students could check to make sure that the reaction mixture had reached equilibrium. 

When the equilibrium was reached, the equilibrium moles of each component in the mixture were as follows:

    - Ethanoic acid = 0.378

    - Methanol = must be calculated 

    - Methyl ethanoate = 0.716

    - Water = 1.08

K_c for the reaction was 7.21.  

Adding more ethanoic acid to the reaction mixture will increase the yield of the ester produced. 

Use Le Chatelier’s principle to explain the above statement.