9.3.C - Acid Equilibrium


In a chemical reaction, equilibrium is the state in which the concentrations of the reactants and products do not change with time. It occurs only in reversible reactions because at equilibrium, the forward reaction proceeds at the same rate as the reverse reaction. Because the forward and reverse reaction rates are equal and not zero, there are no net changes in the concentrations of the reactant and product. This process is called dynamic equilibrium.

Systems will only come to equilibrium when they are closed and it was the French chemist, Le Chatelier, who developed principles to predict how equilibrium systems respond to changes in concentrations of reactants and products and to the temperature and pressures of equilibrium systems. This meant that manipulating the concentrations of reactants and products, temperature and pressure of the system could change the relative amounts of reactant and product at equilibrium, there by increasing the yield. These predictions are made using what is now known as Le Chatelier's Principle.

The dissolution of carbon dioxide in water sets up an equilibrium system containing carbon dioxide, water and the weak acid, carbonic acid (H2CO3) and it is this system that is used to carbonate soft drinks as well as lowering the pH of unpolluted rainwater to around 5.6.

Strongs acid are those that ionise completely in water. Since weak acids s are only partially ionised in water, they can be considered equilibrium systems. The degree to which the equilibrium favours the products is a measure of the realtive strength of the acid.

In this unit you will learn:

  • About the features of equilibrium systems,
  • To predict how changes to temperature, pressure and concentration affect the position of equilibrium,
  • About features of the equilibrium system setup when carbon dioxide is dissolved in water,
  • How to calculate the volumes gases produced in chemical reactions where gaseous reactants and products are involved, and
  • To distinguish between strong, weak, concentrated and dilute acids.


Equilibrium

Many chemical reactions can be made to run in reverse when they are carried out in a closed system. A closed system is one where reactants and products are unable to escape. Reversible reactions can go in the forward direction and in the backward direction. Consider the following example:

A + B ⇔ 2C + D

Initially when 1 mole of A and 1 mole of B are mixed, the reaction proceeds quickly in the forward direction to produce 2 moles of C and 1 mole of D. As soon as C and D are produced, the reaction starts to proceed in the backward direction slowly at first but then speeds up as more C and D become available. In this way the reaction goes backwards and forwards until equilibrium is established. The point of equilibrium is when the rate of the forward reaction is equal to the rate of the backward reaction. Because both reactions are still occurring this is also known as a dynamic equilibrium.

The proportion of products to reactants determines the position of equilibrium. The position of equilibrium lays to the left if the conversion of A and B into C and D is small and to the right if the conversion is large. For a system to come to equilibrium, it must be a closed system. Open systems will cause reactions to go to completion.

Let's consider the reaction between nitrogen dioxide (NO2) and dinitrogen tetroxide (N2O4). Nitrogen dioxide is a brown gas while dinitrogen tetroxide is a colourless gas.




N2O4 (g) 2NO2 (g)


This reaction is reversible and for the system to come to equilibrium it must be a closed system. This is the most important consideration for an equilibrium system. It must be closed or it will never reach equilibrium. The graph shows how the concentrations of reactants and products change over time. Note that when the system has come to equilibrium, the graphs have flattened out indicating that the rate of the forward and reverse reactions are the same. This is a microscopic property of a system at equilibrium.



Two graphs showing how the concentration of reactants and products changes over time for the same
equilibrium system approached from the reactant side (a) and the product side (b).

The graphs above show how the concetrations of reactant and product change with time for the reaction above. Why two graphs? The first graph (a) shows the equilibrium being approached from the reactant side. The reaction began with a 0.04 M concentration of N2O4 and no NO2. In the second graph (b), the equilibrium is approached by filling the flask with NO2 and no N2O4. This brings us to another very important point about equilibrium. It does not matter from which side (reactants or products) the equilibrium is approached - the position of equilibrium will always be the same. If the reaction favours the products, it does not matter whether you start with reactants, products or a bit of both; the final position of equilibrium will always favour the products.

Graph showing how the rates of forward and reverse
reactions change over time for a system
approaching equilibrium.

The graph on the right shows how the rates of reaction change for the system as it approaches equilibrium. This graph shows the rates for graph (a) above where only reactants were placed in the flask to begin. The forward rate (tangent to the curve) decreases over time while the reverse rate increase. At equilibrium the forward and reverse reaction have the same rates. This is a microscopic property of a system at equilibrium.

For industrial chemists making gaseous products from gaseous reactants, equilibrium can pose a major problem. Since gases are involved, reactions must be performed in closed systems to stop reactants and products from escaping. This will produce an equilibrium situation and if the equilibrium favours the reactants rather than the products, this produces only a small amount of the desired product (a low yield). It was Le Chatelier who worked out how to manipulate equilibrium systems to increase the yield or change the position of equilibrium and it is to this that we turn next.

 

Le Chatelier's Principle

There are three factors that can be adjusted to manipulate the position of equilibrium. The temperature of the whole system can be increased or decreased, the pressure of a gaseous system can be increased or decreased and the relative concentration of reactants and products can be increased or decreased. If a reaction at equilibrium is subjected to a change in any of these factors, the position of equilibrium will shift to counteract the change. Think of it as a naughty child - ask a naughty child to sit down and it stands up! This is known as Le Chatelier's Principle.

If an equilibrium system is subjected to a change, the system will respond in such a way as to counteract that change.

Let's consider another equilibrium system involving the oxidation of sulfur dioxide (SO2) to sulfur trioxide
(SO3).



2SO2 + O2 2SO3 ΔH = -141 kJ mol-1

Concentration

At equilibrium (a) there are 0.68 mol of sulfur trioxide present. This
increases to 1.68 mol when more is added (b). When the new
equilibrium is established, the concentration decreases to 1.46 mol (c).

If a substance becomes more concentrated in a reaction, the equilibrium will shift to reduce its concentration. If more sulfur trioxide is added to the system above at equilibrium without changing the volume, the concentration of sulfur dioxide will increase. Le Chatlier's Principle tells us that the system will repond by decreasing the concentration of sulfur trioxide. This is achieved by increasing the rate of the reverse reaction until a new equilibrium is reached with a lower concentration of sulfur trioxde than the concentration it had when it was disturbed. The equilibrium will shift to the left (reactants) and the equilibrium concentrations of the reactants will increase as shown in the diagram.

Pressure

Increasing the pressure of the system will increase the amount of
products and decrease the amount of reactants .

If the pressure of a system is increased, it responds in such a way as to decrease the pressure. Pressure is a measure of the force per unit area exerted by molecules as they collide with the walls of a container. The unit of pressure is newtons per metre squared (Nm-2) or pascals (Pa) for short. An increase in pressure is usually achieved by decreasing the volume of the system and this increases the number of collisions with the walls of the container (and hence the pressure). According to Le Chatelier’s Principle the system will respond to decrease the pressure by ultimately reducing the number of molecules in the system and the number of collisions with the walls of the container.

If the pressure of the sulfur dioxide/trioxide system above is increased by decreasing the volume, the reaction will favour the products because there are less moles on the product side of the equation. The concentrations of the reactants increase and the concentration of the products decrease as shown on the right.

Temperature

To predict what effect this will have on a reaction we will need to know whether the reaction is endothermic or exothermic in the formward direction.  In the example above the enthalpy change for the reaction is a negative and this tells us that forward reaction is exothermic.  The backward reaction would, therefore, be endothermic.

An increase in temperature means that the system will adjust itself so as to reduce the temperature. It can only do this by favouring the endothermic direction which will absorb heat from the system, converting it into chemical potential energy. This will result in the rate of the reverse reaction increasing up so the equilibrium will shift to the left hand side. Correspondingly, decreasing the temperature of the system would favour the forward reaction.

 

Carbon Dioxide Equilibrium

Carbon dioxide is soluble to some extent in water but it also reacts with water to form carbonic acid. The equation for the solubility of carbon dioxide in water can be represented as follows:

CO2 (g) ⇔ CO2 (aq) + heat

The equation for the reaction of carbon dioxide with water can be represented as follows:

CO2 (g) + H2O (l) ⇔ 2H+ + CO32- (aq) + heat

In a can of soft drink, these two chemical processes are occurring at the same time. Firstly, the carbon dioxide dissolves in the water and then the dissolved carbon dioxide reacts with the water to form carbonic acid. Carbonic acid cannot exist alone as a pure solid. It only exists dissolved in water as hydrogen and hydrogen carbonate ions. If you tried to evaporate the water from a solution of carbonic acid it would just beccome carbon dioxide and water.

The data in the tables below shows how changes in pressure and temperature affect the amount of carbon dioxide in a closed equilibrium system.

Temperature (C) Conentration CO2
(mL/mL)
  Pressure (kPa) Mass CO2 in Soda Water
(g)
0 1.42   100 0.9
5 1.19   125 1.0
10 1.16   150 1.1
15 0.98   175 1.3
20 0.85   200 1.6
25 0.74   225 2.0
30 0.65   250 2.5
35 0.50   275 3.0
40 0.41   300 3.8
45 0.36   325 4.5


It can be seen that an increase in temperature reduces the concentration of carbon dioxide in the system. Because the forward reaction is exothermic, increasing the temperature will favour the endothermic (reverse) reaction and shift the equilibrium to the left. Macroscopically you would see more bubbles of carbon dioxide appear in the soda water. This is also why soft drinks go flat faster on hot days!

If the pressure is increased, more carbon dioxide dissolves in the soda water. There is one molecule of gas on the left hand side of the equation and none on the right. Increasing the pressure will favour the side with the least number of molecules, so the equilibrium shifts to the right.

You should also note that the equilibrium can be pushed towards the products by adding hydroxide ions. They react with the hydrogen ions and effectively reduce their concentration prompting the system to produce more.

 

Acid Strength

Ionisation of Acids in Water

The reaction of an acid with water (ionisation) can be written in two ways. According to the Bronsted-Lowry theory (9.2.E - Acid Behaviour), an acid will give its proton away to a base. The reaction of covalent hydrogen chloride with water can be written as:

HCl (aq) + H2O (l) ⇒ H3O+ (aq) + Cl- (aq)

HCl - this is an acid, because it has a proton available to be transferred.
H2O - this is a base, since it gets the proton that the acid lost.

This process results in the formation of a water molecule with a proton added to it. This ion is known as the hydronium ion.

For convenience, the ionisation of acids in water is often abbreviated to:

HCl (aq) ⇒ H+ (aq) + Cl- (aq)

It is assumed that the proton on the right hand side of this equation actually represents the hydronium ion. You must be able to recognise and write the ionisation of acids in water using both types of equation.

Acid Strength

The strength of an acid is defined by the degree to which the covalent acid molecules are ionised when dissolved in water.

Strong acids are those that ionise completely when dissolved in water. All of the covalent acid molecules lose their protons to produce hydronium ions and anions. Consider the following example of a strong acid.

HX (g) + H2O (l) ⇒ X- (aq) + H3O+ (aq)

Because HX is a strong acid, all of the covalent acid molecules of HX will be ionised. This means that if the concentration of the original acid was 0.1 mol L-1, the concentration of H3O+ ions and X- ions would also be 0.1 mol L-1. Because this reaction effectively goes to completion, we use an arrow in the equation rather than an equilibrium arrow.

Weak acids are those that are only partially ionised in water. Not all of the covalent acid molecules react to form hydronium ions and anions. Consider the ionisation of a weak acid, HZ.

HX (g) + H2O (l) ⇔ X- (aq) + H3O+ (aq)

If the original concentration of the acid was 0.1 mol L-1, the concentration of H3O+ ions in the solution would be less than 0.1 mol L-1. If we determined the concentration of hydronium ions by measuring the pH of the solution, we could work out the degree to which the acid was ionised. If a solution of HZ had a pH of 2.5, the concentration of hydronium ions would be 0.003 mol L-1 which means that only 3% of the acid molecules have been ionised. This makes HZ a very weak acid.

Aqueous solutions of weak acids are essentially equilibrium systems. The stronger the acid, the more the equilibrium lies toward the products. Strong acids have high values for the the equilibrium constant which is called the acid dissociation constant, Ka, when applied to acids.

Click here to see an interactive showing the difference between strong and weak acids.

The table below compares the properties of some monoprotic acids of varying strengths. You should note that for monoprotic acids of the same concentration, the higher the pH the weaker the acid. This is beacuse the hydronium ion concentration is decreasing with increasing pH.

Acid Hydrochloric acid
(HCl)
Hydrofluoric acid
(HF)
Ethanoic acid
(CH3COOH)
Ionisation reaction HCl (g) + H2O (l) ⇒
Cl- (aq) + H3O+ (aq)
HF (g) + H2O (l) ⇔
F- (aq) + H3O+ (aq)
CH3COOH (g) + H2O (l) ⇔
Cl- (aq) + H3O+ (aq)
Initial concentration
of acid
0.1 mol L-1 0.1 mol L-1 0.1 mol L-1
Concentration of hydronium ions 0.1 mol L-1 0.008 mol L-1 0.0013 mol L-1
Concentration of anions 0.1 mol L-1 0.008 mol L-1 0.0013 mol L-1
pH 1.0 2.1 2.9
Percentage ionisation 100% 8% 1.3%

Acid dissociation
constant, Ka

1.3 x 106 6.8 x 10-4 1.8 x 10-5

 

Polyprotism

Some acids have more than one hydrogen ion or proton to give away and can therefore, be ionised more than once. We have seen above that acids with only one proton to donate are called monoprotic acids. Acids with two protons are called diprotic acids and those with three protons are called triprotic acids.

When considering acid strength, we must also consider the protism of the acid and the extent to which succesive protons are ionised.

Sulfuric acid is a diprotic acid that ionises in two steps. The first ionisation of the sulfuric acid molecule can be represented as follows:

H2SO4 (l) + H2O (l) ⇒ HSO4- (aq) + H3O+ (aq)

This first ionisation is complete which makes sulfuric acid a strong acid.

We can represent the second ionisation where the hydrogen sulfate ion (HSO4-) loses its proton as follows:

HSO4- (aq) + H2O (l) ⇔ SO42- (aq) + H3O+ (aq)

Only about 38% of the hydrogen sulfate ions are ionised in a 0.1 mol L-1 solution so this makes the hydrogen sulfate ion a weak acid. It is important to distinguish between acids and the ions produced in successive ionisations. Correctly stated, sulfuric acid is a strong acid while the hydrogen sulfate ion is a weak acid.

Citric acid is a triprotic acid that has three protons available for ionisation. Citric acid is the acid found in citrus fruits and goes by the systematic name, 2-hydroxypropane-1,2,3-tricarboxylic acid. The equations for first and successive ionisations would be:

C4H6O(COOH)3 (s) + H2O ⇔ C4H6O(COOH)2COO- (aq) + H3O+ (aq)

C4H6O(COOH)2COO- (aq) + H2O ⇔ C4H6O(COOH)(COO)22- (aq) + H3O+ (aq)

C4H6O(COOH)(COO)22- (aq) + H2O ⇔ C4H6O(COO)33- (aq) + H3O+ (aq)

The structure of the weak polyprotic acid,
citric acid, known as 2-hydroxypropane-
1,2,3-tricarboxylic acid.

The degree of ionisation is dependant on the concentration of the acid, but if we started with a 0.1 mol L-1 solution of citric acid, the first ionisation would see about 11% of citric acid molecules being ionised. The second ionisation occurs to only a miniscule 0.0001% and the third to even less than that. The pH of a 0.1 mol L-1 solution of citric acid would be around 2.1 due to the hydronium ion concentration coming from the first and the other two successive ionisations of the acid. Successive ionisations in polyprotic acids always occur to lesser extents than the previous and citric acid is no exception. You should note though in this example that the first ionisation contributes significantly more to the hydrogen ion concentration than the second and third. From this analysis we could describe citric acid as a weak triprotic acid with each ionisation producing a successively weaker acid.

The table below shows a number of common acids classified according to decreasing strength. The percentage ionisation is shown for 0.1 mol L-1concentrations.

Acid Chemical Formula Classification Percentage Ionisation (%)
Hydrochloric acid HCl Strong 100
Sulfuric acid H2SO4 Strong 100
Nitric acid HNO3 Strong 100
Hydrogen sulfate ion HSO4- Weak 38
Phosphoric acid H3PO4 Weak 32
Citric acid C4H6O(COOH)3 Weak 11
Hydrofluoric acid HF Weak 8
Ethanoic acid CH3COOH Weak 2
Dihydrogen phosphate ion H2PO4- Weak 0.3
Carbonic acid H2CO3 Weak 0.1
Hydrogen carbonate ion HCO3- Weak 0.003
Monohydrogen phosphate ion HPO42- Weak 0.0002