Acid-base equilibria (Topic 12)
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Not all hydrogen-containing substances are acidic, although all conventional acids contain hydrogen in their formulae.
is known as a hydrogen ion or a proton. It is formed when a hydrogen atom loses an electron.
The hydrogen in a molecule must be releasable as a proton in aqueous solution for a substance to be a Brønsted–Lowry acid.
Brønsted–Lowry acid–base reactions involve the transfer of protons.
Brønsted–Lowry acids are chemical substances that release ions in an aqueous solution.
dissociates in water releasing ions as follows:
The ions further combine with molecules forming hydronium ( ) ions:
The overall equation for the dissociation of in water (with state symbols) is:
A Brønsted–Lowry acid is defined as a chemical species which donates protons.
An example of this is the reaction between sulfuric acid and water.
A Brønsted–Lowry base is a chemical species which accepts protons.
An example of this is the reaction between a hydrogen ion and ammonia molecule, where a proton is accepted by the ammonia molecule:
Note that does NOT release hydroxide ions. It produces an excess of hydroxide ions by deprotonation of water in solution.
The chemical reaction of an acid with a base produces water. This is known as the neutralisation reaction.
The ions from the acid react with ions from the alkali, producing water (a neutral substance).
The final solution has a of at s.t.p.
Conjugate acid: The species formed when a base gains a proton.
Conjugate base: The species formed when an acid loses a proton.
A conjugate acid–base pair consists of two species that transform into each other by the gain or loss of a proton.
In this reaction:
- is the acid, and is its conjugate base.
- is the base, and is its conjugate acid.
Question walkthrough
Conjugate acid-base pairs
Identification of conjugate pairs in an acid-base reaction
A strong acid, , completely dissociates in aqueous solution to form and .
In strong acids:
Prominent examples of strong acids are , , and .
Both concentration (the total amount of the acid per unit volume) and strength (the degree of dissociation) of the acid impact the overall of a solution.
Strong acids will have a lower than weak acids when matched by concentration.
Weak acids only partially dissociate in water (usually less than 10%), releasing a limited number of their ions.
The partial dissociation can be identified by use of a double headed arrow (⇌) showing reversibility.
In weak acids:
Carboxylic acids, such as acetic acid, are weak acids.
The scale is a logarithmic scale used to measure the acidity or basicity of a solution. It is based on the concentration of hydrogen ions, , in the solution.
The of a solution is defined as the negative logarithm of the hydrogen ion concentration:
where:
- is the measure of the acidity or basicity of the solution.
- [] is the concentration of hydrogen ions in .
The hydrogen ion concentration can be calculated from the using the inverse logarithmic function:
The concentration of hydrogen ions [] in a solution of a strong monobasic acid, is equal to the initial concentration of the acid, since it fully dissociates.
A higher value indicates a stronger acid, which dissociates more in solution, producing more ions per mole of acid.
A lower is derived from a higher value, thus a lower indicates a stronger acid.
Approximations are required to calculate the of a weak acid.
The concentration of the undissociated acid remains almost the same at equilibrium because the dissociation is minimal.
The concentration of hydrogen ions is approximately equal to the concentration of the conjugate base formed. This is due to the negligible dissociation of compared to the amount of hydrogen ions produced by dissociation of the weak acid.
For a weak acid dissociates as follows:
The acid dissociation constant is:
Using the approximations:
Which rearranges to give:
Allowing pH to be calculated from :
To calculate the for a weak acid, given the of a solution containing a known mass of acid, follow the steps below:
Determine initial concentration, using the mass and molar mass of the weak acid () to find initial concentration:
Convert the pH to the hydrogen ion concentration []:
Write down an expression for for weak acids applying the appropriate approximations:
Input the values to calculate .
Question walkthrough
Ka calculations with weak bases
Calculating the concentration of a weak base using Ka approximations
Water undergoes slight dissociation into and ions.
The ionic product of water, , is a special equilibrium constant that applies to the self-ionisation of water.
It quantifies the extent to which water dissociates into hydrogen ions () and hydroxide ions () at a given temperature.
Water molecules self-ionise according to the following equilibrium reaction:
The equilibrium constant for this dissociation, the ionic product of water, , and is defined as:
At (), the value of is:
This value changes with temperature; as temperature increases, increases because the dissociation of water is an endothermic process.
Calculating the of a strong base requires the use of the ionic product of water.
At ()
- Determine the concentration of hydroxide ions from the concentration of the strong base.
- Rearrange the equation for , making the subject.
- Use the value obtained for [] to calculate pH.
Question walkthrough
Kw calculations
Using Kw to calculate the pH of a strong base
The is the negative logarithm of the acid dissociation constant :
The scale is used as values, like [], cover many orders of magnitude. This relationship provides a more convenient way to express acid strength on a logarithmic scale, which compresses the range of values.
The is defined as the negative logarithm of the ionic product of water ().
It is expressed mathematically as:
At 25 °C (298 K), the value of is approximately 1.0 × 1014.
When a strong acid is diluted the pH of the solution increases.
Strong acids are fully dissociated in solution and the following equation is used to calculate the pH:
There is no change to the moles of acid present during dilution therefore, to determine the new concentration of an acid after dilution, the following equation can be applied:
where:
- is initial concentration
- is initial volume
- is final concentration
- is final volume.
The table below shows the initial concentration of the strong acid and effect of the dilution factor on the .
Note that as concentration reduces by a factor of 10, increases by 1,
The logarithmic scale can be used to see the difference in and in strong acids.
As the concentration of strong acid increases by a factor of 10, the decreases by 1
As you dilute a strong acid, there are fewer hydrogen ions per unit volume; the decreases
Because water itself has a small amount of (about 1.0 × 10-7 mol dm-3), its is 7 under standard conditions. As the acid gets more and more dilute, its moves closer to that of pure water; the moves closer to 7 with dilution. However, always remains below 7 because the solution still contains hydrogen ions from the original acid.
When a weak acid is diluted the of the solution increases.
There is no change to the moles of acid present during dilution, therefore, to determine the new concentration of an acid after dilution, the following equation can be applied:
where:
- is initial concentration
- is initial volume
- is final concentration
- is final volume.
Weak acids are partially dissociated in solution according to their acid dissociation constant, , and the following equations are used to calculate the pH:
Step 1: Calculate []
Step 2: Calculate
The table below shows the initial concentration of a weak acid and effect of the dilution factor on the .
Note that as concentration reduces by a factor of 10, increases by 0.5,
When you dilute a weak acid:
The total concentration of acid decreases, but the equilibrium shifts to the right, so a higher proportion of the acid dissociates.
Therefore, you reduce ion concentration because of dilution, but the percentage of acid molecules that dissociate increases. The net result is that the concentration decreases, but not as fast as with a strong acid with the same dilution. As the [] decreases, the increases.
As the concentration of a weak acid increases by a factor of 10, the decreases by around 0.5.
A calibrated probe can be used to measure the of equimolar solutions of strong acids and weak acids at constant temperature.
The lower the , the stronger the acid.
Stronger acids release more per mole. The strong acid will show a lower ( ≈ 1) due to complete dissociation.
The weak acid will show a higher ( ≈ 2-5) due to partial dissociation.
A calibrated probe can be used to measure the of equimolar solutions of strong bases and weak bases at constant temperature.
The higher the , the stronger the base.
Strong bases fully dissociate in water. The high concentration of ions per mole results in a higher .
Weak bases partially dissociate in water. Fewer ions per mole are produced, resulting in a lower .
A salt is formed from a neutralisation reaction:
When dissolved in water, salts can form neutral, acidic, or basic solutions.
The of a salt depends on the strength of the acid and base it came from.
titration curves represent the change in as an acid is incrementally neutralised by a base, or vice versa.
Titration curves are crucial for understanding the neutralisation process and for selecting appropriate indicators to determine the endpoint of a titration.
Strong acid with strong base
Example: Hydrochloric acid () titrated with sodium hydroxide ().
Starts at a low (strong acid), rises slowly initially, then steeply at the point of neutralisation.
There are a range of values which can represent neutralisation centring at an equivalence point of 7.
Following neutralisation the quickly levels off at a high .
Weak base with a strong acid
Example: Ammonia () titrated with .
Starts at a lower than a strong base, initially falls gradually then remains steady for a period of acid addition. This is the buffer region; the solution contains a mixture of the weak base and its conjugate acid.
There is then a sharp fall near the point of neutralisation. There are a range of values which can represent neutralisation centering at an equivalence point of below .
The levels off at a low value quickly following neutralisation.
Weak acid with strong base
Example: Ethanoic acid () titrated with ().
Starts at a higher than a strong acid. rises gradually initially then remains steady for a period of base addition. This is the buffer region; the solution contains a mixture of the weak acid and its conjugate base.
There is a steep increase in as the neutralisation point approaches. There are a range of values which can represent neutralisation centering at an equivalence point above .
Following neutralisation, the quickly levels off at a high .
Weak base with weak acid
Example: Ammonia () titrated with ethanoic acid ().
Starts at a lower than a strong base and steadily reduced as the solution approaches neutralisation.
There is only a short range of values, centred around , which can be used to indicate neutralisation.
Following neutralisation the continues to fall gradually.
At the point of neutralisation there is a steep change in . The midpoint of this range is the equivalence point.
In order for an indicator to be effective at identifying the endpoint of a neutralisation reaction it must exhibit a colour change within the range of the steep change of .
The best indicators will exhibit a change at, or very close to, the equivalence point .
Suitable indicator for a strong acid/strong base titration
The range around the equivalence point is typically wide, from around .
Use indicators with a colour change at a within this range, such as phenolphthalein or methyl orange ().
Suitable indicator for a weak acid/strong base titration
The range around the equivalence point is typically narrower and at a higher equivalence point than a strong acid/strong base titration. It is around .
Use indicators with a colour change at a range above 7, such as phenolphthalein ().
Suitable indicator for a strong acid/weak base titration
The range around the equivalence point is typically narrower and at a lower equivalence point than a strong acid/strong base titration. It is around .
Use indicators with a colour change at a range below 7, such as methyl orange ().
There is no suitable indicator for titrations of weak acids with weak bases, as there is no sharp equivalence point. As a result, these pairings are not used in quantitative analysis.
A buffer solution is a system that minimises changes in when small amounts of an acid or a base are added.
Stability in is crucial for many chemical and biological processes
A buffer solution typically consists of a mixture of:
- a weak acid () and its salt containing conjugate base ()
- a weak base () and its salt containing conjugate acid ().
The weak acid and its conjugate base, or the weak base and its conjugate acid, work together to maintain the equilibrium constant and neutralise added acids or bases, thus maintaining the of the solution within a narrow range.
Le Chatelier’s principle explains how the buffer system shifts equilibrium to minimise changes.
In an acidic buffer solution containing a weak acid () and its conjugate base () the buffer system responds to the addition of acids and bases in the following way:
Addition of acid (): The excess conjugate base () reacts with the added to form more of the weak acid (), thus reducing the increase in concentration and minimising the pH change:
Addition of base (): The undissociated weak acid () reacts with the added to form water and more conjugate base (), thus reducing the increase in concentration and minimising the pH change:
In a basic buffer solution containing a weak base () and its conjugate acid , the buffer system responds to the addition of acids and bases in the following way:
Addition of acid (): The weak base () reacts with the added to form its conjugate acid (), reducing the increase in concentration and minimising the change:
Addition of Base (): The excess of conjugate acid () reacts with the added to form water and the weak base (), reducing the increase in concentration and minimising the change:
In an acidic buffer solution contain a ethanoic acid mixed with its salt, sodium ethanoate, the solution contains both the weak acid and its conjugate base.
Chemical equilibrium is maintained according to the value of the weak acid.
Buffer action and Le Chatelier’s principle:
Addition of acid (): The ethanoate ions () react with the added to form more ethanoic acid (). According to Le Chatelier’s principle, the system will shift to the left to counter the increase in , thus minimising the change.
Addition of base (): The ethanoic acid () reacts with the added to form water and ethanoate ions (). The system will shift to the right to counter the removal of by , again minimising the change.
When a weak acid is mixed with a strong base, the strong base neutralises part of the weak acid, forming its conjugate base and water.
If the weak acid is in excess, the remaining acid and the formed conjugate base create a buffer solution:
The of a buffer solution can be calculated by directly using the acid dissociation constant (), the concentrations of the weak acid, and the concentration of the conjugate base.
Substitute the concentrations into the equation:
Solve for []:
Calculate the pH:
Remember that, when a pair of solutions are mixed to form a buffer, new concentrations must be calculated based on the combined volume.
The calculation process when a buffer solution is formed through the reaction of an excess of weak acid with a strong base needs to factor in the reduction of the moles of following reaction with the base.
The amount of conjugate acid, , can be calculated directly from the amount of strong base used.
The reaction stoichiometry can be used to work out the remaining amount of weak acid, .
Both amounts should be converted to concentration using the combined volume of the solutions.
To calculate the concentration of solutions required to prepare a buffer solution of a given , the ratio of []:[] required to produce a certain [] must be obtained.
The example below uses information for a weak acid and conjugate base:
- Identify the and relevant
- From the pH calculate the required []
- Calculate the required ratio of []:[] by using the following expression for .
- Substitute in the values for [] and to get a value for the ratio
- Calculate appropriate values for [] and [] to align to the ratios.
In a weak acid–strong base titration, the buffer action can be seen in the initial part of the titration curve, where there is a gradual change in pH.
This region is known as the buffer region, which occurs before reaching the equivalence point.
In the buffer region, the weak acid is partially neutralised by the strong base, forming its conjugate base.
The presence of both and in significant amounts allows the solution to resist changes in pH, demonstrating the buffer effect.
can be determined using the half-equivalence point, which is halfway to the equivalence point, where half the weak acid has been neutralised.
At the half-equivalence point:
therefore
To determine from the titration curve of a weak acid
- Identify the half-equivalence point on the titration curve.
- This is the point where half the volume of base required to reach the equivalence point has been added.
- Measure the at this point.
- Calculate
At the half-equivalence point:
therefore
Question walkthrough
Buffer solutions
Calculating the pH of a buffer solution based on composition and Ka
The enthalpy change of neutralisation is the enthalpy change when one mole of water is formed from the reaction of an acid with a base under standard conditions.
Strong acids are fully dissociated in solution. Since all the hydrogen ions are available in solution, the neutralisation process does not involve any endothermic bond breaking.
This results in a higher enthalpy change of neutralisation than with weak acids.
For reactions involving strong acids and alkalis, the values are typically around -57 kJ mol-1. Recalling this is useful when evaluating if your answer is ‘about right’.
Weak acids are partially dissociated in solution.
During neutralisation, additional energy is required to further ionise the weak acid to produce more ions.
This additional ionisation absorbs energy, which reduces the overall heat released during the neutralisation reaction.
Consequently, the enthalpy change of neutralisation for weak acids is less negative (less exothermic) than for strong acids.
Maintaining the of blood within the narrow range of 7.35 to 7.45 is crucial for proper physiological function; in particular, the stability of enzymes.
The carbonic acid () – hydrogencarbonate () buffer system plays a key role in this process.
- Carbonic acid (): A weak acid that can donate protons () to the solution.
- Hydrogencarbonate (): The conjugate base of carbonic acid, capable of accepting protons.
The equilibrium between these components can be represented as:
When a small amount of acid is added to the blood:
The additional hydrogen ions () from the strong acid react with to form .
This minimises change: The formation of reduces the concentration of ions, mitigating the decrease.
When a small amount of base is added to the blood:
The hydroxide ions from the base react with to form and .
This minimises change: The conversion of to and water consumes ions, mitigating the increase.