Weak Acids Weak acids are only partially ionized in aqueous solution. There is a mixture of ions and un-ionized acid in solution. Therefore, weak acids are in equilibrium: HA(aq) + H 2 O(l) H 3 O + (aq) + A – (aq) Or: HA(aq) H + (aq) + A – (aq) We can write an equilibrium constant expression for this dissociation: Ka = or Ka =
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Weak Acids
Weak acids are only partially ionized in aqueous solution.
There is a mixture of ions and un-ionized acid in solution.
Therefore, weak acids are in equilibrium:
HA(aq) + H2O(l) H3O+(aq) + A–(aq) Or:
HA(aq) H+(aq) + A–(aq)
We can write an equilibrium constant expression for this dissociation:
Ka =
or
Ka =
Ka is called the acid-dissociation constant.
Note that the subscript a indicates that this is the equilibrium constant for the dissociation of an acid.
Note that [H2O] is omitted from the Ka expression. (H2O is a pure liquid.)
The larger the Ka, the stronger the acid.
Ka is larger since there are more ions present at equilibrium relative to un-ionized molecules.
If Ka >> 1, then the acid is completely ionized, and the acid is a strong acid.
Weak Bases
Weak bases remove protons from substances.
There is an equilibrium between the base and the resulting ions:
Weak base + H2O(l) conjugate acid + OH–(aq) Example:
NH3(aq) + H2O(l) NH4+(aq) + OH–(aq).
The base-dissociation constant, Kb, is defined as
[NH 4+][OH −] Kb
=
[NH 3]
The larger the Kb, the stronger the base.
Conjugate Acid-Base Pairs
Whatever is left of the acid after the proton is donated is called its conjugate base.
Similarly a conjugate acid is formed by adding a proton to the base.
Consider HA(aq) + H2O(l) H3O+(aq) + A–(aq):
HA and A– differ only in the presence or absence of a proton.
They are said to be a conjugate acid-base pair.
A– is called the conjugate base.
When HA (acid) loses its proton it is converted into A– (base).
Therefore HA and A– are a conjugate acid-base pair.
When H2O (base) gains a proton it is converted into H3O+ (acid). H3O+
is the conjugate acid.
Therefore, H2O and H3O+ are a conjugate acid-base pair.
Relative Strengths of Acids and Bases
The stronger an acid is, the weaker its conjugate base will be.
We can categorize acids and bases according to their behavior in water.
1. Strong acids completely transfer their protons to water.
No undissociated molecules remain in solution.
Their conjugate bases have negligible tendencies to become protonated.
Example: HCl.
2. Weak acids only partially dissociate in aqueous solution.
They exist in solution as a mixture of molecules and component ions.
Their conjugate bases show a slight tendency to abstract protons from water.
These conjugate bases are weak bases.
Example: Acetic acid is a weak acid; acetate ion (conjugate base) is a weak base.
3. Substances with negligible acidity do not transfer a proton to water.
Their conjugate bases are strong bases.
Example: CH4.
In every acid-base reaction, the position of the equilibrium favors the transfer of a proton from the stronger acid to the stronger base.
H+ is the strongest acid that can exist in equilibrium in aqueous solution.
OH– is the strongest base that can exist in equilibrium in aqueous solution.
Calculating Ka from pH
In order to find the value of the Ka, we need to know all of the equilibrium concentrations.
The pH gives the equilibrium concentration of H+.
Thus, to find Ka, we use the pH to find the equilibrium concentration of H+ and then the stoichiometric coefficients of the balanced equation to help us determine the equilibrium concentrations of the other species.
We then substitute these equilibrium concentrations into the equilibrium constant expression and solve for Ka.
Using Ka to Calculate pH
Using Ka, we can calculate the concentration of H+ ( and hence the pH ).
Write the balanced chemical equation clearly showing the equilibrium.
Write the equilibrium expression. Look up the value for Ka (in a table).
Write down the initial and equilibrium concentrations for everything except pure water.
It is customary to use x for the change in concentration of H+.
Substitute into the equilibrium constant expression and solve.
Remember to convert x to pH if necessary.
What do we do if we are faced with having to solve a quadratic equation in order to determine the value of x?
Often this cannot be avoided.
However, if the Ka value is quite small, we find that we can make a simplifying assumption.
Assume that x is negligible compared with the initial concentration of that species.
This will simplify the calculation.
It is always necessary to check the validity of any assumption.
Once you have the value of x, check to see how large it is compared with the initial concentration.
If x < 5% of the initial concentration, the assumption is probably a good one.
If x > 5%of the initial concentrtion, then it may be best to solve the quadratic equation or use successive approximations.
[H+]equilibrium
% ionization = ×100
[HA]initial
Weak acids are only partially ionized.
Percent ionization is another way to assess acid strength.
For the reaction HA(aq) H+(aq) + A–(aq)
Percent ionization relates the equilibrium H+ concentration, [H+]equilibrium, to the initial HA concentration, [HA]initial.
The higher the percent ionization, the stronger the acid.
However, we need to keep in mind that percent ionization of a weak acid decreases as the molarity of the solution increases.
Acid-Base Titrations
The plot of pH versus volume during a titration is called a titration curve.
Strong Acid–Strong Base Titrations
Consider adding a strong base (e.g., NaOH) to a solution of a strong acid (e.g.,
HCl).
We can divide the titration curve into four regions.
1. Initial pH (before any base is added).
The pH is determined by the concentration of the strong acid solution.
Therefore, pH < 7.
2. Between the initial pH and the equivalence point (see next slide).
When base is added, before the equivalence point, the pH is given by the
amount of strong acid in excess.
Therefore, pH < 7.
3. At the equivalence point.
The amount of base added is stoichiometrically equivalent to the amount of acid originally present.
Therefore, the pH is determined by the hydrolysis of the salt in solution.
Therefore, pH = 7.
4. After the equivalence point.
The pH is determined by the excess base in the solution.
Therefore, pH > 7.
How can we analyze the titration (i.e., how will we know when we are at the
equivalence point)?
Consider adding a strong base (e.g., NaOH) to a solution of a strong acid (
e.g., HCl ).
We know that the pH at the equivalence point is 7.00.
To detect the equivalence point, we use an indicator that changes color
somewhere near 7.00.
Usually, we use phenolphthalein, which changes color between pH 8.3 and
10.0.
In acid, phenolphthalein is colorless.
As NaOH is added, there is a slight pink color at the addition point.
When the flask is swirled and the reagents mix, the pink color disappears.
At the end point, the solution is light pink.
If more base is added, the solution turns darker pink.
The equivalence point in a titration is the point at which the acid and base
are present in stoichiometric quantities.
The end point in a titration is the point where the indicator changes color.
The difference between equivalence point and end point is called the titration error.
The shape of a strong base–strong acid titration curve is very similar to a strong
acid–strong base titration curve.
Initially, the strong base is in excess, so the pH > 7.
As acid is added, the pH decreases but is still greater than 7.
At the equivalence point, the pH is given by hydrolysis of the salt solution (
i.e., pH = 7).
After the equivalence point, the pH is given by the strong acid in excess, so
the pH < 7.
Weak Acid–Strong Base Titration
Consider the titration of acetic acid, HC2H3O2, with NaOH.
Again, we divide the titration into four general regions:
1. Before any base is added :
The solution contains only weak acid.
Therefore, pH is given by the equilibrium calculation.
2. Between the initial pH and the equivalence point.
As strong base is added it consumes a stoichiometric quantity of weak
acid:
HC2H3O2(aq) + OH–(aq) C2H3O2–(aq) + H2O(l)
However, there is an excess of acetic acid.
Therefore, we have a mixture of weak acid and its conjugate base.
Thus the composition of the mixture is that of a buffer.
The pH is given by the buffer calculation.
First, the amount of C2H3O2– generated is calculated, as well
as the amount of HC2H3O2 consumed. (stoichiometry.) Then
the pH is calculated using equilibrium conditions.
(Henderson-Hasselbach equation)
3. At the equivalence point, all the acetic acid has been consumed and all the
NaOH has been consumed.
However, C2H3O2– has been generated.
Therefore, the pH is given by the C2H3O2– solution.
This means pH > 7.
More importantly, the pH of the equivalence point > 7 for a weak acid–
strong base titration.
4. After the equivalence point:
The pH is given by the concentration of the excess strong base.
The pH curve for a weak acid–strong base differs significantly from that of a strong acid–strong base titration.
For a strong acid–strong base titration:
The pH begins at less than 7 and gradually increases as base is added.
Near the equivalence point, the pH increases dramatically.
For a weak acid–strong base titration:
The initial pH rise is steeper than that for a strong acid–strong base
titration.
However, then there is a leveling off due to buffer effects.
The inflection point is not as steep for a weak acid–strong base titration.
The shape of the two curves after the equivalence point is the same because
pH is determined by the strong base in excess.
The pH values at the equivalence points differ also:
The pH = 7.00 for the strong acid–strong base equivalence point.
The pH >7.00 for the weak acid–strong base equivalence point.
How to choose indicators: we select the appropriate indicator based upon the pH
of the salt solution formed at the equivalence point.
The pH curve for the titration of a weak base with a strong acid also differs significantly from that of a strong base-strong acid titration.
Consider the titration of NH3 with HCl.
The equivalence point occurs at pH 5.28 so phenolphthalein should not be used for this titration.
The color change for methyl red occurs in the pH range from 4.2 to 6.0 so it is a good indicator to use for this titration.
Acid-Base Properties of Salt
Solutions
Nearly all salts are strong electrolytes.
Therefore, salts in solution exist entirely as ions.
Acid-base properties of salts are a consequence of the reaction of their ions in solution.
Many salt ions can react with water to form OH– or H+.
This process is called hydrolysis.
Anions from weak acids are basic.
Anions from strong acids are neutral.
Anions with ionizable protons (e.g., HSO4–) are amphoteric.
They are capable of acting as an acid or a base.
All cations, except those of the alkali metals or heavier alkaline earth metals, are weak acids.
The pH of a solution may be qualitatively predicted using the following
guidelines:
Salts derived from a strong acid and a strong base are neutral.
Examples: NaCl, Ca(NO3)2.
Salts derived from a strong base and a weak acid are basic.
Examples: NaClO, Ba(C2H3O2)2.
Salts derived from a weak base and a strong acid are acidic.
Example: NH4Cl.
Salts derived from a weak acid and a weak base can be either acidic or basic.
Equilibrium rules apply!
We need to compare Ka and Kb for the hydrolysis of the anion and the cation.
For example, consider NH4CN.
Both ions undergo significant hydrolysis.
Is the salt solution acidic or basic?
The Ka of NH4+ is smaller than the Kb of CN–, so the solution should be
basic.
Buffered Solutions
A buffered solution or buffer is a solution that resists a change in pH upon addition of
small amounts of acid or base.
Composition and Action of Buffered Solutions
A buffer consists of a mixture of a weak acid (HX) and its conjugate base (X–).
Thus a buffer contains both:
An acidic species (to neutralize OH–) and A
basic species (to neutralize H+).
When a small amount of OH– is added to the buffer, the OH– reacts with HX to produce X–
and water.
But the [HX]/[X–] ratio remains more or less constant, so the pH is not significantly
changed.
When a small amount of H+ is added to the buffer, X– is consumed to produce HX.
Once again, the [HX]/[X–] ratio remains more or less constant, so the pH does not
change significantly.
Buffer capacity is the amount of acid or base that can be neutralized by the
buffer before there is a significant change in pH.
Buffer capacity depends on the concentrations of the components of the buffer.
The greater the concentrations of the conjugate acid-base pair, the greater the
buffer capacity.
The pH of the buffer is related to the Ka and on the relative concentrations of the
acid and base.
We can derive an equation that shows the relationship between conjugate
acidbase concentrations, pH, and the Ka.
By definition:
Ka =
Rearranging, we get:
[H+]=Ka[HA− ]
[A ]
If we take the negative log of each side of the equation we get:
− log[H+ ] =−log Ka − log
By definition:
pH = pKa −log
An alternative form of this equation is:
The preceding equation is the Henderson-Hasselbach equation.
Note that this equation uses equilibrium concentrations of acid and conjugate base.
However, if Ka is sufficiently small (i.e., if the equilibrium concentration of undissociated acid is close to the initial concentration), then we can use the initial values of the acid and base concentrations in order to get a good estimate of the pH.
Addition of Strong Acids or Bases to Buffers
We break the calculation into two parts:
A stoichiometric calculation.
An equilibrium calculation.
The addition of strong acid or base results in a neutralization reaction:
X– + H3O+ ↔ HX + H2O
[ ]
[ ]
[ ]
[ ] acid
base log pK
HA
A log pK pH a a + = + =
−
HX + OH– ↔ X– + H2O
By knowing how much H3O+ or OH– was added, we know how much HX or X– is formed.
This is the stoichiometric calculation.
From the concentrations of HX and X– (note the change in volume of solution) we can calculate the pH from the Henderson-Hasselbalch equation: