Transcript The concept of pH and pKa

The concept of pH and pKa
Lecture 3
Handout
Introduction
• Why is pH so important for maintaining
homeostasis?
• pH of blood
• pH and diseases
Introduction
• pH = the measure of the acidity or alkalinity of a
solution (pH stands for "power of hydrogen“)
• a measure of the activity of dissolved hydrogen
ions (H+)
• for very dilute solutions  the molarity (molar
concentration) of H+ may be used as a
substitute with little loss of accuracy
• In solution  hydrogen ions occur as a number
of cations including hydronium ions (H3O+)
continued
• pure water at 25 °C  the concentration of H+
equals the concentration of hydroxide ions (OH-)
• "neutral" and corresponds to a pH level of 7.0
• Solutions  the concentration of H+ exceeds
that of OH- have a pH value lower than 7.0 =
acids
• Solutions  OH- exceeds H+ have a pH value
greater than 7.0 = bases
• pH is dependent on ionic activity
Definition
• pH = a measurement of the concentration of hydrogen
ions in a solution
• low pH values  associated with solutions with high
concentrations of hydrogen ions
• high pH values  solutions with low concentrations of
hydrogen ions
• Pure water  a pH of 7.0, and other solutions are
usually described with reference to this value
• Acids  solutions that have a pH less than 7 (i.e. more
hydrogen ions than water)
• Bases  a pH greater than 7 (i.e. less hydrogen ions
than water)
continued
• definitions of weak and strong acids, and
weak and strong bases do not refer to pH
• It describe whether an acid or base ionizes
in solution
Explanation of pH
• the number (pH) arises from a measure of the
activity of hydrogen ions or their equivalent in
the solution
• pH scale = an inverse logarithmic representation
of hydrogen proton (H+) concentration
• pH unit is a factor of 10 different than the next
higher or lower unit
• a change in pH from 2 to 3 represents a 10-fold
decrease in H+ concentration, and a shift from 2
to 4 represents a one-hundred (10 × 10)-fold
decrease in H+ concentration
. The formula for calculating pH
• αH+ denotes the activity of H+ ions, is
dimensionless
• Activity = a measure of the effective
concentration of hydrogen ions (rather than the
actual concentration)
• other ions surrounding hydrogen ions will shield
them and affect their ability to participate in
chemical reactions
dilute solutions (tap water)  activity is
approximately equal to the numeric value of the
concentration of the H+ ion:
denoted as [H+] ([H3O+])
measured in moles per litre (also known as
molarity)
often convenient to define pH as
continued
• log10 denotes the base-10 logarithm
• therefore pH defines a logarithmic scale
of acidity
continued
• . For example, if one makes a lemonade
with a H+ concentration of 0.0050 moles
per litre, its pH would be:
continued
• A solution of pH = 8.2
• have an [H+] concentration of 10−8.2 mol/L, or
about 6.31 × 10−9 mol/L
• its hydrogen activity αH+ is around 6.31 × 10−9
• solution at 25 °C, a pH of 7 indicates neutrality
(i.e. the pH of pure water)
• because water naturally dissociates into H+ and
OH− ions with equal concentrations of 1×10−7
mol/L
continued
• lower pH value (for example pH 3)
indicates increasing strength of acidity
• higher pH value (for example pH 11)
indicates increasing strength of basicity
• (pure water, when exposed to the
atmosphere, will take in carbon dioxide,
some of which reacts with water to form
carbonic acid and H+, thereby lowering the
pH to about 5.7)
Calculation of pH for weak and
strong acids
• stronger or weaker acids are a relative concept
• a strong acid = a species which is a much
stronger acid than the hydronium (H3O+) ion
• the dissociation reaction (strictly
HX+H2O↔H3O++X− but simplified as
HX↔H++X−) goes to completion, i.e. no
unreacted acid remains in solution
• Dissolving the strong acid HCl (hydrochloric
acid) in water:
– HCl(aq) → H+ + Cl−
continued
• in a 0.01 mol/L solution of HCl it is
approximated that there is a concentration
of 0.01 mol/L dissolved hydrogen ions
• the pH is: pH = −log10 [H+]:
pH = −log (0.01)
It equals 2
continued
• weak acids
• dissociation reaction does not go to completion
• equilibrium is reached between the hydrogen ions and
the conjugate base
• equilibrium reaction between methanoic acid and its
ions:
• HCOOH(aq) ⇌ H+ + HCOO−
• We must know  the value of the equilibrium constant of
the reaction for each acid in order to calculate its pH
• In the context of pH  this is termed the acidity
constant (Ka) of the acid
• Ka = [hydrogen ions][acid ions] / [acid]
continued
• For HCOOH: Ka = 1.6 × 10−4
• When calculating the pH of a weak acid, it
is usually assumed that the water does not
provide any hydrogen ions
• it simplifies the calculation, and the
concentration provided by water, 1×10−7
mol/L, is usually insignificant
continued
•
With a 0.1 mol/L solution of methanoic
acid (HCOOH), the acidity constant is
equal to:
Ka = [H+][HCOO−] / [HCOOH]
•
Given that an unknown amount of the
acid has dissociated, [HCOOH] will be
reduced by this amount, while [H+] and
[HCOO−] will each be increased by this
amount
continued
• [HCOOH] may be replaced by 0.1 − x, and
[H+] and [HCOO−] may each be replaced
by x, giving us the following equation:
• Solving this for x yields 3.9×10−3 = the
concentration of hydrogen ions after
dissociation
• the pH is −log(3.9×10−3) or about 2.4
pH can be measured
• by addition of a pH indicator into the
solution under study
• by using a pH meter together with pHselective electrodes
• by using pH paper, indicator paper that
turns colour corresponding to a pH on a
colour key
Fluid
pH in body fluids
gastric acid
pH
0.7
lysosome
5.5
granule of chromaffin cell
5.5
Neutral H2O at 37°C
6.81
cytosol
7.2
CSF
7.3
arterial blood plasma
7.4
mitochondrial matrix
7.5
exocrine secretions of pancreas
8.1
Acids
• An acid (often represented by the generic
formula HA [H+A-])  any chemical
compound that, when dissolved in water,
gives a solution with a hydrogen ion
activity greater than in pure water (a pH
less than 7.0)
• an acid as a compound which donates a
hydrogen ion (H+) to another compound
(called a base)
continued
• In water the following equilibrium occurs
between a weak acid (HA) and water,
which acts as a base:
• HA(aq) + H2O ⇌ H3O+(aq) + A-(aq)
• acidity constant (or acid dissociation
constant) is the equilibrium constant for
the reaction of HA with water:
• Strong acids have large Ka values (the reaction
equilibrium lies far to the right; the acid is almost
completely dissociated to H3O+ and A-)
• Strong acids include the heavier hydrohalic
acids: hydrochloric acid (HCl), hydrobromic acid
(HBr), and hydroiodic acid (HI)
continued
• Weak acids  have small Ka values (i.e.
at equilibrium significant amounts of HA
and A− exist together in solution; modest
levels of H3O+ are present; the acid is
only partially dissociated)
• Most organic acids  weak acids
• nitrous acid, sulfurous acid and
hypochlorous acid are all weak acids
Neutralization
• the reaction between an acid and a base,
producing a salt and neutralized base
• hydrochloric acid and sodium hydroxide
form sodium chloride and water:
• HCl(aq) + NaOH(aq) → H2O(l) +
NaCl(aq)
continued
• Neutralization  the basis of titration,
where a pH indicator shows equivalence
point when the equivalent number of
moles of a base have been added to an
acid
• It is often wrongly assumed that
neutralization should result in a solution
with pH 7.0 (is only the case with similar
acid and base strengths during a reaction)
continued
• Neutralization with a base weaker than the
acid  weakly acidic salt
• E.g. weakly acidic ammonium chloride
(produced from the strong acid hydrogen
chloride and the weak base ammonia)
• neutralizing a weak acid with a strong
base gives a weakly basic salt, e.g.
sodium fluoride from hydrogen fluoride
and sodium hydroxide
Biological occurrence of acids
• In humans  hydrochloric acid is a part of
the gastric acid secreted within the
stomach:
– hydrolyze proteins and polysaccharides
– converting the inactive pro-enzyme,
pepsinogen into the enzyme, pepsin
Bases
• A strong base  a base which hydrolyzes
completely, raising the pH of the solution
towards 14
• weak bases (ammonia)
• Arrhenius bases  water-soluble and these
solutions always have a pH greater than 7
• alkali is a special example of a base, where in
an aqueous environment, hydroxide ions (also
viewed as OH−) are donated
Bases and pH
• pure water  molecules dissociate into
hydronium ions (H3O+) and hydroxide ions
(OH−), according to the following equation:
• 2H2O(l) → H3O+(aq) + OH−(aq)
• concentration, measured in molarity (M or moles
per dm³), of the ions  indicated as [H3O+] and
[OH−]
continued
• their product is the dissociation constant
of water; has the value 10−7 M
• A base accepts (removes) hydronium ions
(H3O+) from the solution, or donates
hydroxide ions (OH−) to the solution
• Both actions will lower the concentration of
hydronium ions, and thus raise pH
• an acid donates H3O+ ions to the solution
or accepts OH−, thus lowering pH
continued
• base dissociation constant (or Kb)  a
measure of basicity
• pKb is the negative log of Kb and related
to the pKa by the simple relationship pKa
+ pKb = 14
• Alkalinity is a measure of the ability of a
solution to neutralize acids to the
equivalence points of carbonates or
bicarbonates
Neutralization of acids
• When dissolved in water, the strong base sodium
hydroxide decomposes into hydroxide and sodium ions:
• NaOH → Na+ + OH−
• in water hydrogen chloride forms hydronium and chloride
ions:
• HCl + H2O → H3O+ + Cl−
• When the two solutions are mixed, the H3O+ and OH−
ions combine to form water molecules:
continued
• H3O+ + OH− → 2 H2O
• If equal quantities of NaOH and HCl are
dissolved  the base and the acid exactly
neutralize, leaving only NaCl (table salt) in
solution
Confusion between alkali and
base
• The terms "base" and "alkali" are often used
interchangeably, since most common bases are
alkalis
• . It is common to speak of "measuring the
alkalinity of soil" when what is actually meant is
the measurement of the pH (base property). In a
similar manner, bases that are not alkalis, such
as ammonia, are sometimes erroneously
referred to as alkaline
• not all or even most salts formed by alkali metals
are alkaline; this designation applies only to
those salts that are basic
continued
• most electropositive metal oxides are
basic; only the soluble alkali metal and
alkaline earth metal oxides can be
correctly called alkalis
• This definition of an alkali as a basic salt of
an alkali metal or alkaline earth metal does
appear to be the most common, based on
dictionary definitions (however conflicting
definitions of the term alkali do exist)
Weak acid/weak base equilibria
• In order to lose a proton, it is necessary
that the pH of the system rise above the
pKa of the protonated acid
• decreased concentration of H+ in that
basic solution shifts the equilibrium
towards the conjugate base form (the
deprotonated form of the acid)
continued
• In lower-pH (more acidic) solutions, there
is a high enough H+ concentration in the
solution to cause the acid to remain in its
protonated form, or to protonate its
conjugate base (the deprotonated form)
• Solutions of weak acids and salts of their
conjugate bases form buffer solutions
The Henderson–Hasselbalch
equation
• describes the derivation of pH as a
measure of acidity (using pKa, the acid
dissociation constant) in biological and
chemical systems.
• also useful for estimating the pH of a
buffer solution and finding the equilibrium
pH in acid-base reactions
• Two equivalent forms of the equation:
and
continued
• pKa is − log(Ka)
• where Ka is the acid dissociation constant
that is:
continued
• In these equations:
• A − = the ionic form of the relevant acid
• Bracketed quantities such as [base] and
[acid] denote the molar concentration of
the quantity enclosed
• In analogy to the above equations, the
following equation is valid:
continued
• B + denotes the salt of the corresponding
base B
Inorganic buffer
• A buffer solution = an aqueous solution
consisting of a mixture of a weak acid and its
conjugate base or a weak base and its
conjugate acid
• has the property that the pH of the solution
changes very little when a small amount of acid
or base is added to it
• Buffer solutions are used as a means of keeping
pH at a nearly constant value in a wide variety of
chemical applications
In a simple buffer solution  an
equilibrium between a weak acid,
HA, and its conjugate base, A-
HA + H2O  H3O+ + A−
continued
•
•
•
hydrogen ions are added to the solution  the
equilibrium moves to the left (as there are
hydrogen ions on the right-hand side of the
equilibrium expression)
hydroxide ions are added  the equilibrium
moves to the right (as hydrogen ions are
removed in the reaction H+ + OH- → H2O)
some of the added reagent is consumed in
shifting the equilibrium and the pH changes by
less than it would do if the solution were not
buffered
The acid dissociation constant
for a weak acid, HA, is defined
as
Simple manipulation with
logarithms gives the HendersonHasselbalch equation, which
describes pH in terms of pKa:
continued
• [A−] is the concentration of the conjugate
base
• [HA] is the concentration of the acid
• Applies  when the concentrations of acid
and conjugate base are equal
• often described as half-neutralization,
pH=pKa
The same considerations apply
to a mixture of a weak base, B
and its conjugate acid BH+
• B + H2O   BH+ + OH-
continued
• In general  a buffer solution may be
made up of more than one weak acid and
its conjugate base
• if the individual buffer regions overlap a
wider buffer region is created by mixing
the two buffering agents
Applications
• resistance to changes in pH  makes buffer
solutions very useful for chemical manufacturing
and essential for many biochemical processes
• ideal buffer for a particular pH has a pKa equal
to that pH, since such a solution has maximum
buffer capacity
• Buffer solutions are necessary to keep the
correct pH for enzymes in organisms to work
continued
• Many enzymes work only under very
precise conditions; if the pH strays too far
out of the margin, the enzymes slow or
stop working and can denature, thus
permanently disabling its catalytic activity
• A buffer of carbonic acid (H2CO3) and
bicarbonate (HCO3−) is present in blood
plasma  to maintain a pH between 7.35
and 7.45
Textbook
• In your text (by Kier and Dowd)
• Pg 56-65