The concept of pH and pKa

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The concept of pH and pKa

• Lecture 3
• Handout

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Introduction

• Why is pH so important for maintaining
  homeostasis?
• pH of blood
• pH and diseases

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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)

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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

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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)

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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

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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

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. The formula for calculating pH

• aH 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

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dilute solutions (tap water) ? activity is
approximately equal to the numeric value of the
concentration of the H iondenoted as H
(H3O)measured in moles per litre (also known
as molarity)often convenient to define pH as
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continued

• log10 denotes the base-10 logarithm
• therefore pH defines a logarithmic scale of
  acidity

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continued

• . For example, if one makes a lemonade with a H
  concentration of 0.0050 moles per litre, its pH
  would be

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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 aH 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 110-7 mol/L

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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)

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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
  HXH2O?H3OX- but simplified as HX?HX-) goes
  to completion, i.e. no unreacted acid remains in
  solution
• Dissolving the strong acid HCl (hydrochloric
  acid) in water
• HCl(aq) ? H Cl-

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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

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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 ionsacid ions / acid

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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, 110-7 mol/L, is
  usually insignificant

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continued

• With a 0.1 mol/L solution of methanoic acid
  (HCOOH), the acidity constant is equal to
• Ka HHCOO- / 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

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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 3.910-3 the
  concentration of hydrogen ions after dissociation
• the pH is -log(3.910-3) or about 2.4

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pH can be measured

• by addition of a pH indicator into the solution
  under study
• by using a pH meter together with pH-selective
  electrodes
• by using pH paper, indicator paper that turns
  colour corresponding to a pH on a colour key

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Fluid pH
gastric acid 0.7
lysosome 5.5
granule of chromaffin cell 5.5
Neutral H2O at 37C 6.81
cytosol 7.2
CSF 7.3
arterial blood plasma 7.4
mitochondrial matrix 7.5
exocrine secretions of pancreas 8.1
pH in body fluids
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Acids

• An acid (often represented by the generic formula
  HA HA-) ? 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)

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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

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• 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)

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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

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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)

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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)

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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

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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

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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

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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-

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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

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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

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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

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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

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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

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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)

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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)

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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

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The HendersonHasselbalch 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

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                            and
                                  
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continued

• pKa is - log(Ka)
• where Ka is the acid dissociation constant that
  is

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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

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continued

• B denotes the salt of the corresponding base B

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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

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In a simple buffer solution ? an equilibrium
between a weak acid, HA, and its conjugate base,
A-

• HA H2O ?? H3O A-

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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

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The acid dissociation constant for a weak acid,
HA, is defined as
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Simple manipulation with logarithms gives the
Henderson-Hasselbalch equation, which describes
pH in terms of pKa
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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, pHpKa

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The same considerations apply to a mixture of a
weak base, B and its conjugate acid BH

• B H2O ? ? BH OH-

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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

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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

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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

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Textbook

• In your text (by Kier and Dowd)
• Pg 56-65