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Water Molecule Structure

Water is a tiny V-shaped molecule with the molecular formula H2O a. Its molecular diameter is about 2.75
Å.g In the liquid state, in spite of 80% of the electrons being concerned with bonding, the three atoms do
not stay together as the hydrogen atoms are constantly exchanging between water molecules due to
protonation/deprotonation processes. Both acids and bases catalyze this exchange and even when at its
slowest (at pH 7), the average time for the atoms in an H2O molecule to stay together is only about a
millisecond. As this brief period is, however, much longer than the timescales encountered during
investigations into water's hydrogen bonding or hydration properties, water is usually treated as a
permanent structure.
Water molecules (H2O) are symmetric (point group C2ν) with two mirror planes of symmetry and a 2-fold
rotation axis. The hydrogen atoms may possess parallel or antiparallel nuclear spin.h The water molecule
consists of two light atoms (H) and a relatively heavy atom (O). The approximately 16-fold difference in
mass gives rise to its ease of rotation and the significant relative movements of the hydrogen nuclei,
which are in constant and significant relative movement.

Water's lone pairs?
The water molecule is often described in school and
undergraduate textbooks of as having four, approximately
tetrahedrally arranged, sp3-hybridized electron pairs, two of
which are associated with hydrogen atoms leaving the two

remaining lone pairs. In a perfect tetrahedral arrangement the
bond-bond, bond-lone pair and lone pair-lone pair angles would
all be 109.47° and such tetrahedral bonding patterns are found
in condensed phases such as hexagonal ice.
Ab initio calculations on isolated molecules, however, do not
confirm the presence of significant directed electron density
where lone pairs are expected.

Note. This cartoon of water does not represent its actual
outline, which is more rotund (see below).

Early 5-point molecular models, with explicit negative charge where the lone pairs are purported to be,
faired poorly in describing hydrogen bonding, but a recent TIP5P model shows some promise. Although

there is no apparent consensus of opinion [116], such descriptions of substantial sp3-hybridized lone pairs
in the isolated water molecule should perhaps be avoided [117], as an sp2-hybridized structure (plus a pz
orbital) is indicated. This rationalizes the formation of (almost planar) trigonal hydrogen bonding that can
be found around some restricted sites in the hydration of proteins and where the numbers of hydrogen
bond donors and acceptors are unequal.

Note that the average electron density
around the oxygen atom is about 10x that
around the hydrogen atoms.
The approximate shape and charge distribution of water.
The electron density distribution for water is shown above right with some higher density contours around
the oxygen atom omitted for clarity. The polarizability of the molecule is centered around the O-atom
(1.4146 Å3) with only small polarizabilities centered on the H-atoms (0.0836 Å3) [736]. For an isolated
H216O, H217O or H218O molecule, the calculated O-H length is 0.957854 Å and the H-O-H angle is 104.500°
(D216O, 0.957835 Å, 104.490°) [836]. The charge distribution depends significantly on the atomic
geometry and the method for its calculation but is likely to be about -0.7e on the O-atom (with the equal
but opposite positive charge equally divided between the H-atoms) for the isolated molecule [778].d The
experimental values for gaseous water molecule are O-H length 0.95718 Å, H-O-H angle 104.474° [64].e
These values are not maintained in liquid water, where ab initio (O-H length 0.991 Å, H-O-H angle 105.5°
[90]) and neutron diffraction studies (O-D length 0.970 Å, D-O-D angle 106° [91])f suggest slightly greater
values, which are caused by the hydrogen bonding weakening the covalent bonding. These bond lengths
and angles are likely to change, due to polarization shifts, in different hydrogen-bonded environments
and when the water molecules are bound to solutes and ions. Commonly used molecular models use O-H
lengths of between 0.957 Å and 1.00 Å and H-O-H angles of 104.52° to 109.5°.

Water electronic structure

The electronic structure has been proposed as 1sO2.00 2sO1.82
2pxO1.50 2pzO1.12 2pyO2.00 1sH10.78 1sH20.78 [71], however it now
appears that the 2s orbital may be effectively unhybridized
with the bond angle expanded from the (then) expected angle
of 90° due to the steric and ionic repulsion between the
partially-positively charged hydrogen atoms (as proposed by
Pauling over 50 years ago [99]). The molecular orbitals of
water, (1a1)2(2a1)2(1b2)2(3a1)2(1b1)2, are shown on another page
(24 KB).
Shown opposite is the electrostatic potential associated with
the water structure. Although the lone pairs of electrons do not
appear to give distinct directed electron density in isolated
molecules, there are minima in the electrostatic potential in
approximately the expected positions.
The mean van der Waals diameter of water has been reported
as identical with that of isoelectronic neon (2.82 Å) [112].
Molecular model values and intermediate peak radial
distribution data indicates however that it is somewhat greater
(~3.2Å). The molecule is clearly not spherical, however, with
about a ±5% variation in van der Waals diameter dependent
on the axis chosen; approximately tetrahedrally placed slight
indentations being apparent opposite the (putative) electron

Van der Waals radii [206]

Water dimer
Much effort has been expended on the structure of small isolated water clusters. The most energetically
favorable water dimer is shown below with a section through the electron density distribution (high
densities around the oxygen atoms have been omitted for clarity). This shows the tetrahedralityb of the
bonding in spite of the lack of clearly seen lone pair electrons; although a small amount of distortion
along the hydrogen bond can be seen. This tetrahedrality is primarily caused by electrostatic effects (that
is, repulsion between the positively charged non-bonded hydrogen atoms) rather than the presence of
tetrahedrally placed lone pair electrons. The hydrogen-bonded proton has reduced electron density
relative to the other protons [222]. Note that, even at temperatures as low as a few kelvin, there are
considerable oscillations (< ps) in the hydrogen bond length and angles [591]. The molecular orbitals of
the water dimer are shown on another page (50 KB)

R = 2.976 (+0.000, -0.030) Å, α = 6
± 20°, β = 57 ± 10° [648]; α is the
donor angle and β is the acceptor
angle. The dimer (with slightly
different geometry) dipole moment
is 2.6 D [704]. Although β is close to
as expected if the lone pair
electrons were tetrahedrallly placed
(= 109.47°/2), the energy minimum
(~21 kJ mol-1) is broad and extends
towards β = 0°.

Water models
Simplified models for the water molecule have been developed to agree with particular physical
properties (for example, agreement with the critical parameters) but they are not robust and resultant
data are often very sensitive to the precise model parameters [206]. Models are still being developed and
are generally more complex than earlier but they still generally have poor predictive value outside the
conditions and physical parameters for which they were developed.

Although not often perceived as such, water is a very reactive molecule available at a high concentration.
This reactivity, however, is greatly moderated at ambient temperatures due to the extensive hydrogen
bonding. Water molecules each possess a strongly nucleophilic oxygen atom that enables many of life‘s
reactions, as well as ionizing to produce reactive hydrogen and hydroxide ions. Reduction of the hydrogen
bonding at high temperatures, or due to electromagnetic fields, results in greater reactivity of the water


Water's composition (two parts hydrogen to one part oxygen)
was discovered by the London scientist Henry Cavendish (17311810) in about 1781. He reported his findings in terms of
phlogiston (later the gas he made was proven to be hydrogen)
and dephlogisticated air (later this was proven to be oxygen).
Cavendish died (1810) in his Laboratory just 30 minutes walk
from the present site of London South Bank University.

It has recently been suggested that H1.5O may better reflect the formula at very small (attosecond)
timescales when some of the H-atoms appear invisible to neutron and electron interaction [515]. The
experimental results have since been questioned [630] and described as erroneous [796], but have been
recently confirmed and thought due to a failure of the Born-Oppenheimer approximation (this assumes
that the electronic motion and the nuclear motion in molecules can be separated) [1134]. Thus the
formula H1.5O is incorrect but such suggestions do, however, add support to the view that observations
concerning the structure of water should be tempered by the timescale used. [Back]

The tetrahedral angle is 180-cos-1(1/3)°; 109.47122° = 109° 28' 16.39". Tetrahedrality (q, the

orientational order parameter) may be defined as
, where φjk is the angle
formed by lines drawn between the oxygen atoms of the four nearest and hydrogen-bonded water
molecules [169]. It equals unity for perfectly tetrahedral bonding (where cos(φ jk) = -1/3) and averages
zero (±0.5 SD) for random arrangements, with a minimum value of -3. The density order parameter is
described elsewhere. [Back]
ortho-H2O rotates in its ground state with energy 23.79 cm-1 [1150]. Due to deuterium's nuclear spin of 1
(compare 1/2 for H's spin), the lowest energy form of D2O is ortho. D2O converts to a 2:1 ortho:para ratio
at higher temperatures. HDO, having non-equivalent hydrogen atoms, does not possess an ortho/para
distinction. T2O behaves similarly to H2O as tritium also possesses a nuclear spin of 1/2. [Back]

The charge on the hydrogen atoms across the
periodic table are shown opposite [820]. The
hydrogen atom charges are blue and the charges on
the other atoms are indicated red. [Back]

The actual values depend on the vibrational state of the molecule with even values of 180° being
attainable during high order bend vibrations (v2 >= 7, λ < 900 nm) for the H-O-H angle [860]. Vibrations
are asymmetric around the mean positions. In the ground state, the bond angle (104.5°) is much closer to
the tetrahedral angle than that of the other Group VI hydrides, H2S (92.1°), H2Se (91°) or H2Te (89°).

The H-O-H angle in ice Ih is reported as 106.6°±1.5° [717], whereas recent modeling gives values of
108.4°±0.2° for ice Ih and 106.3°±4.9° for water [1028]. [Back]

The atomic diameter can be determined from interpolation of the effective ionic radii of the isoelectronic
ions (from crystal data) of O2- (2.80 Å), OH- (2.74 Å) and H3O+ (2.76 Å) [1167]. Coincidentally, this
diameter is similar to the length of a hydrogen bond. The water molecule is smaller than ammonia or
methane, with only H2 and HF being smaller molecules. [Back]

As is found in molecular hydrogen (H2), the hydrogen atoms in water (H2O) may possess parallel
(paramagnetic ortho-H2O, magnetic moment = 1) or antiparallel (nonmagnetic para-H2O, magnetic
moment = 0) nuclear spin. The equilibrium ratio in H2O is all para at zero Kelvin, where the molecules
have no rotational spin in their ground state, shifting to 3:1 ortho:para at less cold temperatures (>50 K);c
the equilibrium taking months to establish itself in ice (or gas) and nearly an hour in ambient water [410].
This means that liquid H2O effectively consists of a mixture of non-identical molecules and the properties
of pure liquid ortho-H2O or para-H2O are unknown. The differences in the properties of these two forms of
water are expected to be greater in an electric field [1186], which may be imposed externally, from
surfaces or from water clustering itself. Many materials preferentially adsorb para-H2O due to its nonrotation ground state [410, 835]. The apparent difference in energy between the two states is a
significant 1-2 kJ mol-1, far greater than expected from spin-spin interactions (< μJ mol-1) [835]. It is
possible that ortho-H2O and para-H2O form separate hydrogen bonded clusters [1150]. [Back]

Details of water's molecular vibrations and absorptions are given on another page.

Please submit any comments and suggestions you may have.
Site Index | Easier introduction | Water vibrations | H2O orbitals | Notes

This page was last updated by Martin Chaplin
on 13 August, 2007


Structural Forms in the Icosahedral Water Cluster
Figures 3, 4, 5 and 6

Figure 3. Sub-structures found in the
expanded (ES; a, d, f, h) and equivalent
forms in the collapsed (CS; b, c, e, g, i)
water structure. Note that the 10-molecule
unit (a) shows the least signs of collapse
when in the collapsed structure (b, c) and
therefore may play a major role in the
cluster equilibrium. Structure (d) shows the
hexameric box formed by the faces of the
tetrahedral. Structure (f) shows the
dodecahedron formed by the vertices of
the tetrahedral. Structure (h) shows the
pentagonal box formed by the edges using
similar molecules from five tetrahedron
edges, meeting at two pentagonal faces.
Each tetrahedron unit has a fifth share in
each pair of such units that form on each of
its six edges. The number of the
substructures in ES is given below in Figure

Figure 4. Connectivity map of the water

The inner, middle and outer shells are shown
separately below.

Figure 5. A super cluster of thirteen water icosahedra,
showing the tessellation ability. Thirteen complete but
overlapping icosahedral clusters form this supericosahedral structure (an icosahedron of
interpenetrating icosahedra; that is, a tricontahedron)
containing 1820 water molecules (an outer shell of an
additional 360 water molecules is also shown). This
structure is for illustrative purposes only of the type of
superclustering possible. It is not likely to be a
preferred minimum-energy structure due to the
increased strain on full tessellation [295]; However the
icosahedral structures can form part of fully tessellated
clathrate I-type structures.
The volume of the central (H2O)280 icosahedron is about
1/4 of the volume of a single gaseous H2O molecule.
Although there is presently no evidence for this and the
mechanism of formation is unclear, the stabilization
offered by the surrounding optimal hydrogen bonding
may indicate a possible route to bulk nanobubble (that
is, nanocavity) formation.
Only the oxygen atoms are shown (for interactive structures see: Chime, 50KB). The spherical

coordinates of this structure are shown on another page. Strand-like super-clusters are also possible
(and are preferred in the related polytetrahedral Dzugutov clusters [295]) and may explain the
properties of deeply supercooled water.
Figure 6. This illustrates the
number of structural forms that
exist within the 280-molecule
water cluster (ES); (the number
of type a, b and c molecules, as
described in Figure 1, are given
as (na,nb,nc), see below.
Interestingly clusters d, f, g and
h are the (only) four clusters
singled out by Stillinger from
early molecular dynamics
calculations [729]. These
clusters are key to the
formation of the 280-molecule
water cluster (ES).
It is worthy of note that cyclic
pentamers (c) and boat-form
hexamers (b) appear to be the
most stable water pentamer
and hexamer structures in the
gas phase [466], with cyclic
pentamers most likely to remain
intact at higher temperatures
There are 80 complete all-gauche chair-form hexamers (a) (0,3,3), 360 all-gauche boat-form
hexamers (b) (67% 2,2,2 and 33% 0,2,4) of which 90 are made up of partial bits, 72 all-cis
pentamers (c) (5,0,0) of which 36 are made up of partial bits, 20 all-gauche ten-molecule tetrahedra
(d) (0,4,6), 40 all-gauche hexameric boxes (e) (0,6,6) of which 10 are made up of partial bits, 120
all-gauche eight-molecule structures (f) (2,2,4) of which 30 are made up of partial bits, 48 cis- and
gauche-bonded pentameric boxes (g) (5,5,5) of which 24 are made up of partial bits, and 4 all-cis
dodecahedra (h) (20,0,0) of which 3 are made up of partial bits (that is,12 quarterdodecahedra). Cis-hydrogen bonding allows a favorable overlap of the molecular orbitals [165].

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Home > Water (Molecule of the Month for
January 2006)

Water has the chemical formula H2O, composed of
two hydrogen atoms and one oxygen atom. It is often
referred to in science as the universal solvent. Water
is the only pure substance found naturally in all three
states of matter: solid; liquid and gas. Water may
take many forms; the solid state of water is
commonly known as ice or amorphous solid water;
the gaseous state is known as water vapour or steam;
and the common liquid phase is generally called:
simply, water.

click on the picture above to interact
with the 3D model of the
Water structure
(this will open a new browser window)

An important feature of water is its polar nature. The
water molecule forms an angle, with hydrogen atoms
at the tips and oxygen at the vertex. Since oxygen
has a higher electronegativity than hydrogen, the side
of the molecule with the oxygen atom has a partial
negative charge. A molecule with such a charge
difference is called a dipole. The charge differences
cause water molecules to be attracted to each other
(the relatively positive areas being attracted to the
relatively negative areas) and to other polar
molecules. This attraction is known as hydrogen
bonding, and explains many of the properties of
water. Although hydrogen bonding is a relatively
weak attraction compared to the covalent bonds
within the water molecule itself, it is responsible for
a number of water's physical properties. One such
property is its relatively high melting and boiling point temperatures; more heat energy is required to break
the hydrogen bonds between molecules. Hydrogen bonding also gives water its unusual behavior when
freezing. When cooled to near freezing point, the presence of hydrogen bonds means that the molecules, as
they rearrange to minimize their energy, form the hexagonal crystal structure of ice that is actually of lower
density: hence the solid form, ice, will float in water. In other words, water expands as it freezes, whereas
virtually all other materials shrink on solidification.
Water is also a good solvent due to its polarity. When an ionic or polar compound enters water, it is
surrounded by water molecules. The relatively small size of water molecules typically allows many water
molecules to surround one molecule of solute. The partially negative dipole ends of the water are attracted to
positively charged components of the solute, and vice versa for the positive dipole ends. In general, ionic and
polar substances such as acids, alcohols, and salts are relatively soluble in water, and nonpolar substances
such as fats and oils are not. Nonpolar molecules stay together in water because it is energetically more
favorable for the water molecules to hydrogen bond to each other than to engage in van der Waals interactions

with nonpolar molecules. An example of an ionic solute is table salt; the sodium chloride, NaCl, separates into
Na+ cations and Cl- anions, each being surrounded by water molecules. The ions are then easily transported
away from their crystalline lattice into solution. An example of a nonionic solute is table sugar. The water
dipoles make hydrogen bonds with the polar regions of the sugar molecule (OH groups) and allow it to be
carried away into solution. The solvent properties of water are vital in biology, because many biochemical
reactions take place only within aqueous solutions (e.g., reactions in the cytoplasm and blood).

Overheads for Secton 1
Scientific Method
Pope and evolution
Vatican & ID_1/19/06
Chapter 1
Life it's own self
Cell fractionation
Phylogeny of Kingdoms
Organism classes
Isolating organelles
Biochem Organization
Chemical Composition of cells
Noncovalent Interactions
Functional Groups
Chemical properties
Protein Interactions
Physical concepts
DNA complementarity
Molecular Biology Paradigm
DNA point mutations
Genetic Diversity
Prebiotic Evolution
Evolutionary Time Line
Acquistion of mitochondria?
Genomic Data
Chapter 2
Weak bonds
Water structure
water Clathrates
Dissolution of ions

Hydrogen bonding
Nonpolar interactions
Solute interactions
Colligative properties
water has unusal properties
Acids and pH
Ionization of water
proton hopping
estimate Ka
acid species and pH
Common acids
titration of acids
table of pKs
pKa with dielectric
Buffer example
Practical buffer calculations
Blood buffering
Ionization of protein side chains

Chapter 3
Amino acid nomenclature
The RS system
The 20 standard amino acids
Titration of AA
Opical absorbance
Aromatic absobance
Table of AA properties
Nonstandards AAs
Chemical Reactions
Peptide formation
Levels of protein structure
Protein assays
Acrylamide gels
Animation of SDS run
MW from PAGE
Salt fractionation and Dialysis
Ion exchamge chromatography
Molecular seive chromatography
MW from gel filtration
Affinity chromatography
2D gels
ELISA assays
The Edman reaction
Chemical sequencing of proteins
A simple example of overlapping peptides
Cytochrome C sequences

Species relations
Evolutionary trees
Aligning protein sequences
Chapter 4
Peptide Bond
Phi/Psi definitions
Extended chain
Phi/Psi Demo
Ramachandran Plot
Peptide helices
α -helix
β -sheets
Peptide turns
Fibrous Proteins
Collagen bonding
Globular Proteins
Simple motifs
Helix interactions
Motifs to domains
Four-helix Bundle
antiparallel beta barrel
Beta Sandwhich
Simple Greek Key Barrel
Jelly-roll beta barrel
The beta-alpha barrel
The NAD binding domain
Domain structure
Table of composition
Protein Structure Demo
X-ray Structure Determination-1
X-ray Structure Determination-2
Electron density
Protein folding forces
Examples of atom distribution
Quaterary Structure
Simple quaternary structure
Molecular Symmetry
Virus symmetry
Protein Folding
Folding Barnase

Chapter 5
Nonenzyme protein examples
Oxygen transport
O2 binding to Mb
Hemeoglobin structure
Cooperative binding
Hill Plots
A simple cooperative model
Two states for Hb
Heme interaction with O2
Hb quaterary shifts1
Hb quaterary shifts2
Simple Hb quat. model
The Bohr Effect
Hb allosteric effectors
BPG binds T state Hb
Molecular evolution
Example of deamination
Sickle cell anemia
Trait inheritance
Evolution and expression of globins
Humoral immunity
Ig G Antibody structure
IgG sequences
Antigen binding
Binding a small antigent to an antibody
   A deep antibody pocket
   Some chemical interactions
Antibody binding to a protein
Antibody-like domains are common in the immune response
Clonal selection
Cellular immunity
MHC sytem
Immune response
Motor proteins: actin & myosin
Skeletal muscle
Myosin and actin
Actin-myosin assembly
Sliding filament model of muscle contraction
Molecular mech of power stroke
Back to main index

Living things are about 70% water. Biochemical reactions occur in aqueous solution.

Water is a dipolar molecule. |This dipole is responsible
for the properties of water.

Water molecules form transient H-bonds with each other.
These H-bonds are more stable in ice. When ice melts the
collapse of water structure means that liquid water is
more dense than ice.

Molecule Mr
H-bonding increases the cohesivness of water which
increases the melting point and boiling point compared to
similar sized molecules.

Melting point

Boiling point













Polar and ionic substances dissolve in water - they are said to be hydrpohillic.
Non-polar substances are insoluble - they are said to be hydrophobic.
Why is water such a good solvent for polar and ionic substances?
a) It has a high dielectric constant: The force between 2 ions in a vaccuum is proportional to:
q1q2/r2 (where q1 and q2 are charges on molecules and r is their distance of separation).
If there is material between the ions the force is reduced. The reduction depends on the dielectric (D) constant
of the material such that force is proportional to:

q1q2/ r2D.
The dielectric constant for water is 80 which is much higher than hexane for example which has a dielectric
constant of 2. The force between two ions at a given separation is therefore about 40 times greater in hexane
than water. Ionic compounds will therefore dissolve in water more easily than hexane.
b) Solvation of ions by water molecules shields them from ions of opposite charge and reduces their tendency
to reform the ionic solid.
c) Water can H-bond with a molecule or groups on a molecule, then the molecule will be soluble.
Biomolecules (e.g. proteins, sugars, nucleic acids etc.) contain many charged and polar groups like hydroxyl,
keto, carboxyl and amino which can hydrogen bond with water making them soluble.

Amphiphilic molcecules contain hydrophillic and hydrophobic groups e.g. fatty acids (soap ions):

The hydrophobic hydrocarbon chain is excluded by water while the hydrophillic carboxyl group hydrogen
bonds with water. The hydrophobic properties of biomolecules are very important because they often dictate
the structural and conformational properties of biomolecules in the aqueous environment. For example fatty
acids are driven into various structures as the hydrophobic hydrocarbon chains cluster away from the water:

This principle extends to proteins where hydrophobic amino acids tend to be found in the interior of proteins
while hydrophillic amino acids tend to be found at the surface of the protein. These hydrophobic interactions
are a major force in driving protein folding.

Water undergoes reversible ionisation:

H+ + OH-

As can be seen from the equilibrium constant for the reaction the degree of ionisation of water is very small:
Keq = 1.8x10-16M = [H+][OH-] /[H2O] (at 25°C)
Given that the concentration of H2O in water = 55.5M and cross multiplying:
1.8x10-16 x 55.5 = [H+][OH-]

1x10-14M2 = [H+][OH-]
1x10-14M2 = Kw (the ionic product of water)
[H+][OH-] (the ionic product of water) always equals 1x10-14M2 at 25°C. If either H+ or OH- are added to water
the equilibrium adjusts so that the ionic product returns to 1x10 -14M2.
When [H+] = 1x10-7M and [OH-] = 1x10-7M (amount of H+ and OH- are equal) the solution is neutral.
When [H+] > [OH-] the solution is acidic.
When [H+] < [OH-] the solution is basic.

pH and pOH
pH is mathmatically defined as -log10[H+]. It provides a convienent way of stating H+ and OH- concentrations.
For example when [H+] = 1x10-7M = pH 7.
Subtracting the pH from 14 gives the pOH value of a solution which is a measure of [OH-]. Since [H+][OH-]
always equals 1x10-14M2 it follows that pH + pOH always equals 14.

A weak acid (HA) ionises to give its conjugate base (A-) and a proton:

A- + H+

The rate of the forward reaction is proportional to concentration of the reactant [HA]
The rate of the reverse reaction is proportional to the products [A-] [H+]
By inserting constants (so called rate constants) we can turn these proportionalities into equalaties:

Rate of the forward reaction = kF [HA]
Rate of reverse reaction = kR[A-][H+]

At equilibrium the rate of the forward and reverse reactions are equal and therefore:
kR/kF= [A-][H+] /[HA]
A constant divided by another constant gives us a new constant
in this case kR/kF is the dissociation constant Ka
hence, Ka = [A-][H+]/[HA]

Ka gives us a measure of the strength of the acid. If Ka is a small number it follows that the product [A -][H+]
must be small compared to [HA]. This tells us that the acid is only slightly dissociated - in other words be a
weak acid. If Ka is relatively large then the acid must dissociate to larger extent - in other words be a stronger

The equation: Ka = [A-][H+] /[HA] can be rearranged to give:
[H+] = Ka ([HA] /[A-])
Taking negative logarithim of both sides of this equation we get:
-log [H+] = -logKa - log ([HA] /[A-])

-log [H+] is of course equal to pH.
-logKa is known as pKa.

Substituting these terms into the above equation we get:
pH = pKa - log ([HA] /[A-])
or more usually: pH = pKa + log ([A-] /[HA])
This is the Henderson Hasselbach equation and it relates the pH of a solution to the proportion of dissociated
acid molecules present. It is especially useful when working with buffer solutions (see next section).

A buffer is able to resist small changes in pH when acid or base is added. The behaviour of acetic acid as it is
titrated with NaOH demonstrates the important points concerning buffers:

In this experiment,
acetic acid has been
titrated from pH 1.8 to
pH 8.5 by addition of
NaOH to give water and
acetate ions (the
conjugate base of acetic
The pH of the acetic
acid has been recorded
throughout the titration
and plotted against the
amount of NaOH
added. The important
features of this titration

At the start (at
pH 1.8) all the
acid is in the
form of
At the mid point
of the titration
(when half the
acid has been
neutralised) the
amount of
CH3COO-. The
pH at this mid
point = 4.8.
At the end of the
titration (pH 8.5)
all of the acid
has been
neutralised to

At the point when [CH3COOH] = [CH3COO-] the pH of the solution is equal to the pK of acetic acid. This can
be predicted from the Henderson-Hasselbach equation:
pH = pKa + log ([CH3COO-] /[CH3COOH])

Convince yourself that when [CH3COO-] = [CH3COOH] the log term reduces to zero and you are left with
pH = pK. For acetic acid this occurs at pH 4.8 hence pK for acetic acid is 4.8

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