What you should be able to do

Acid-base Introduction
Chem1 General Chemistry Virtual Textbook → Acid­base concepts → Introduction
What is an acid? What is a base?
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The concepts of an acid, a base, and a salt are very old
On this page:
ones that have undergone several major refinements as
Acids and the hydrogen ion
chemical science has evolved. Our treatment of the
subject at this stage will be mainly conceptual and
qualitative, emphasizing the definitions and fundamental
ideas associated with acids and bases. We will not cover
What you should be able to do
calculations involving acid-base equilibria in these
Concept map
1 Acids
The term acid was first used in the seventeenth century; it comes from the
Latin root ac­, meaning “sharp”, as in acetum, vinegar. Some early writers
suggested that acidic molecules might have sharp corners or spine­like
projections that irritate the tongue or skin.
Acids have long been recognized as a distinctive class of compounds whose
aqueous solutions exhibit the following properties:
A characteristic sour taste
(think of lemon juice!);
ability to change the color of
litmus* from blue to red;
react with certain metals to
produce gaseous H2;
*Litmus is a natural dye found in certain
lichens. The name is of Scandinavian origin,
e.g. lit (color) + mosi (moss) in Icelandic.
"Litmus test" has acquired a meaning that
transcends both Chemistry and science to
denote any kind of test giving a yes/no
react with bases to form a salt
and water.
How oxygen got mis­named
The first chemistry­based definition of an acid turned out to be wrong: in
1787, Antoine Lavoisier, as part of his masterful classification of
substances, identified the known acids as a separate group of the “complex
substances” (compounds). Their special nature, he postulated, derived
from the presence of some common element that embodies the “acidity”
Acid-base Introduction
principle, which he named oxygen, derived from the Greek for “acid
Lavoisier had recently assigned this name to the new gaseous element
that Joseph Priestly had discovered a few years earlier as the essential
substance that supports combustion. Many combustion products (oxides)
do give acidic solutions, and oxygen is in fact present in most acids, so
Lavoisier’s mistake is understandable. In 1811 Humphrey Davy showed
that muriatic (hydrochloric) acid (which Lavoisier had regarded as an
element) does not contain oxygen, but this merely convinced some that
chlorine was not an element but an oxygen­containing compound.
Although a dozen oxygen­free acids had been discovered by 1830, it was
not until about 1840 that the hydrogen theory of acids became generally
accepted. By this time, the misnomer oxygen was too well established a
name to be changed. The root oxy comes from the Greek word οξνς,
which means "sour".
2 Acids and the hydrogen ion
The key to understanding acids (as well as bases and salts) had to await
Michael Faraday’s mid­nineteenth century discovery that solutions of salts
(known as electrolytes) conduct electricity. This implies the existence of
charged particles that can migrate under the influence of an electric field.
Faraday named these particles ions (“wanderers”). Later studies on
electrolytic solutions suggested that the properties we associate with acids
are due to the presence of an excess of hydrogen ions in the solution. By
1890 the Swedish chemist Svante Arrhenius (1859­1927) was able to
formulate the first useful theory of acids:
[image link]
"an acidic substance is one whose
molecular unit contains at least
one hydrogen atom that can
dissociate, or ionize, when
dissolved in water, producing a
hydrated hydrogen ion and an
hydrochloric acid
HCl → H+(aq) + Cl–(aq)
sulfuric acid
H2SO4→ H+(aq) + HSO4–(aq)
hydrogen sulfite
HSO3–(aq) → H+(aq) + SO32–(aq)
acetic acid
H3CCOOH → H+(aq) +
Strictly speaking, an “Arrhenius acid” must contain hydrogen. However,
there are substances that do not themselves contain hydrogen, but still
yield hydrogen ions when dissolved in water; the hydrogen ions come from
the water itself, by reaction with the substance. A more useful operational
definition of an acid is therefore the following:
An acid is a substance that yields an excess of hydrogen
ions when dissolved in water.
Acid-base Introduction
There are three important points to understand about hydrogen in acids:
Although all Arrhenius acids contain hydrogen, not all hydrogen atoms in a
substance are capable of dissociating; thus the –CH3 hydrogens of acetic acid
are “non­acidic”. An important part of knowing chemistry is being able to
predict which hydrogen atoms in a substance will be able to dissociate into
hydrogen ions; this topic is covered in a later lesson of this set.
Those hydrogens that do dissociate can do so to different degrees. The strong
acids such as HCl and HNO3 are effectively 100% dissociated in solution. Most
organic acids, such as acetic acid, are weak; only a small fraction of the acid is
dissociated in most solutions. HF and HCN are examples of weak inorganic
Acids that possess more than one dissociable hydrogen atom are known as
polyprotic acids; H2SO4 and H3PO4 are well­known examples. Intermediate
forms such as HPO42–, being capable of both accepting and losing protons, are
called ampholytes.
sulfuric acid
HSO4– hydrogen
→ sulfate ("bisulfate")
hydrosulfide ion
sulfate ion
→ sulfide ion
→ dihydrogen phosphate → hydrogen phosphate
oxalic acid
hydrogen oxalate ion
oxalate ion
phosphate ion
You will find out in a later section of this lesson that hydrogen ions cannot
exist as such in water, but don't panic! It turns out that chemists still find
it convenient to pretend as if they are present, and to write reactions that
include them.
3 Bases
The name base has long been associated with a class of compounds whose
aqueous solutions are characterized by:
a bitter taste;
a “soapy” feeling when applied to the skin;
ability to restore the original blue color of litmus that has been turned red by
ability to react with acids to form salts.
react with certain metals to produce gaseous H2;
Just as an acid is a substance
that liberates hydrogen ions into
solution, a base yields
hydroxide ions when dissolved
in water:
The word “alkali” is often applied to
strong inorganic bases. It is of Arabic
origin, from al­kali ("the ashes") which
refers to the calcined wood ashes that
were boiled with water to obtain potash
Acid-base Introduction
NaOH(s) → Na+(aq) + OH–(aq)
which contains the strong base KOH,
used in soap making. The element name
potassium and its symbol K (from the
Latin kalium) derive from these sources.
Sodium hydroxide is an
Arrhenius base because it
contains hydroxide ions. However, other substances which do not contain
hydroxide ions can nevertheless produce them by reaction with water, and
are therefore also classified as bases. Two classes of such substances are
the metal oxides and the hydrogen compounds of certain nonmetals:
Na2O(s) + H2O → [2 NaOH] → 2 Na+(aq) + 2 OH–(aq)
NH3 + H2O → NH4+(aq) + OH–(aq)
We can therefore define a base as follows:
A base is a substance that yields an excess of hydroxide
ions when dissolved in water.
4 Neutralization
Acids and bases react with one another to yield two products: water, and
an ionic compound known as a salt. This kind of reaction is called a
neutralization reaction.
This "molecular" equation is convenient to write, but we need to re­cast it
as a net ionic equation to reveal what is really going on here when the
reaction takes place in water, as is almost always the case.
H+ + Cl– + Na+ + OH–→ Na+ + Cl– + H2O
If we cancel out the ions that appear on both sides (and therefore don't
really participate in the reaction), we are left with the net equation
H+(aq) + OH–(aq) → H2O (1)
which is the fundamental process that occurs in all neutralization reactions.
Confirmation that this equation describes all neutralization reactions that
take place in water is provided by experiments indicating that no matter
what acid and base are combined, all liberate the same amount of heat
(57.7 kJ) per mole of H+ neutralized.
In the case of a weak acid, or a base that is not very soluble in water,
more than one step might be required. For example, a similar reaction can
occur between acetic acid and calcium hydroxide to produce calcium
2 CH3COOH + Ca(OH)2 → CH3COOCa + 2 H2O
Acid-base Introduction
If this takes place in aqueous solution, the reaction is really between the
very small quantities of H+ and OH– resulting from the dissociation of the
acid and the dissolution of the base, so the reaction is identical with (1):
H+(aq) + OH–(aq) → H2O If, on the other hand, we add solid calcium hydroxide to pure liquid acetic
acid, the net reaction would include both reactants in their "molecular"
2 CH3COOH(l) + Ca(OH)2 (s) → 2 CH3COO– + Ca2+ + 2 H2O
The “salt” that is produced in a neutralization reaction consists simply of
the anion and cation that were already present. The salt can be recovered
as a solid by evaporating the water.
What you should be able to do
Make sure you thoroughly understand the following essential ideas which
have been presented above.
Suggest simple tests you could carry out to determine if an unknown
substance is an acid or a base.
State the chemical definitions of an acid and a base in terms of their behavior
in water.
Write the formula of the salt formed when a given acid and base are
Concept Map
Acid-base Introduction
Page last modified: 09.09.2010
⇐ index intro | pH | Brønsted | competition | electrons | structures | gallery © 2007 by Stephen Lower ­ Simon Fraser University ­ Burnaby/Vancouver Canada
For information about this Web site or to contact the author, please see the Chem1 Virtual Textbook home page.
This work is licensed under a Creative Commons Attribution­NonCommercial 2.5 License.
pH and titration
Chem1 General Chemistry Virtual Textbook →Acid­base concepts →pH and titration
pH and titration
Aqueous solutions of acids and bases
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On this page:
Ion product of water
pH ­ definition
The pH scale
Acid­base titration
What you should be able to do
Concept map
As you will see in the lesson that follows this one, water
plays an essential role in acid-base chemistry as we
ordinarily know it. To even those who know very little
about chemistry, the term pH is recognized as a
measure of "acidity", so the major portion of this unit is
devoted to the definition of pH and of the pH scale. But
since these topics are intimately dependant on the
properties of water and its ability do dissociate into
hydrogen and hydroxyl ions, we begin our discussion with
this topic. We end this lesson with a brief discussion of
acid-base titration— probably the most frequently
carried-out chemistry laboratory operation in the world.
1 Dissociation of water
The ability of acids to react with bases depends on the
tendency of hydrogen ions to combine with hydroxide
ions to form water:
H+(aq) + OH–(aq) → H2O (1)
All chemical reactions that
take place in a single
phase (such as in a
solution) are theoretically
"incomplete" and are said
to be reversible.
This tendency happens to be very great, so the reaction is practically complete
— but not "completely" complete; a few stray H+ and OH– ions will always be
present. What's more, this is true even if you start with the purest water
attainable. This means that in pure water, the reverse reaction, the
"dissociation" of water
H2O → H+(aq) + OH–(aq) (2)
will proceed to a very slight extent. Both reactions take place simultaneously,
but (1) is so much faster than (2) that only a minute fraction of H2O molecules
are dissociated.
Liquids that contain ions are able to conduct an electric current. Pure water is
practically an insulator, but careful experiments show that even the most highly
purified water exhibits a very slight conductivity that corresponds to a
concentration of both the H+ ion and OH– ions of almost exactly 1.00 × 10–
7mol L–1 at 25°C.
pH and titration
Problem Example 1
What fraction of water molecules in a litre of water are dissociated
Solution: 1 L of water has a mass of 1000 g. The number of moles in 1000 g of
H2O is
(1000 g)/(18 g mol–1) = 55.5 mol. This corresponds to (55.5 mol)(6.02E23 mol­1)
= 3.34E25 H2O molecules.
An average of 10­7 mole, or (10­7)(6.02E23) = 6.0E16 H2O molecules will be
dissociated at any time. The fraction of dissociated water molecules is therefore
(6.0E16)/(3.3E25) = 1.8E–9.
Thus we can say that only about two out of every billion (109) water molecules will
be dissociated.
Ion product of water
The degree of dissociation of water is so small that you might wonder why it is
even mentioned here. The reason stems from an important relationship that
governs the concentrations of H+ and OH– ions in aqueous solutions:
[H+][OH–] = 1.00 × 10–14 (3) must know this!
in which the square brackets [ ] refer to the
concentrations (in moles per litre) of the substances
they enclose.
The quantity 1.00 x 10–14
is commonly denoted by
Kw. Its value varies
slightly with temperature,
pressure, and the
presence of other ions in
the solution.
This expression is known as the ion product of
water, and it applies to all aqueous solutions, not just
to pure water. The consequences of this are far­
reaching, because it implies that if the concentration of
H+ is large, that of OH– will be small, and vice versa. This means that H+ ions
are present in all aqueous solutions, not just acidic ones.
This leads to the following important definitions, which you must know:
acidic solution
[H+] > [OH–]
alkaline ("basic")
[H+] < [OH–]
neutral solution
[H+] = [OH–] = 1.00×10–7
mol L–1
Take special note of the followng definition:
A neutral solution is one in which the concentrations of H+ and
OH– ions are identical.
The values of these concentrations are constrained by Eq. 3. Thus, in a neutral
solution, both the hydrogen­ and hydroxide ion concentrations are 1.00 × 10–
7 mol L–1:
pH and titration
[H+][OH–] = [1.00 × 10–7][1.00 × 10–7] =1.00 × 10–14
Hydrochloric acid is a typical strong acid that is totally dissociated in solution:
HCl → H+(aq) + Cl–(aq)
A 1.0M solution of HCl in water therefore does not really contain any significant
concentration of HCl molecules at all; it is a solution in of H+ and Cl– in which
the concentrations of both ions are 1.0 mol L–1. The concentration of hydroxide
ion in such a solution, according to Eq 2, is
[OH–] = (Kw)/[H+] = (1.00 x 10–14) / (1 mol L–1) = 1.00 x 10–14 mol L–1.
Similarly, the concentration of hydrogen ion in a solution made by dissolving
1.0 mol of sodium hydroxide in water will be 1.00 x 10–14 mol L–1.
2 pH
When dealing with a range of values (such as the variety of hydrogen ion
concentrations encountered in chemistry) that spans many powers of ten, it is
convenient to represent them on a more compressed logarithmic scale. By
convention, we use the pH scale to denote hydrogen ion concentrations:
pH = – log10 [H+] (4) must know this!
or conversely, [H+] = 10–pH .
This notation was devised by the Danish chemist Søren
Sørensen (1868­1939) in 1909. There are several accounts of
why he chose "pH"; a likely one is that the letters stand for the
French term pouvoir hydrogène, meaning "power of
hydrogen"— "power" in the sense of an exponent. It has since
become common to represent other small quantities in "p­
notation". Two that you need to know in this course are the
pOH = – log10 [OH–]
pKw = – log Kw (= 14 when Kw = 1.00 × 10–14)
Note that pH and pOH are expressed as numbers without any units, since
logarithms must be dimensionless.
Recall from Eq 3 that [H+][OH–] = 1.00 × 10–14; if we write this in "p­
notation" it becomes
pH + pOH = 14 (5) must know this!
In a neutral solution at 25°C, pH = pOH = 7.0. As pH increases, pOH
diminishes; a higher pH corresponds to an alkaline solution, a lower pH to an
acidic solution. In a solution with [H+] = 1 M , the pH would be 0; in a
0.00010 M solution of H+, it would be 4.0. Similarly, a 0.00010 M solution of
pH and titration
NaOH would have a pOH of 4.0, and thus a pH of 10.0. It is very important that
you thoroughly understand the pH scale, and be able to convert between [H+]
or [OH–] and pH in both directions.
Problem Example 2
The pH of blood must be held very close to 7.40. Find the hydroxide ion
concentration that corresponds to this pH.
Solution: The pOH will be (14.0 – 7.40) = 6.60.
[OH–] = 10–pOH = 10–6.6 = 2.51 x 10–7 M
The pH scale
The range of possible pH values
runs from about 0 to 14.
The word "about" in the above
statement reflects the fact
that at very high
concentrations (10 M
hydrochloric acid or sodium
hydroxide, for example,) a
significant fraction of the ions
will be associated into neutral
pairs such as H+·Cl–, thus
reducing the concentration of
“available” ions to a smaller
value which we will call the
effective concentration. It is
the effective concentration of
H+ and OH– that determines
the pH and pOH. For solutions
in which ion concentrations
don't exceed 0.1 M, the
formulas pH = –log [H+] and
pOH = –log[OH–] are
generally reliable, but don't expect a 10.0 M solution of a strong acid to have a
pH of exactly –1.00!
The table shown here will help give you a general feeling for where common
substances fall on the pH scale. Notice especially that
most foods are slightly acidic;
the principal "bodily fluids" are slightly alkaline, as is seawater— not surprising,
since early animal life began in the oceans.
the pH of freshly­distilled water will drift downward as it takes up carbon dioxide
from the air; CO2 reacts with water to produce carbonic acid, H2CO3.
the pH of water that occurs in nature varies over
a wide range. Groundwaters often pick up
additional CO2 respired by organisms in the soil,
but can also become alkaline if they are in contact
with carbonate­containing sediments. "Acid" rain
is by definition more acidic than pure water in
equilibrium with atmospheric CO2, owing mainly
to sulfuric and nitric acids that originate from
fossil­fuel emissions of nitrogen oxides and SO2.
pH indicators
pH and titration
The colors of many dye­like compounds depend on the pH, and can serve as
useful indicators to determine whether the pH of a solution is above or below
a certain value.
Here is a list of ordinary foods and household substances that can serve as indicators
Natural indicator dyes
known of these is of course litmus,
which has served as a means of
distinguishing beween acidic and
alkaline substances since the early
18th century.
pigments are also dependent on
the pH. You may have noticed that
the flowers of some hydrangea
shrub species are blue when grown
in acidic soils, and white or pink in
alkaline soils.
Red cabbage is a popular make­it­yourself indicator. Here is a typical recipe.
Universal indicators
Most indicator dyes show only one color change, and
thus are only able to determine whether the pH of a
solution is greater or less than the value that is
characteristic of a particular indicator. By combining a
variety of dyes whose color changes occur at different
pHs, a "universal" indicator can be made.
Commercially­prepared pH test papers of this kind are
available for both wide and narrow pH ranges.
3 Titration
Since acids and bases readily react with each other, it is
experimentally quite easy to find the amount of acid in a solution
by determining how many moles of base are required to
neutralize it. This operation is called titration, and you should
already be familiar with it from your work in the Laboratory.
We can titrate an acid with a base, or a base with an acid. The
substance whose concentration we are determining (the analyte)
is the substance being titrated; the substance we are adding in
measured amounts is the titrant. The idea is to add titrant until
the titrant has reacted with all of the analyte; at this point, the number of
moles of titrant added tells us the concentration of base (or acid) in the
pH and titration
solution being titrated.
36.00 ml of a solution of HCl was titrated with 0.44 M KOH. The volume of KOH
solution required to neutralize the acid solution was 27.00 ml. What was the
concentration of the HCl?
Solution: The number of moles of titrant added was (.027 L)(.44 mol L–1) = .0119 mol. Because one mole of KOH reacts with one mole
of HCl, this is also the number of moles of HCl; its concentration is therefore
(.0119 mol) ÷ (.036 L) = 0.33 M .
Titration curves
The course of a titration can be followed
by plotting the pH of the solution as a
function of the quantity of titrant added.
The figure shows two such curves, one
for a strong acid (HCl) and the other for
a weak acid, acetic acid, denoted by HAc.
Looking first at the HCl curve, notice how
the pH changes very slightly until the
acid is almost neutralized. At that point,
which corresponds to the vertical part of
the plot, just one additional drop of
NaOH solution will cause the pH to jump to a very high value— almost as high
as that of the pure NaOH solution.
Compare the curve for HCl with that of HAc. For a weak acid, the pH jump near
the neutralization point is less steep. Notice also that the pH of the solution at
the neutralization point is greater than 7. These two characteristics of the
titration curve for a weak acid are very important for you to know.
If the acid or base is polyprotic, there will be
a jump in pH for each proton that is titrated.
In the example shown here, a solution of
carbonic acid H2CO3 is titrated with sodium
hydroxide. The first equivalence point (at
which the H2CO3 has been converted
entirely into bicarbonate ion HCO3–) occurs
at pH 8.3. The solution is now identical to
one prepared by dissolving an identical
amount of sodium bicarbonate in water.
Addition of another mole equivalent of hydroxide ion converts the bicarbonate
into carbonate ion and is complete at pH 10.3; an identical solution could be
prepared by dissolving the appropriate amount of sodium carbonate in water.
Finding the equivalence point: indicators
When enough base has been added to react completely with the hydrogens of a
monoprotic acid, the equivalence point has been reached. If a strong acid and
strong base are titrated, the pH of the solution will be 7.0 at the equivalence
point. However, if the acid is a weak one, the pH will be greater than 7; the
pH and titration
“neutralized” solution will not be “neutral” in terms of pH. For a polyprotic acid,
there will be an equivalence point for each titratable hydrogen in the acid.
These typically occur at pH values that are 4­5 units apart, but they are
occasionally closer, in which case they may not be readily apparent in the
titration curve.
The key to a successful titration is knowing when the equivalance point has
been reached. The easiest way of finding the equivalence point is to use an
indicator dye; this is a substance whose color is sensitive to the pH. One such
indicator that is commonly encountered in the laboratory is phenolphthalein; it
is colorless in acidic solution, but turns intensely red when the solution
becomes alkaline. If an acid is to be titrated, you add a few drops of
phenolphthalein to the solution before beginning the titration. As the titrant is
added, a local red color appears, but quickly dissipates as the solution is
shaken or stirred. Gradually, as the equivalence point is approached, the color
dissipates more slowly; the trick is to stop the addition of base after a single
drop results in a permanently pink solution.
Different indicators change color at different pH values; see here for an
illustrated list. Since the pH of the equivalance point varies with the strength of
the acid being titrated, one tries to fit the indicator to the particular acid. One
can titrate polyprotic acids by using a suitable combination of several
indicators, as is illustrated above for carbonic acid.
What you should be able to do
Make sure you thoroughly understand the following essential ideas which have
been presented above. It is especially imortant that you know the precise
meanings of all the highlighted terms in the context of this topic.
Define the ion product of water, and know its room­temperature value.
State the criteria, in terms of H+ and OH– concentrations, of an acidic, alkaline,
and a neutral solution.
Given the effective hydrogen ion concentration in a solution, calculate the pH.
Conversely, find the hydrogen­ or hydroxide ion concentration in a solution having a
given pH.
Find the pH or pOH of a solution when either one is known.
Describe the process of acid­base titration, and explain the significance of the
equivalence point.
Sketch a typical titration curve for a monoprotic or polyprotic acid.
Concept Map
pH and titration
Page last modified: 17.02.2007
⇐ index | intro pH Brønsted | competition | electrons | structures | gallery< © 2007 by Stephen Lower ­ Simon Fraser University ­ Burnaby/Vancouver Canada
For information about this Web site or to contact the author, please see the Chem1 Virtual Textbook home page.
This work is licensed under a Creative Commons Attribution­NonCommercial 2.5 License.