Lesson 7:
Acids and Bases


In this lesson we will answer the following questions:

  • What are acids and bases?
  • How do acids and bases participate in chemical reactions?
  • How are acids and bases measured?



Reading Assignment

In addition to the online lecture, read chapter 6 in Basic Chemistry for Water and Wastewater Operators and Chapter 2 and Chapter 21 in Simplified Procedures for Water Examination.


Acids and Bases


Acid-base chemistry is based on one simple reaction - the ionization of water:

H2O double-sided arrow H+ + OH-

As we saw in the last lesson, this equation means that water can break apart into a hydrogen ion and a hydroxide ion.  A hydrogen and a hydroxide ion can also join together to form a water molecule. 

In pure water, hydrogen and hydroxide ions are present in a 1:1 ratio since the only source of these ions is the ionization of water.  Acids and bases are substances which change the balance of hydrogen and hydroxide ions in water.  In this lesson, we will first explore the chemistry of acids and bases, then we will show how to calculate their concentration mathematically.  In the next lesson, we will find out how to calculate the concentration of acids and bases in the lab.


vinegar and onion

Vinegar contains acetic acid, which makes it taste sour. 
Onions release a gas which turns into sulfuric acid when
it reaches your eyes, making them burn. 

What do you think of when you think of acids?  You might think of sour-tasting acidic foods such as lemons.  Or you might think of strong acids, such as battery acid, which can burn your skin or corrode metal.  In this lesson, we will be concerned with the less visible properties of acids - their chemical properties. 

Chemically, acids are substances which increase the concentration of hydrogen ions when they are placed in water.  In this section we will be concerned only with strong acids.  Weak acids act slightly differently and will be discussed in a later section. 

You can recognize strong acids because they are ionic compounds which contain hydrogen ions.  For example, consider the strong acids listed in the table below.  Notice that each compound consists of a hydrogen ion bonded to some sort of anion. 

Nitric acid
Perchloric acid
H+ ClO4-
Sulfuric acid
H+ SO42-
Hydrochloric acid
H+ Cl-
Hydrobromic acid
H+ Br-
Hydriodic acid
H+ I-

When a strong acid is placed in water, it will ionize completely, breaking down into its constituent ions.  For example, hydrochloric acid reacts as shown below:

HCl yields H+ + Cl-

The ionization of a molecule of hydrochloric acid introduces a hydrogen ion and a chloride ion to the solution.  The chloride ion has no effect on the acidity of the water, but the hydrogen ion makes the solution more acidic. 

Diagrams of solutions with and without hydrochloric acid.

The diagrams above show what happens when hydrochloric acid is added to water.  The top diagram merely contains water.  Notice that most of the water is present in its un-ionized state, but that two water molecules have ionized into hydroxide and hydrogen ions.  Despite the presence of hydrogen ions, this solution is neutral (meaning that it is neither acidic nor basic) because the number of hydroxide ions equals the number of hydrogen ions. 

The bottom diagram shows what happens to the water after the addition of hydrochloric acid.  Notice that all of the hydrochloric acid has ionized, so now there are five hydrogen ions and only two hydroxide ions in the solution.  Since there are more hydrogen ions than hydroxide ions present, the solution has become acidic. 


Common bases.

You probably have less familiarity with bases than with acids, so you may be surprised to learn how many bases you deal with in your everyday life.  Soap, baking soda, milk of magnesia, and ammonia all contain bases.  These substances exhibit some of the physical properties of bases, such as feeling slippery, tasting bitter, and dissolving greases.  Bases also irritate the skin and eyes just as acids do. 

Chemically, a base is a substance which decreases the concentration of hydrogen ions when it is placed in water.  Strong bases decrease the hydrogen ion concentration by increasing the hydroxide ion concentration. 

Let's consider what happens when we put sodium hydroxide (a strong base) in water.  Like strong acids, strong bases ionize completely, so the sodium hydroxide breaks down into a sodium ion and a hydroxide ion:

NaOH yields Na+ + OH-

The hydroxide ion released by the sodium hydroxide then reacts with a hydrogen ion from the water, forming a water molecule:

OH- + H+ yields H2O

The reaction between the hydroxide ion and the hydrogen ion removes the hydrogen ion from the solution, making the solution less acidic and more basic.  The two diagrams below show the net reaction of sodium hydroxide with water schematically:

Reaction of sodium hydroxide with water.

Notice that in the top diagram, three water molecules have ionized to produce hydrogen and hydroxide ions.  When three sodium hydroxide molecules are added (in the bottom diagram) the hydroxide ions from the base's dissociation combine with the three hydrogen ions in the solution, forming water.  So the net result of the addition of sodium hydroxide to the water is that the concentration of hydrogen ions becomes lower and the acidity of the solution is decreased. 

In the table below, I have listed some of the strong bases which you may run into in the lab:

Sodium hydroxide NaOH
Lithium hydroxide LiOH
Potassium hydroxide KOH
Rubidium hydroxide RbOH
Cesium hydroxide CsOH
Calcium hydroxide Ca(OH)2
Strontium hydroxide Sr(OH)2
Barium hydroxide Ba(OH)2

Weak Acids and Bases

So far we have talked about strong acids which contain a hydrogen ion and strong bases which contain a hydroxide ion.  However, some acids and bases work slightly differently.  Technically, an acid is any substance which donates a hydrogen ion to a solution and a base is any substance which accepts a hydrogen ion. 

The table below lists some weak acids and bases:

Weak Acids Weak Bases
Acetic acid
Phosphoric acid
Carbonic acid
Hydrofluoric acid
Fluosilicic acid
Magnesium hydroxide
Aluminum hydroxide
Sodium silicate Na2SiO2
NaOCl and Ca(OCl)2
Soda ash

Some of these weak acids and bases ionize just like their strong counterparts, donating hydrogen or hydroxide ions to the solution.  For example, ammonia will ionize as follows:

yields NH4+ + OH-

The difference between strong and weak bases (and between strong and weak acids) is that weak bases do not ionize completely when placed in solution.  So, while every molecule of sodium hydroxide will break down into a sodium ion and a hydroxide ion when placed in solution, only some of the ammonia molecules will ionize under the same conditions.   The illustration below  gives a schematic representation of what happens under these two circumstances. 

comparison of a strong and a weak acid

The top rectangle is an example of a solution containing sodium hydroxide. 
All of the molecules have ionized into their constituent ions.  The bottom rectangle is an example of a solution containing ammonia.  Most of the ammonia stayed in its current state, with only a small percentage breaking apart into ammonium and hydroxide ions. 

Some weak bases not only do not ionize fully, they also do not release a hydroxide ion.  For example, ammonia in its gaseous form reacts as follows:

H2O + NH3 yields NH4+ + OH-

Notice that the ammonia accepted a hydrogen ion from the water, decreasing the acidity of the solution.  So it acted as a base even though it didn't produce hydroxide by ionization. 





You should already be familiar with pH, which is the scale we use to measure the acidity or alkalinity of water.  You will remember that the pH scale runs from 0 to 14, with numbers less than 7 being acidic and with numbers more than 7 being basic (also known as alkaline.)  A pH of 7 means that the substance is neutral. 

pH scale

Although this elementary understanding of the pH scale is enough for many water and wastewater treatment processes, you will need to know more in order to fully understand the chemistry of acids and bases.  pH is actually a measure of the concentration of hydrogen ions in the solution.  Since acids donate hydrogen ions to a solution, they tend to make the pH lower.  Bases, by accepting hydrogen ions, make the pH higher.  A neutral pH of 7, which is the pH of distilled water, contains the same number of hydrogen ions as hydroxide ions. 

The math used to calculate a solution's pH is relatively complicated, and we will not present it here.  Instead, you just need to remember that the lower the pH value, the higher the concentration of hydrogen ions.  For example, stomach acid with a pH of 1 has a much higher concentration of hydrogen ions than tomatoes do with a pH of 4.  Baking soda with a pH of 8 has more hydrogen ions than household ammonia with a pH of 11. 

You shouldn't find it surprising that pH is a measure of the hydrogen ion concentration of a solution, since we have already explained that acids and bases change that concentration.  What you may not realize is that the pH scale only covers a small range of acidity and alkalinity.  In fact, the pH scale is meant to mimic nature by covering the acidity and alkalinity values which might be found in natural waters.  Strong acids and bases, like those discussed on the last page, have pH values at the far ends of the scale or even off the scale.  Concentrated hydrochloric acid has a pH of 0, and one drop of 33% hydrochloric acid in a liter of distilled water can lower the pH from neutral to about 3.  We will discuss ways to measure the concentration of strong acids and bases in a later section.


A neutral pH of 7 may mean that you are dealing with distilled water containing no acids and bases.  In this case, the amount of hydrogen ions and hydroxide ions will be equivalent because they will both be due to the ionization of water.  However, a neutral pH can also be achieved in a solution containing acids and bases as long as the acids and bases have neutralized each other, meaning that the acids have donated as many hydrogen ions as have been accepted by the bases. 

Neutralization reactions occur whenever acids and bases are placed in proximity.  An acid combines with a base to create water and a salt, as shown below:

HCl + NaOH yields H2O + NaCl

Titration, which we will introduce in a later lesson, is based on this neutralization reaction.  You will also need to understand neutralization if you spill an acid or base in lab and want to clean it up safely.  Neutralizing an acid with a base (or vice versa) can aid in cleanup, but you should also be aware that strong acids and bases can react explosively.  Always use weak or low concentration acids or bases for neutralization reactions. 

Neutralization occurs in nature as well.  For example, organisms living in very acidic environments tend to excrete basic wastes which bring the environment back into equilibrium.  Organisms living in basic environments excrete acids instead.  This is one of the reasons that most natural waters, including septic tanks and wastewater treatment ponds which have been allowed to work for some time, tend to have a pH near 7.  In addition, buffers (which we will explain in the next section) neutralize acids and bases both in natural waters and in the laboratory. 


A buffer is a solution containing a weak acid and one of its salts or a weak base and one of its salts.  This solution is able to neutralize acids and bases without allowing the pH of the solution to change greatly.  In lab, buffers are used when the pH of a solution must remain stable. 

Some examples of the pairs which make up buffer solutions are shown in the table below.

Acid or Base
Acetic acid
Sodium acetate
Phosphoric acid
Potassium phosphate
Oxalic acid
Lithium oxalate
Carbonic acid
Sodium carbonate
Ammonium hydroxide
Ammonium nitrate

Let's consider the reactions which occur in the first buffer solution listed - acetic acid (HCH3CO2) plus sodium acetate (NaC2H3O2).  When these two substances are placed in water, the salt will promptly ionize into its constituent ions:

yields C2H3O2- + Na+

The acid, on the other hand, is a weak acid, so it will tend to stay in its current state without ionizing.  So the solution will contain primarily
HCH3CO2, C2H3O2-, and Na+.  The pH of the solution will not have changed since the acid did not ionize. 

What happens if a base is added to the solution?  If we add some sodium hydroxide, the strong base promptly ionizes into its constituent ions, making the solution more basic.  This makes the acetic acid more likely to ionize, so the following reaction occurs:

OH- + HCH3CO2 yields H2O + CH3CO2-

The hydroxide ion from the sodium hydroxide is used up during the reaction.  The pH of the solution remains the same as it was before the addition of sodium hydroxide since the acetic acid neutralized the base. 

How about if we add some acid to the solution?  If we add hydrochloric acid, it will ionize and make the solution more acidic.  But the acidity is promptly neutralized by the
C2H3O2- ions, which combine with the hydrogen ions from the hydrochloric acid to produce acetic acid. 

H+ + C2H3O2- yields HCH3CO2

Of course, a buffer will not continue to neutralize the solution indefinitely.  Eventually, the acid or salt will be used up, and the pH of the solution will begin to change.  The amount of acid or base which a buffer solution is able to neutralize is known as the buffer capacity

Buffer solutions are not limited to the lab.  In natural water systems, carbon dioxide from the air often enters the water, forming carbonic acid.  A salt of carbonic acid, such as calcium carbonate (limestone), may become dissolved in the water from the surrounding rocks and soil.  Thus, a natural buffer solution is formed. 





While pH is used to record the acidity or alkalinity of natural waters, we use a measurement known as normality to show the concentration of the much stronger acid and base solutions we use in the lab.  Normality is based on molarity, but also takes into account a characteristic of acids and bases which we will call "equivalents" and will describe in the next section. 


Although molarity can be used to measure the concentration of acids, it is a relatively unuseful measurement for understanding neutralization reactions.  Why?  Because not every acid or base can add (or remove) the same number of hydrogen ions from solution.  Let's consider two different acids:

Reactions of hydrochloric acid
Reactions of sulfuric acid
HCl yields H+ + Cl- H2SO4 yields H+ + HSO4-

HSO4- yields H+ + SO4-2

As we see in the left side of the table, one molecule of hydrochloric acid adds one hydrogen ion to the solution.  On the other hand, sulfuric acid releases one hydrogen ion, as shown in the first equation, then ionizes again, releasing a second hydrogen ion.  So one molecule of hydrochloric acid could neutralize one molecule of a base while one molecule of sulfuric acid could neutralize two molecules of a base:

HCl + NaOH
yields H2O + NaCl

H2SO4 + 2NaOH yields 2H2O + 2NaSO4

When talking about the concentration of acids or bases, we use measurements which involve equivalents.  An equivalent is the number of moles of hydrogen ions one mole of an acid will donate or one mole of a base will accept.  For example, hydrochloric acid has an equivalent value of 1 because each molecule of acid donates only one hydrogen ion, so one mole of hydrochloric acid will donate one mole of hydrogen ions.  Sulfuric acid, on the other hand, has an equivalent value of 2.  To give you a couple more examples, sodium hydroxide has an equivalent value of 1 while calcium hydroxide has an equivalent value of 2. 


Let's simplify equivalents here:

For instance, you have calcium hydroxide, Ca(OH)2. You can see there are 2 oxygen ions and 2 hydrogen ions, therefore the equivalent is 2. Another instance, sulfuric acid which is listed above, H2SO4. You can see there are 2 Hydrogen ions and 4 Oxygen ions. Since you have to have equal amounts to remove the ions, this equivalent will be 2. If you had 3 Hydrogen ions and 4 Oxygen ions, the equivalent would be 3 because you had enough oxygen ions to take care of the 3 hydrogen ions. Sodium Hydroxide, NaOH, has an equivalent of 1 since there is 1 Oxygen ion and 1 Hydrogen ion. You have to be able to have one oxygen ion for every hydrogen ion you are trying to get rid of.


Normality is the most common measurement used for showing the concentration of acids and bases.  Normality takes into account both the molarity of the solution and the equivalent content of the acid or base, using the equation shown below:

Normality (N) = Molarity (M) × Equivalent (N/M)

If you cancelled units in the equation above, you would find that normality is equal to the number of moles of acid or base per liter. 

Let's consider a 0.5 M solution of HCl.  Since we know that one mole of HCl contains 1 equivalent acid, we can calculate normality as follows:

Normality = (0.5 M) × (1 N/M)

Normality = 0.5 N

For all acids and bases with an equivalent value of 1, the normality of the solution will be equal to the molarity of the solution. 

But not every acid and base will have a normality equal to its molarity.  How about a 3 M solution of barium hydroxide?  Barium hydroxide releases two hydroxide ions per molecule of the base, so the equivalent value is 2.  As a result, we would calculate normality as follows:

Normality = (3 M) × (2 N/M)

Normality = 6 N

Calculating Normality From Grams

To calculate the normality of a solution you are preparing, you need to combine the equation for calculating molarity and the equation for calculating normality.  To simplify matters, we've combined the two equations for you:

Formula for calculating normality

So what would the normality of the solution be if we dissolved 6.80 grams of calcium hydroxide in water to produce a 0.50 L solution?  First, we have to calculate the molar mass of calcium hydroxide -  74.10 g/mol.  Then we have to figure out the equivalent value of calcium hydroxide - 2.  And, finally, we can just plug numbers into the equation:


The normality of the resulting solution would be 0.37 N.

Calculating Dilutions

Once you have calculated the normality of an acid or base solution, you can easily calculate the concentration of any dilutions of that solution.  The formula used is essentially the same as that used for any other dilution calculation:

N1V1 = N2V2

N1 = normality of the first solution
V1 = volume of the first solution
N2 = normality of the second solution
V2 = volume of the second solution

For example, after producing the 0.5 L of a 0.37 N solution of calcium hydroxide in the last section, how would you dilute it to form a 0.25 N solution? 

(0.37 N) (0.50 L) = (0.25 N) V2

0.74 L = V2

Based on the calculations above, we know that we have to add enough water to the 0.37 N solution so that the total volume reaches 0.74 L.  Then we would have a 0.25 N solution. 

Converting from Other Units

Converting the concentration of a solution between normality and molarity was explained in an earlier section.  We can combine the equation introduced there with the equations introduced in Lesson 4 to convert from normality to the other types of concentration (assuming aqueous solutions.)

convert to mg/L

converting to ppm

convert to %

For example, if you had a solution of 1 N strontium hydroxide, what is its percent concentration?






The final topic we will introduce in this lesson is alkalinity, which is the capacity of a solution to neutralize a strong acid.  Despite the name, you should not think of alkalinity as the amount of base found in the solution; instead, alkalinity is a measurement of the buffering ability of the solution.  Water high in alkalinity will be able maintain its pH despite the addition of acids. 

Alkalinity in natural waters is caused primarily by carbonate (CO3-2) and bicarbonate (HCO3-) ions.  A few other causes of alkalinity may also be present in water, but usually at much lower concentrations.  These other types of alkalinity can include hydroxide, borate, silicate, phosphate, ammonium, and sulfide. 

How are hardness and alkalinity related? They are both expressed as mg/L CaCO3. In tap water, when the concentration of hardness and alkalinity are the same, both are probably due to dissolved calcium carbonate. Calcium carbonate does not dissolve well above pH 7.0, so other chemicals like calcium chloride and sodium bicarbonate can be used to adjust hardness and alkalinity independently.

Alkalinity usually enters the water as salts, such as calcium carbonate (also known as limestone).  Carbonate and bicarbonate can also be formed when carbon dioxide from the air is dissolved in the water. 

In any case, all forms of alkalinity operate similarly to neutralize acids.  Let's see what happens when we add sulfuric acid to water containing bicarbonate alkalinity:

2HCO3- + H2SO4 yields 2H2CO3 + SO42-

First, the sulfuric acid loses its hydrogen ions, which would usually increase the acidity of the water.  However, the bicarbonate accepts the hydrogen ions, turning into carbonic acid.  Since carbonic acid is a weak acid, it tends to stay in its un-ionized state, so the pH of the water remains neutral.

The Carbonate System

The relationship between alkalinity and pH is relatively complex.  As mentioned in the last section, higher alkalinity tends to prevent water from becoming acidic.  In addition, pH influences the type of alkalinity found in water.  In this section, we will consider the carbonate system, which is the relationship between pH and the different forms of carbonate - carbonic acid, bicarbonate, and carbonate. 

The graph above summarizes the carbonate system.  Notice that the form of carbonate in the water is very dependent upon pH.  At a low pH, the carbonate is present as carbonic acid.  Bicarbonate can be found in water with a pH between 4.3 and 12.3.  Above a pH of 8.3, carbonate is also present. 

What causes this relationship between carbonate species and pH?  Carbon dioxide, carbonic acid, bicarbonate, and carbonate can transform back and forth by gaining or losing hydrogen ions in the reactions shown below:

CO2 + H2O double-sided arrow H2CO3

H2CO3 double-sided arrow HCO3- + H+

HCO3- double-sided arrow CO32- + H+

Based on the concentration of hydrogen ions in the solution (the acidity of the solution), various of these reactions will be more or less likely to take place.  For example, when the water is very acidic (containing a high concentration of hydrogen ions), the hydrogen ions tend to attach to carbonate or bicarbonate, forming carbonic acid.  However, if the water is very basic (containing a lower concentration of hydrogen ions), then carbonic acid tends to break apart, adding hydrogen ions to the solution. 

In the Treatment Plant

Alkalinity is of little sanitary significance, although extremely high levels of alkalinity in water can be problematic.  It has been reported that a carbonate concentration of 350 ppm is unhealthy.  In addition, free caustic (hydroxide) alkalinity may impart a bitter taste to the water and can even cause a burning sensation at high concentrations.  However, in most water treatment plants, operators are more concerned with ensuring that there is enough alkalinity in the water to promote coagulation and prevent corrosion than they are with removing alkalinity from water.

Alkalinity is essential for proper coagulation.  When alum is added to raw water, the alum reacts with the alkalinity present to form floc.
  As a rule of thumb, coagulation usually requires an alkalinity equal to half of the amount of alum used.  So, if your plant treats raw water with 25 ppm of alum, then a minimum of 12.5 ppm of alkalinity must be present in the water for floc to form.  If insufficient alkalinity is present in the water during coagulation, then dense floc with not form and soluble alum will be left in the water. 

Since coagulation uses up alkalinity in the water, treated water often tends to be corrosive (acidic).  The operator must make sure that an adequate amount of alkalinity is present in the treated water as well as in the raw water to prevent corrosion of pipes in the distribution system.  We will discuss the math used to determine the appropriate alkalinity of treated water in the alkalinity lab. 

Water treatment may require the addition of artificial alkalinity to enhance coagulation or to prevent corrosion.  If the source water does not contain an adequate amount of natural alkalinity, treatment will usually include the addition of lime or soda ash to artificially increase the amount of alkalinity in the water. 


Acids and bases are substances which change the balance of hydrogen and  hydroxide ions in water.  Both are divided into two categories - strong acids or bases which ionize completely in water, and weak acids or bases which ionize only partially in water. 

Acids and bases undergo a variety of chemical reactions.  Acids donate hydrogen ions to water while bases remove hydrogen ions from water.  When acids and bases are brought together, they neutralize each other.  Buffers can neutralize both acids and bases. 

pH can be used to measure the balance of acidity and alkalinity in water.  Normality, in contrast, is used to measure the concentration of a specific acid or base in a relatively strong solution. 

Alkalinity is the buffer capacity of water, usually caused by carbonate and bicarbonate ions.  The type of alkalinity found in water will depend on the pH of the water.  Regardless of the type of alkalinity, a certain concentration of alkalinity is required in the water treatment plant to promote good coagulation and to prevent corrosive water. 


"Acids and Bases."  1997-2004.  Chemtutor. 

Ferwerda, E.  2004.  "Chemistry: Objectives - Chapters 20 and 21."  Chemistry Teacher's Work Site.

Fretzin, L.  2001.  "The Properties of Acids and Bases."  Science is Fun.

Jacobs, B.  April 2004.  "
Acids Bases and Salts."  Chemistry Coach. 

Kerri, K.D.  2002.  Water Treatment Plant Operation.  California State University: Sacramento.

Olmsted, J., and G.M. Williams.  1997.  Chemistry: The Molecular Science.  Wm. C. Brown Publishers: Boston. 


Table 3: Acids, Bases, and Buffers



New Formulas Used

To calculate normality from molarity:

Normality (N) = Molarity (M) × Equivalent (N/M)

To calculate normality from amount of solute:

Formula for calculating normality

To calculate normality during dilutions:

N1V1 = N2V2

To calculate normality from mg/L:

convert to mg/L

To calculate normality from ppm:

To calculate normality from percent concentration:

convert to %


Complete the interactive exercises in Assignment 7

This assignment will give you practice with the math covered in Lesson 7 as well as information covered in the pH and alkalinity labs listed below.  You should print the assignment and write out your calculations on a separate sheet of paper so that you can go back and check for errors if you get a question wrong. You may do the Assignment online to get credit or print it out and send it to the instructor.  It will require the Flash flayer to view, which should already be installed on your machine.



Read the pH and alkalinity labs and do the assignment listed above, there are questions concerning the virtual labs included.



Answer the questions in the Lesson 7 quiz When you have gotten all the answers correct, print the page and either mail or fax it to the instructor. You may also take the quiz online and directly submit it into the database for a grade.