Lesson 12:

Titration, Hardness and Alkalinity



In this lesson we will answer the following questions:
  • How is titration used to measure the normality of an acid or base solution?
  • What is hardness?

Reading Assignment

Along with the online lecture read chapter 13 in Basic Chemistry for Water and Wastewater Operators and Chapters 2 and 14 in Simplified Procedures for Water Examination.



This lesson begins where the last lesson left off, continuing with our explanation of acid-base chemistry.  First, you will learn how to test the normality of an acid or base in the lab using a technique known as titration.  Then we will discuss how to titrate using comparison to a known standard.  Finally, we will introduce alkalinity, which is a natural type of buffer found in water. 



Titration is a method used to determine the concentration of a solute in a solution.  In this lesson, we will be concerned with using titration to determine the normality of an acid or base. 

Titration is based on the neutralization reaction introduced in the last lesson.  The idea is very simple - if you add a base to an acid until the acid reaches a neutral pH, then the number of moles of base added will equal the number of moles of acid in the original solution.  You can also add an acid to a base to determine the number of moles of base in the original solution.  In lab, we will use titration for a different, but related, purpose - to measure the alkalinity of a solution.  We'll discuss alkalinity in a later section. 

As you will see in the following sections, titration involves two steps.  First you perform a laboratory procedure to determine how much base (or acid) is required to neutralize your sample acid (or base.)  Then you perform mathematical calculations to determine the normality of your sample. 

Laboratory Procedure

In this section, we will present a brief overview of the lab procedure used to determine the normality of an acid or base using titration.  You will learn more about the specifics of the titration procedure in lab.  In addition, you can view a step by step explanation of titration on Dartmouth's Chemlab page.  Our goal here is merely to give you an broad overview of the procedure so that you will understand where the numbers we will use in our calculations come from.

The laboratory portion of titration has two requirements:
  1. You must be able to very accurately determine the amount of acid or base added to the sample.
  2. You must be able to determine when the pH of the solution reaches 7.
The first requirement is met by using the titration setup below:

titration setup

The titrant, which is the acid or base used to neutralize your sample, is placed in a buret.  A buret allows you to slowly add small amounts of titrant to your sample by opening and closing the stopcock.  The buret is also ruled off in small increments, so that you can read precisely how much titrant you have added to your solution.

The second criteria for titration is met by using an indicator, which is a chemical which changes color when the sample reaches a pH of 7.  The indicator does not participate in the reaction; instead, it allows us to tell when the sample has been neutralized. 

The laboratory procedure merely involves adding titrant to the sample until the indicator changes color.  Then the amount of titrant used is read off the buret.  Now we're ready to move on to the mathematical calculations portion of the titration procedure.

Titration Calculations

As mentioned previously, the number of moles of acid or base added in the form of titrant will be equal to the number of moles of acid or base in the unknown.  So we can use the following equation to calculate the normality of our sample acid or base:

(Normality of the titrant) × (Volume of the titrant) = (Normality of the unknown) × (Volume of the unknown)

Let's consider a sample titration.  We have 100.0 mL of a hydrochloric acid solution with an unknown concentration.  Titrating with 2.00 N sodium hydroxide, it takes 29.3 mL of the base to reach the endpoint.  What was the concentration of our acid solution?

Since we know the that the titrant is the sodium hydroxide solution and the hydrochloric acid is the unknown, we can simply plug in the numbers and solve the equation:

(2.00 N) × (29.3 mL) = (Normality of the unknown) × (100.0 mL)

0.586 = Normality of the unknown.

So the assayed concentration of the acid is found to be 0.586 N.  The accuracy of this concentration will depend on the precision with which we made our measurements and calculations. 

Keep in mind when using the equation introduced above that it can only be used when the acid and base's concentrations are stated as normality.  Since 1 N of any base will contain 1 mole of base per liter and 1 N of any acid will contain 1 mole of acid per liter, this unit prevents us from having to worry about the equivalent values of the acid and the base. 

Also notice that our example titration involved adding a base to an acid.  If we had a base with an unknown concentration, we would have used an acid for titration.  Then the acid would have been the titrant and the base would have been the unknown. 



Comparison to a Standard


Every measurement is made by comparing an unknown value to a standard value.  For example, we could measure the length of a computer screen using a ruler.  The computer screen's length is an unknown value, but we can measure it using the known value of an inch on a ruler.  By counting how many of the known values are equal to the unknown value, we are able to estimate the unknown value using the formula below:

Unknown value = (Known value) × (Number of known values)

For example, we might calculate the length of the screen as follows:

Unknown value = (1 inch) × (12)

Unknown value = 12 inches

This, of course, is how we've always made measurements, though we don't usually think of it in this manner.  However, thinking of measurement as multiplying a number of knowns by the value of the known can be helpful during certain calculations.  Consider a situation in which you need to measure the width of a board, but had no measuring tape with you.  Instead, you might use the pencil in your pocket to estimate the board's width.  You find that it takes two and a half pencil lengths to go across the board.  Later, you can measure the length of the pencil (8 inches) and then calculate the width of the board:

Unknown value = (8 inches) (2.5)

Unknown value = 20 inches

So you know that the board is about 20 inches wide.

On this page we'll consider how we use the concept of measuring with respect to a known standard in order to measure acidity.

Measuring Normality

In most cases, it will be simplest to measure an unknown acid or base's concentration using the titration method outlined on the last page.  However, if  you do not know the identity of the unknown and do not know the concentration of the titrant, you can still calculate an acid or base's concentration by comparing it to a known standard. 

Let's consider a sample situation in which you want to measure the acidity of coal ashes.  The coal ashes could contain a variety of different types of acids, all of which would be difficult to extract from the ashes.  So you might decide to measure the acidity of the ashes' acids by comparing them to a known standard. 

The only base you have on hand to use as a titrant is baking soda (sodium bicarbonate.)  You have mixed up a solution of the baking soda, but you do not know its concentration.  However, you do have an acid solution on hand that you know has a concentration of 0.1 N.  You also have a pH indicator. 

You set up your titration as shown below:

titration of a known and an unknown

You will perform two titrations, both using the baking soda solution as the titrant.  One will be a titration of the known acid solution and one will be a titration of the unknown coal ashes solution. 

Then you can calculate the normality of the unknown using the following equation:

V1 N2 = V2 N1

V1 = volume of titrant used for the known solution
V2 = volume of titrant used for the unknown solution
N1 = normality of the known solution
N2 = normality of the unknown solution

Notice that this is not the same as the formula used to calculate dilutions.  Also notice that this formula assumes that the volumes of the known and unknown solutions used in the titration were equal.  If they were not equal, you will have to perform a dilution calculation as well. 

In our example, it required 10 mL of the baking soda solution to change the color of the indicator in the known acid solution.  It took 20 mL of the titrant to change the color of the coal ashes solution.  So we can calculate the normality of the coal ashes solution as follows:

(10 mL) N2 = (20 mL) (0.1 N)

N2 = 0.2 N

We still do not know the identity of the acids found in the wood ash solution, but we know that their concentration is 0.2 N in the solution we produced. 




Perhaps you have on occasion noticed mineral deposits on your cooking dishes, or rings of insoluble soap scum in your bathtub. These are not signs of poor housekeeping, but are rather signs of hard water from the municipal water supply. "Hardness" is a measure of the concentration of calcium and magnesium salts in water. "Alkalinity" is a measure of the concentration of carbonate, bicarbonate and hydroxide and contributes to the formation of scale in hard water areas.

Hardness reacts chemically with soap, the higher the hardness, the more soap is required to form a lather (hence the development of detergents which are not similarly affected by hardness).

Hardness due to calcium bicarbonate is destroyed by boiling and is therefore sometimes referred to as "temporary hardness". Boiling changes it to insoluble carbonate, which is seen as a scale in kettles or a slight film on hot drinks.  Hardness due to calcium and magnesium sulphates is not affected by boiling and is sometimes referred to as "permanent hardness".The hardness of a water supply generally depends on the soil or rocks from which the water is derived. High hardness waters are derived from chalk and limestone, soft waters from moorland.  We use water from a different sources and consequently our supplies range from very soft, mainly in the west, to very hard, mainly in the east of our region.



Problems with Hard Water

Mineral deposits are formed by ionic reactions resulting in the formation of an insoluble precipitate. For example, when hard water is heated, calcium ions react with bicarbonate ions to form insoluble calcium carbonate (CaCO3). This precipitate, known as scale, coats the vessels in which the water is heated, producing the mineral deposits on your cooking dishes. In small quantities, these deposits are not harmful, but they may be frustrating to try to clean. As these deposits build up, however, they reduce the efficiency of heat transfer, so food may not cook as evenly or quickly in pans with large scale deposits. More serious is the situation in which industrial-sized water boilers become coated with scale. Furthermore, scale can accumulate on the inside of appliances such as dishwashers and pipes. As scale builds up, water flow is impeded and hence appliance parts and pipes must be replaced more often than if calcium and magnesium ions were not present in the water.



Causes of Hard Water

Approximately 22 percent of the earth's fresh water is ground water, and naturally, as it flows through soil and rock, it picks up minerals. Hard water results when an excessive amount of calcium and magnesium are present. Total hardness is measured in milligrams per liter (mg/L) or parts per million (ppm). Parts per million measures the unit(s) of a substance for every one million units of water. Milligrams per liter and parts per million are roughly equal in water analysis. Below is a chart explaining the determination of your water supply.

Milligrams per Liter (mg/L) or Parts per Million (ppm)
less than 17.1 Soft
17.1 - 60 Slightly Hard
60 - 120 Moderately Hard
120-180 Hard
over 180 Very Hard




Treatment of Hard Water

For large-scale municipal operations, a process known as the "lime-soda process" is used to remove calcium and magnesium from the water supply. The water is treated with a combination of slaked lime, Ca(OH)2, and soda ash, Na2CO3. Calcium precipitates as CaCO3, and magnesium precipitates as Mg(OH)2. These solids can be collected, thus removing the scale-forming cations from the water supply.

The most common method to treat hard water is through ion exchange water softening. Ion exchange water softening is a process in which the hardness ions, magnesium and calcium, are exchanged with either sodium or occasionally, potassium ions. This is accomplished by directing the flow of hard water over a bed of plastic resin beads. Each bead has a slight electric charge, which holds the sodium on the bead. As the water flows over the beads, the hardness minerals are attracted to the beads. When the hardness minerals attach themselves to the beads, the sodium ions are displaced. Hence, the hardness ions are replaced by sodium ions.

At some point the plastic resin beads will be covered with hardness ions and will no longer be able to remove hardness from the water. In order to remove the hardness ions from the beads, a brine or salt (sodium chloride) solution is added to the resin bed. This solution contains a high concentration of sodium ions, which remove the hardness ions from the beads. Next the solution and the hardness ions are flushed out of the resin bed with fresh water, and once again the beads can remove hardness from the water. This process is called regeneration.




Titration consists of a laboratory procedure followed by a mathematical calculation.  In the lab, an acid or base is added to the sample until a certain pH value is reached.  Then the number of moles of acid or base in the sample is calculated.  This procedure allows us to calculate the normality of an acid or base solution using a titrant with a known normality.

If we do not know the normality of the titrant, we can calculate normality of an acid or base by comparing it to a standard.  In this case, both the sample and the standard are titrated using the same titrant.  Then we calculate the normality of the sample based on the normality of the standard and on the amount of titrant used in both titrations. 




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



New Formulas Used

To calculate normality during a titration:

(Normality of the titrant) × (Volume of the titrant) = (Normality of the unknown) × (Volume of the unknown)

To measure by comparison to a standard:

Unknown value = (Known value) × (Number of known values)

To measure the concentration of an acid or base by comparison to a standard:

V1 N2 = V2 N1


Complete the math problems in Assignment 12 online and the grade will be submitted directly into the gradebok.

If you need hints in working these problems please review the math worksheet.



Read the Hardness lab and do the assignment listed above, there are questions concerning the virtual lab included.


Answer the questions in the Lesson 12 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.