Equivalents and Normality

In this part of Lesson 6 we’ll study some of the concepts you’ll need to understand the technique of acid-base titration.

An acid-base titration is a technique in which precisely measured volumes of acid and base solutions are mixed until the two just neutralize each other. Then, from the measured volumes and the known concentration of one solution, the concentration of the other can be calculated. With simple equipment, the technique can be used to determine the concentration of an unknown acid or base solution to within a few tenths of a percent or less.

Polyprotism & Polybasism

First, we'll briefly review a topic from Lesson 5. Recall that some of the acids we encountered had only one positive hydrogen ion, while others had two or three. Hydrochloric acid, for example, has only one hydrogen ion, while sulfuric acid has two and phosphoric acid has three.

The reason, of course, is that the chloride ion has a charge of 1-, and so requires only one H⁺ ion to balance its charge. The sulfate ion, on the other hand, has a charge of 2- and so requires two hydrogen ions to balance its charge. The phosphate ion has a charge of 3- and requires three H⁺ ions.

Acids that have more than one ionizable hydrogen are called "polyprotic" whereas acids with only one ionizable hydrogen are "monoprotic." Sulfuric acid and acids like it are "diprotic" and phosphoric acid and acids like it are "triprotic."

Similarly, bases can have different numbers of hydroxide ions in their formulas. Bases like NaOH that have a single hydroxide ion are "monobasic" whereas a base like Mg(OH)₂ is dibasic and Al(OH)₃ is tribasic. Even though it has no hydroxide ions, ammonia (NH₃) is also considered monobasic because it can react with water to accept just one proton (producing one hydroxide ion).

Moles and Equivalents

By now you should be very familiar with the concept of the mole, and you should be comfortable converting amounts of substances from grams to moles and vice versa. The mole is a great way of putting substances on an equal footing when expressing amounts of substances involved in reactions, or in the gas laws.

However, when dealing with acids and bases, we sometimes find that using moles when working with acids and bases is not the most useful concept. Instead, we use a related concept, the concept of equivalents.

An equivalent is defined as the amount of an acid that contains one mole of H⁺ ions or the amount of a base that contains one mole of OH^- ions.

Since a monoprotic acid has only one hydrogen ion per molecule, one mole of a monoprotic acid is the same as one equivalent. If you want to use HCl in a neutralization reaction, one mole of HCl would be able to donate one mole of H⁺ ions, because each HCl molecule has one ionizable hydrogen. Another way to express that is with the conversion factor at the right, which shows the 1:1 ratio of equivalents and moles for HCl and other monoprotic acids.

The same can be said of a monoprotic base like NaOH. Each mole of NaOH can release one mole of hydroxide (under the Arrhenius definition) or accept one mole of hydrogen ions (under the Bronsted-Lowry definition) so there is a 1:1 relationship between moles and equivalents for NaOH and other monobasic substances.

A diprotic acid has two hydrogen ions per molecule, so that one mole of a diprotic acid is the same as two equivalents. That is, a diprotic acid has two equivalents per mole. Similarly, a dibasic base has two equivalents per mole.

As you might imagine, a triprotic acid or tribasic base has three equivalents per mole.

To convert from moles to equivalents and vice versa, conversion factors like the ones above can be used. As always, the arrangement of units allows you to know which way to orient the conversion factor.

You will be expected to be able to convert from moles of an acid or base to equivalents, and vice versa.

Equivalent Mass

You should certainly be familiar by now with the concept of molar mass, and should be able to calculate it for any substance using a periodic table. As its name indicates, molar mass indicates the mass (almost always in grams) of one mole of a substance. For example, HCl has a molar mass of 36.48 g/mol, and H₂SO₄ has a molar mass of 98.08 g/mol.

Similarly, the equivalent mass of an acid or base is the mass (again in grams) of one equivalent of the acid/base, under the definition of equivalents above. Its units are g/eq rather than g/mol. The same conversion factors we used above to convert between grams and moles can convert between molar mass and equivalent mass.

For a monoprotic acid like HCl there is a 1:1 ratio of moles to equivalents, so the equivalent mass of HCl is the same as its molar mass.

For a diprotic acid like H₂SO₄ the ratio is 2:1, so the equivalent mass is half the molar mass.

Note: it is not possible for an acid or base's equivalent mass to be greater than its molar mass.

To determine the number of equivalents in a given amount of substance, you use the equivalent mass the same way you would the molar mass. At right, you can see a calculation of the mass of 0.25 equivalents of H₂SO₄.

In the lab for this week, you will be determining the equivalent mass of a substance from experimental data. In order to do this kind of calculation, you must know the mass of a sample of acid/base as well as the equivalents present in that sample.

For example, if you have a 2.59 g sample of base that you find to contain 0.100 equivalents, you would divide the values to find an equivalent mass of 25.9 g/eq.

Normality

In Lesson 4 we learned the definition of molarity and gained experience with calculations involving molarity. Molarity measures the moles of solute per liter of solution; for further review, revisit Lesson 4.

Normality is defined exactly the same way, except in place of moles, equivalents are used; that is, it measures equivalents of acid/base per liter of solution. The symbol for the new unit is N, similar to the M used for molarity.

Because the number of equivalents is the same as the number of moles of H⁺ ions in an acid or the number of moles of OH^- ions in a base, normality is essentially just the molarity of the H⁺ or OH^- ions, depending on whether we’re dealing with an acid or a base. You can see that normality is a convenient way to express the “acid strength” or an acidic solution or the “base strength” of a basic solution. (This is not the same as expressing whether the acid is a "strong acid" compared to a "weak acid" or whether the base is a "strong base" or a "weak base." We'll talk more about those terms in the next section of the lesson.)

If you know the molarity of a solution and whether the acid/base is mono-/di-/triprotic, you can calculate the normality, and the conversion goes exactly like the conversions we have seen so far. You just use the ratio of equivalents to moles for whatever acid or base you have.

So for a diprotic base like Mg(OH)₂, if you have a 1.25 M solution, multiplying by the 2:1 ratio gives you a normality of 2.50 N. If you are told an H₃PO₄ solution (triprotic) is 2.40 N, then its molar concentration is 0.80 M.

Once you get used to dealing with equivalents instead of moles, calculations with normality are exactly like those involving molarity, including calculations of dilution. At right, you can see how we calculate the equivalents of base present in 3.00 L of a 0.40 N base solution.

Before moving on to the next section, complete the practice problems below. The next section, Titration, will rely heavily on the concept and mathematics of normality, so it's important you understand it fully.

Practice Problems

How many equivalents are there in each of the following?
2 moles HCl
0.4 mole HCl
0.4 mole H₂SO₄
1.2 mole H₃PO₄
0.7 mole NaOH
4.3 mole Mg(OH)₂
How many moles are there in each of the following?
3.2 eq HBr
0.76 eq. H₂CO₃ 0.76 eq. H₃PO₄
1.56 eq. Ca(OH)₂
Calculate equivalent masses for the following compounds
HBr
H₃PO₄ H₂CO₃
KOH
Ca(OH)₂
What is the normal concentration of a solution made by mixing 3.5 g of Ca(OH)₂ in enough water to make 0.250 L of solution?
What volume of a 3.85 N solution is required to deliver 16.8 equivalents of acid?

Answers to Practice Problems

How many equivalents are there in each of the following?
2 moles HCl = 2 eq
0.4 mole HCl = 0.4 eq
0.4 mole H₂SO₄ = 0.8 eq
1.2 mole H₃PO₄ = 3.6 eq
0.7 mole NaOH = 0.7 eq
4.3 mole Mg(OH)₂ = 8.6 eq
How many moles are there in each of the following?
3.2 eq HBr = 3.2 mol
0.76 eq. H₂CO₃ = 0.38 mol 0.75 eq. H₃PO₄ = 0.25 mol
1.56 eq. Ca(OH)₂ = 0.78 mol
Calculate equivalent masses for the following compounds
HBr = 80.91 g/eq
H₃PO₄ = 32.68 g/eq H₂CO₃ = 31.01 g/eq
KOH = 56.11 g/eq
Ca(OH)₂ = 37.45 g/eq
What is the normal concentration of a solution made by mixing 3.5 g of Ca(OH)₂ in enough water to make 0.250 L of solution?
There are a few ways to calculate this. One is to use the equivalent weight above to convert 3.5 g to equivalents and divide by the volume to get normality. Another is to convert to moles, divide by the volume to get molarity, and multiply by two. The answer should be the same no matter how you approach it.

0.37 M

What volume of a 3.85 N solution is required to deliver 16.8 equivalents of acid?

4.36 L

Google Sites

Report abuse