How To Calculate Equivalent Weight

When chemicals combine, they do so in known, fixed proportions. Even if you have never formally worked with chemicals yourself, you have probably seen your share of chemical reactions written out, and know that they appear in a predictable format. For example, consider the reaction of sulfuric acid and hydroxide ion to produce water and sulfate ion:

H₂SO₄ + 2OH⁻ → 2H₂O + SO₄²⁻

The numbers in front of the molecules, the coefficients, show the numbers of each reactant and product molecule in relation to each other; the subscripts within the compounds show how many atoms of each type are in a given molecule. These numbers are always integers, not fractional numbers like 4.24 or 1.3. But what do they represent?

The concept of equivalent weight allows you to explore the fact that atoms combine to form molecules in fixed number ratios, not mass ratios. That is, while element masses differ, when it comes to bonding with other atoms, the number of atoms, expressed in moles, is the determining factor in how much of a given element or compound will react with a given mass of another.

One mole of a substance is defined as 6.02 × 10²³ individual particles (atoms or molecules) of that substance. (This happens to be the exact number of atoms in 12 grams of carbon.) As you move from left to right and downward on the periodic table, the mass of one mole of a given element, or its molecular weight (MW), is given in the corresponding box for that element, usually at center bottom.

An example helps make sense of this definition. If you have one molecule of water, H₂O, you can see that two H atoms react with one O atom to form this compound. But because the MW of H is about 1.0 and than of O is 16.0, you can see that the molecule contains 2(1) = 2 mass parts of H for every (1)(16) = 16 mass parts of O. Thus only 2/18 = 11/1 percent of the mass of water consists of H, while 16/198 = 88.9 percent consists of O.

The equivalent weight can be thought of as the weight (or mass, to be precise) of a substance that will contain a single reactive proton (or hydrogen ion, H⁺) or a single reactive hydroxide ion (−OH⁻). The former case applies to acids, which are proton donors, while the second applies to bases, which are proton acceptors.

The reason the concept of equivalent weight is needed is that some compounds can donate or accept more than one proton, meaning that for every mole present, the substance is in effect doubly reactive.

The general number of equivalents formula is

E = MW/charge number

Where MW is the molecular weight of the compound and charge number is the number of proton- or hydroxide-equivalents the compound contains. Examples with different acids and bases help illustrate how this works in practice.

Take the example of sulfuric acid from above:

H₂SO₄ + 2OH⁻ → 2H₂O + SO₄²⁻

You can calculate the MW of the acid by referring to a periodic table to get the MW of each element and adding 2(1) + (32) + 4(16) = 98.0.

Note that this acid can donate two protons, as the sulfate ion is left with a charge of −2. This the equivalent weight is 98.0/2 = 49.0.

For a base, the reasoning is the same. Ammonium hydroxide can accept a proton in solution to become an ammonium ion:

NH₄OH + H⁺ = H₂O + NH₄⁺

The MW of ammonium hydroxide is (14) + (4)(1) + (16) + 1 = 35.0. Since only once proton is consumed, E for this compound is 35.0/1 = 35.0.

• A gram equivalent (geq) is the number of grams of substance present divided by its equivalent weight. It can also be expressed as the number of charge elements contained times the number of moles n.

See the Resources for a site that allows you to automatically compute E for different molecular weights and charge combinations, or solve for any one value given the other two for any compound you can come up with.