What is the meaning of "equivalent weight" and its formula?

Question

What is meant by "equivalent weight" and how does its formula E=M/V support the definition?

Answer 1

Definition of Equivalent Weight (also known as equivalent mass):

The simplest definition of equivalent mass I can think of is the following:

The mass of a compound which will combine with 8g of oxygen or 1g of hydrogen is said to be the equivalent weight of the compound.

Lets take an example,

$\ce{2Ca + O2 -> 2CaO}$

From basic stoichiometry, you know that 2 moles of calcium react with 1 mole of oxygen to produce 2 moles of calcium oxide. We can say the same statement in terms of masses as 80g of calcium reacts with 32g of oxygen to produce 112g of calcium oxide.

Since 80g of Calcium reacts with 32g of oxygen, 20g of calcium should react with 8g of oxygen.

Now by the definition of equivalent weight mentioned earlier, the equivalent weight of calcium is 20g.

$$E = \frac{M}{V}$$

The formula you were talking about gives the equivalent weight of an element (can be extended to be used with ions).

Equivalent weight = (Atomic mass)/(Valency)

This could be intuitive and obvious for some. Something with valency of 1 would combine with just 1 hydrogen atom, or in other words, a mole of compound with valency 1 would react with 1g of hydrogen. If the element has a valency of 2, then it would love to combine with 2 hydrogen atoms, or in other words, a mole of the element will combine with 2g of hydrogen. By definition, equivalent weight is the mass of the substance that would react with 1g of hydrogen. Therefore you must divide the mass by 2 to get equivalent weight. In fact, this formula based definition of equivalent weight of an element is identical with the definition mentioned earlier in this answer.

Previously, we determined that equivalent weight of calcium was 20g using the other definition. We should obtain the same equivalent weight for calcium by using the formula.

Equivalent weight = (40g)/2 = 20g

Definition of equivalents: Another terminology you might come across is equivalents.

Equivalents is similar to moles. The number of moles is given by (mass of the compound)/(molecular mass). Similarly the number of equivalents is given by (mass of the compound)/(equivalent weight).

For example, 1 equivalent of calcium contains 20g of calcium. 2 equivalents of calcium contain 40g of calcium.

The utility of equivalent weights is amazing. In any reaction, $N$ equivalents of any compound on the reactants side reacts with N equivalents of another reaction to produce $N$ equivalents of the product(s).

If that sounds complicated, this example should make it clear.

20g of calcium reacts with 8g of oxygen to produce 28g of calcium oxide.

An equivalent statement is, 1 equivalent of calcium reacts with 1 equivalent of oxygen to produce 1 equivalent of calcium oxide.

Answer 2

Y.S. is just plain WRONG.

Equivalent weight is the (mass of) number of moles of one reactant in a balanced reaction (or product) divided by the number of moles of another.

In the simple case where we have two reactants which combine 1:1, then the mass of 1 mole of either is its equivalent weight. This means that the same chemical compound can have a wide variety of Eq. Wts. because the reaction it participates in can have all sorts of different stoichiometries. Eq. Wt. should only be used when the reaction is understood - and often is used to compare two different compounds reacting in the "same" reaction eg:

xM + O₂ → M_aO_b

where the mole ratio is x:1 in this specific case if relative to O₂ or a:b if relative to the product. In other words, the equivalent weight relates to a specific reaction - and by the way, its possible that the exact same two reactants can have different equivalent weights if they can combine in more than one stoichiometry. I should also note that it is possible that your teacher/professor/lecturer/textbook has decided to use the term in a better (standardized) way, but generally if you don't know (for sure) what the reaction is that is being discussed you should avoid thinking you know what Eq. Wt. means.

Answer 3

I'll explain it in simple terms.

If you have

a A + b B->c C

where A, B are the reactants and C is the product and a,b,c are the stoichiometric coefficients of the reaction.

The equivalent weight is in simple terms the mass of one equivalent of a substance.

Now let's see what we mean by one equivalent.

In our reaction let's assume a=2 b=3.

2 moles of A + 3 moles of B react stoichiometrically. The molar ratio of the reaction is 2:3

Suppose we were to say that A and B react in the ratio of 1 equivalent to 1 equivalent. The equivalent ratio of the reaction is ALWAYS 1:1.

So we have to define an equivalent for each compound/element depending on the stoichiometry of how it reacts. So one equivalent of A is in this reaction 1/3rd of a mole and for B, it is 1/2 a mole each of which will be one equivalent. We notice that these amounts make sure that A and B react stoichiometrically.

Now we need to standardise the definition of one equivalent. To be more exact one equivalent is the amount of a substance which is needed to react with 1 g of H2.

The number of Equivalents is generally calculated as: No. of equivalents=n-factor * no. of moles

Where n-factor generally corresponds to the stoichiometric ratio of the other reactant. Or it could be the change in oxidation number of that reactant.Or it could be the (total) valence of the ionic salt(Charge on cation*total no. of cation units present in one molecule/formula unit) or the acidity for a base or basicity for an acid.

The formula for equivalent weight should be simple from this point.

Equivalent weight=Molar weight/n-factor