For an acid or a base, when is the normality of a solution equal to the molarity of the solution and when are the two concentration units different?

Normality (N) is the measure of the concentration of a solution expressed as the equivalent mass per unit volume (grams equivalent per liter), while molarity (M) is the measure of the concentration of a solution expressed as the number of moles of solute per unit volume (moles per liter). Mathematically, Normality can be defined as: \( Normality = \frac{Equivalent\ mass}{Volume\ of\ solution} \) And, Molarity can be defined as: \( Molarity = \frac{Moles\ of\ solute}{Volume\ of\ solution }\)

To find the relationship between normality and molarity, we must consider the equivalent mass, which is the mass of the solute required to react with or replace an equivalent of a reference substance. For acids, an equivalent is the mass that can release one mole of hydrogen ions (H+). For bases, an equivalent is the mass that can absorb one mole of hydrogen ions (H+). We know that: \( Equivalent\ mass = \frac{molar\ mass}{number\ of\ equivalents} \) So, \( Normality = \frac{moles\ of\ solute \times molar\ mass}{volume\ of\ solution \times number\ of\ equivalents} \) We can rewrite this equation in terms of molarity: \( Normality = Molarity \times number\ of\ equivalents \) From this equation, we can analyze when normality is equal to molarity and when they are different.

Normality is equal to molarity when the number of equivalents is 1. This happens when an acid or base has only one ionizable hydrogen (H+) ion or hydroxide (OH-) ion in its molecular structure, i.e., monoprotic acids and bases. For example, in the case of hydrochloric acid (HCl) and sodium hydroxide (NaOH), both have only one ionizable H+ ion and OH- ion, respectively. Thus, the normality of HCl and NaOH solutions will be equal to their molarity.

Normality is different from molarity when the number of equivalents is not 1. This happens when an acid or base has more than one ionizable hydrogen (H+) ion or hydroxide (OH-) ion in its molecular structure, i.e., polyprotic acids and bases. For example, in the case of sulfuric acid (H2SO4) which has two ionizable H+ ions. The normality of a sulfuric acid solution will be double its molarity. Similarly, for a diprotic base like calcium hydroxide (Ca(OH)2), the normality will be double its molarity. In summary, normality and molarity are equal for monoprotic acids and bases when they have only one ionizable hydrogen or hydroxide ion. Normality and molarity are different for polyprotic acids and bases when they have more than one ionizable hydrogen or hydroxide ion.