What is Equivalent Weight of an Acid?
The equivalent weight of an acid is defined as the mass of the acid that provides one mole of replaceable hydrogen ions ($H^+$) in a specific chemical reaction. Unlike molecular weight, which is a fixed property of a substance, the equivalent weight of an acid can change depending on the reaction it undergoes, specifically based on its basicity (or the number of $H^+$ ions it donates).
The formula is given by:
$$\text{Equivalent Weight} = \frac{\text{Molar Mass of Acid}}{\text{Basicity (n-factor)}}$$
Where the n-factor is the number of $H^+$ ions replaced per molecule of the acid in the reaction.
Solving the Problem
Given Reaction:
$$NaOH + H_2SO_4 \rightarrow NaHSO_4 + H_2O$$
Step 1: Determine the n-factor
In this reaction, one molecule of $H_2SO_4$ reacts with one molecule of $NaOH$ to produce $NaHSO_4$. Looking at the stoichiometry, only one hydrogen ion ($H^+$) from $H_2SO_4$ has been replaced by $Na^+$. Therefore, the n-factor for $H_2SO_4$ in this specific reaction is 1.
Step 2: Calculate the Molar Mass of $H_2SO_4$
Using the atomic masses: $H=1$, $S=32$, $O=16$.
$$\text{Molar Mass} = (2 \times 1) + (1 \times 32) + (4 \times 16) = 2 + 32 + 64 = 98 \text{ g/mol}$$
Step 3: Calculate the Equivalent Weight
$$\text{Equivalent Weight} = \frac{98 \text{ g/mol}}{1} = 98 \text{ g/eq}$$
Summary
Because $H_2SO_4$ is diprotic, it usually has an n-factor of 2 (for complete neutralization). However, in this partial neutralization reaction, the equivalent weight is equal to the molar mass because it behaves as a monoprotic acid.