Problem 29 - Chemistry in 30 days

Question

How many grams of a dibasic acid (mol. wt. =200) should be present in \(100 \mathrm{ml}\) of its aqueous solution to give decinormal strength? (a) \(1 \mathrm{~g}\) (b) \(2 \mathrm{~g}\) (c) \(10 \mathrm{~g}\), (d) \(20 \mathrm{~g}\)

Step-by-Step Solution

Answer

1 g of the acid is needed (option a).

Step 1: Understand Normality and Moles

Normality is defined as the number of equivalents of solute per liter of solution. Since the acid is dibasic, it can donate 2 protons (H⁺ ions), which means 1 mole of this acid is equivalent to 2 equivalents.

Step 2: Calculate Equivalents Required

The solution needs to be decinormal (0.1 N), so we require 0.1 equivalents for 1 liter. Since we only have 100 ml or 0.1 liters, the required equivalents is 0.1 N × 0.1 L = 0.01 equivalents.

Step 3: Relate Equivalents to Grams

Since 1 mole of the acid provides 2 equivalents, the molecular weight for 1 equivalent is half, i.e., 100 g/equiv. Thus, to get 0.01 equivalents needed, the mass required is 0.01 equivalents × 100 g/equiv = 1 g.

Step 4: Choose the Correct Option

The mass of the dibasic acid needed to achieve decinormal strength in 100 ml solution is 1 g. Therefore, the correct answer is option (a).

Key Concepts

Dibasic Acid

A dibasic acid is an acid that can donate two protons or hydrogen ions (H⁺) per molecule in a chemical reaction. This characteristic is crucial when dealing with concepts like normality because the number of protons an acid can donate directly affects its equivalent weight.
In simpler terms, if you have an acid capable of donating two protons, it will require fewer moles to achieve the same effect as an acid donating only one proton. For instance, sulfuric acid (H₂SO₄) is a well-known dibasic acid because it can release two hydrogen ions upon ionization.
In the context of our problem, it means that each mole of the dibasic acid contributes two equivalents to a solution, impacting calculations related to normality and equivalent weight significantly.

Molarity vs Normality

Molarity and normality are both ways to express the concentration of a solution, yet they serve distinct purposes. Molarity (M) is defined as the number of moles of solute per liter of solution. It's a straightforward calculation but doesn't directly consider the chemical reactivity of the solute.
Normality (N), on the other hand, takes into account the role a solute plays in a reaction. It's defined as the number of equivalents per liter of solution. An equivalent is the reactive capacity of a molecule, often related to the number of protons exchanged in acid-base reactions.
Because a dibasic acid can donate two hydrogen ions, its normality is generally twice that of its molarity in a reaction setting. For example, a 1 M solution of a dibasic acid will be 2 N due to its ability to produce two equivalents of H⁺ ions. This distinction is especially vital when dealing with chemicals where the effective chemical action involves different numbers of reactive species.

Acid-Base Chemistry

Acid-base chemistry revolves around the interaction between acids and bases, primarily focusing on the transfer of protons. The fundamental idea is that acids donate protons while bases accept them. This transfer is the essence of what makes a reaction an acid-base reaction.
In our exercise, understanding this concept is crucial because the calculation of normality for a dibasic acid relies on the number of protons it can donate. Acid-base reactions are often quantified using normality since it provides a clear picture of the chemical behavior of the acids in question.
Moreover, acid-base chemistry also introduces the concepts of conjugate acid-base pairs, where the loss or gain of a proton transforms a molecule into its conjugate reaction partner. Emphasizing equilibrium between acids and bases, this field of chemistry is a foundational discipline in understanding pH, buffers, titration, and the direct relationship between concentration and chemical reactivity.