Problem 52 - A Complete Resource Book in Chemistry for JEE Main

Question

\(0.1914 \mathrm{~g}\) of an organic acid is dissolved in about 20 \(\mathrm{mL}\) of water \(25 \mathrm{~mL}\) of \(0.12 \mathrm{~N} \mathrm{NaOH}\) is required for the complete neutralization of the acid solution. The equivalent weight of the acid is (a) \(63.8\) (b) \(64.0\) (c) \(65.8\) (d) \(66.2\)

Step-by-Step Solution

Answer

The equivalent weight of the acid is 63.8 (option a).

Step 1: Understanding Normality and Equivalent Weight

Normality (N) is a measure of concentration equivalent to the molar concentration divided by the equivalent factor. The equivalent weight of an acid is defined as the molecular weight divided by its acidity, which corresponds to the number of replaceable hydrogen ions it can donate.

Step 2: Calculating Moles of NaOH

To calculate the moles of NaOH, use the relation between volume, normality, and moles:\[\text{Moles of NaOH} = \text{Normality} \times \text{Volume (L)} = 0.12 \times \left(\frac{25}{1000}\right)\]Calculating this gives us 0.003 moles of NaOH.

Step 3: Applying Mole Concept

The acid undergoes complete neutralization with NaOH, meaning the moles of equivalent acid will equal the moles of NaOH:\[\text{Moles of Acid} = 0.003\]

Step 4: Determining Equivalent Weight of Acid

The equivalent weight of the acid can be obtained by dividing the mass of the acid by the moles of acid calculated:\[\text{Equivalent Weight} = \frac{\text{Mass of Acid}}{\text{Moles of Acid}} = \frac{0.1914}{0.003}\]Simplifying this gives us the equivalent weight of 63.8 g/mol.

Key Concepts

Normality and Molarity

Normality and molarity are two important concepts used to describe the concentration of a solution. While both terms relate to how much solute is present in a given volume of solution, they differ based on the chemical aspect they emphasize.

• Molarity, denoted as "M", is the most straightforward way to convey concentration. It's defined as the number of moles of solute present per liter of solution. For example, a 1 M solution of NaCl has 1 mole of sodium chloride dissolved in 1 liter of water.
• Normality, denoted as "N", is a concentration that reflects the reactive capacity of a solute. It's the number of gram equivalents of a solute per liter of solution. This is particularly useful in reactions where ions or charges are important, such as acid-base reactions.

Normality considers the equivalent factor, which depends on the type of reaction. For acids, the equivalent factor relates to the number of hydrogen ions they can donate. When calculating normality, the following relationship can be used:\[ Normality (N) = Molarity (M) \times n \]where \( n \) is the number of hydrogen ions an acid can donate or the number of hydroxide ions a base can accept.

Neutralization Reaction

A neutralization reaction is a chemical reaction in which an acid and a base interact to form water and a salt. This type of reaction is integral to the field of analytical chemistry, particularly when quantifying the concentration of an acid or base in a given sample through titration. The general form of a neutralization reaction is: \[ \text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water} \]For example, when hydrochloric acid (HCl) reacts with sodium hydroxide (NaOH), they produce sodium chloride (NaCl) and water (H\(_2\)O): \[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]During a neutralization reaction, the protons from the acid combine with the hydroxide ions from the base to form neutral water molecules. The remaining ions form the salt. This reaction can be used to determine the unknown concentration of an acidic or basic solution by titrating it against a solution with a known concentration until neutrality is reached, which is often indicated by a pH indicator.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic world and the macroscopic quantities we can measure in the laboratory. A "mole" is a unit that refers to a quantity of substance. Specifically, one mole is equal to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities of the substance. These entities could be atoms, molecules, ions, or electrons. This concept is crucial because it allows chemists to count these particles by weighing measurable amounts, which is essential for understanding chemical reactions. For calculating moles, the formula is:\[ \text{Moles} = \frac{\text{Mass of sample}}{\text{Molar mass}}\]This calculation reveals how many molecules, ions, or atoms are present in the given mass, and plays a pivotal role in stoichiometry—helping chemists determine the proportions of substances involved in reactions. Whether calculating the amount of reactants needed to completely undergo a reaction or the volume of gas produced, the mole concept simplifies these computations by providing a standard measure of quantity.

Acid-Base Titration

Acid-base titration is a technique used in quantitative chemical analysis to determine the concentration of an unknown acid or base. It involves adding a titrant, which is a solution of known concentration, to the analyte, the solution of unknown concentration, until the reaction reaches the equivalence point.In an acid-base titration, an indicator, a substance that changes color at a certain pH, is often used to signal the equivalence point. Alternatively, a pH meter can be employed for more precise detection. For a common titration setup:

• A burette is filled with the titrant.
• The analyte is placed in a flask with an indicator.
• The titrant is gradually added until the indicator changes color, showing that neutralization has been achieved.

The volume of titrant used to reach the equivalence point is then utilized to calculate the molarity or normality of the unknown solution. This is based on the relationship:\[ \text{N}_1 \times \text{V}_1 = \text{N}_2 \times \text{V}_2 \]where \(\text{N}_1\) and \(\text{V}_1\) are the normality and volume of the titrant, and \(\text{N}_2\) and \(\text{V}_2\) are the normality and volume of the analyte, respectively. This method allows for accurate determination of concentration, which is essential for various applications in both laboratory settings and industrial processes.