Problem 140 - A Complete Resource Book in Chemistry for JEE Main

Question

If 1 mole of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is reacted with 1 mole of \(\mathrm{X}(\mathrm{OH})_{2}\) as: \(\mathrm{H}_{3} \mathrm{PO}_{4}+\mathrm{X}(\mathrm{OH})_{2} \longrightarrow \mathrm{XHPO}_{4}+2 \mathrm{H}_{2} \mathrm{O}\) then (a) The equivalent weight of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) is \(\frac{98}{3}\). (b) The equivalent weight of base is \(\frac{\text { Molecular mass }}{2}\) (c) 1 mole of \(\mathrm{X}(\mathrm{OH})_{2}\) more is required for complete neutralization of \(\mathrm{XHPO}_{4}\). (d) The resulting solution required 1 mole \(\mathrm{NaOH}\) for complete neutralization.

Step-by-Step Solution

Answer

Statements (b), (c), and (d) are true, but (a) is false.

Step 1: Analyze the Reaction Equation

The balanced reaction given is \( \mathrm{H}_{3}\mathrm{PO}_{4} + \mathrm{X(OH)}_{2} \rightarrow \mathrm{XHPO}_{4} + 2\mathrm{H}_2\mathrm{O} \). We need to inspect the reaction to determine the equivalence concept, which often involves the change in oxidation states or number of transferable ions like H⁺ or OH⁻.

Step 2: Determine the Equivalent Weight of H3PO4

The equivalent weight of a compound is its molar mass divided by the number of transferable H⁺ ions involved in the reaction. \( \mathrm{H}_{3}\mathrm{PO}_{4} \) converts into \( \mathrm{XHPO}_{4} \) losing 2 H⁺ ions. Therefore, the equivalent weight is \( \frac{98}{2} = 49 \), not \( \frac{98}{3} \). This statement (a) is false based on this understanding.

Step 3: Equivalent Weight of Base

Since \( \mathrm{X(OH)}_{2} \) provides 2 OH⁻ ions for neutralization, and this matches the 2 H⁺ lost by H₃PO₄, the base's equivalent weight should be its molecular mass divided by 2. Thus, statement (b) is true.

Step 4: Analyze Further Requirements for Neutralization

To neutralize \( \mathrm{XHPO}_{4} \), which still has an acidic hydrogen, 1 more mole of \( \mathrm{X(OH)}_{2} \) is needed, consistent with the stoichiometry in statement (c). Therefore, (c) is true.

Step 5: Consider Further Neutralization with NaOH

The reaction produces \( \mathrm{XHPO}_{4} \), which still has one acidic hydrogen that would react with \( \mathrm{NaOH} \), requiring 1 mole as described in (d). This statement is consistent and true.

Key Concepts

Acid-Base Neutralization

Acid-base neutralization is an important chemical reaction where an acid reacts with a base to produce water and a salt. This type of reaction is essential in many areas, from everyday life to industrial processes. When an acid, such as \( \mathrm{H}_{3}\mathrm{PO}_{4} \) (phosphoric acid), reacts with a base like \( \mathrm{X(OH)}_{2} \), the acid donates hydrogen ions (\( \text{H}^+\)) and the base supplies hydroxide ions (\( \text{OH}^-\)).### Key Points of Neutralization:- **Formation of Water**: In the given equation, \( 2 \text{H}^+ \) ions from \( \mathrm{H}_{3}\mathrm{PO}_{4} \) combine with ·\( 2\text{OH}^- \) ions from \( \mathrm{X(OH)}_{2} \), producing \( \mathrm{H}_{2}\mathrm{O} \).- **Salt Formation**: The remainder of the acid and base forms a salt, seen here as \( \mathrm{XHPO}_{4} \).- **Complete Neutralization**: Occurs when the number of \( \text{H}^+ \) ions equals the \( \text{OH}^- \) ions, leading to fully reacted components without excess acid or base.This balance is crucial for determining equivalent weights and understanding stoichiometry in reactions.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It helps to determine the proportions of different substances that will react perfectly with each other.In the case of our reaction, stoichiometry allows us to predict how much of each reactant is needed for complete neutralization.### The Role of Stoichiometry Here:- **Balanced Equation**: The given balanced reaction \( \mathrm{H}_{3}\mathrm{PO}_{4} + \mathrm{X(OH)}_{2} \rightarrow \mathrm{XHPO}_{4} + 2\mathrm{H}_2\mathrm{O} \) reveals that 1 mole of phosphorus acid reacts with 1 mole of base.- **Mole-to-Mole Comparison**: For every mole of \( \mathrm{H}_{3}\mathrm{PO}_{4} \), 2 moles of water are produced, indicating full alignment with its equivalent weights and thus the statement that the base's equivalent weight is half its molecular weight.- **Further Requirements**: As the reaction shows, additional moles can be calculated for complete neutralization of further reactants, like seen with the need for more \( \mathrm{NaOH} \) if needed.Understanding these ratios is essential for calculating how much reactant will be required in an actual experiment.

Transferable Ions

Transferable ions are ions that move from one molecule to another during chemical reactions.In acid-base reactions, these often involve hydrogen ions (\( \text{H}^+\)) and hydroxide ions (\( \text{OH}^-\)). Knowing the number of transferable ions is crucial for calculating equivalent weights, which indicate how much of a substance is needed to react completely with a given amount of another substance.### Examples in the Current Reaction:- **Hydrogen Ions**: In the reaction, \( \mathrm{H}_{3}\mathrm{PO}_{4} \) loses \( 2 \text{H}^+ \) ions to react with the \( 2 \text{OH}^- \) ions from \( \mathrm{X(OH)}_{2} \).- **Balancing Ions**: The balance of \( \text{H}^+ \) and \( \text{OH}^-\) ions ensures complete neutralization, forming water.- **Further Reactivity**: The incomplete neutralization leaves \( \mathrm{XHPO}_{4} \) with one \( \text{OH}^- \) site free, thus allowing further reaction with either more \( \mathrm{X(OH)}_{2} \) or \( \mathrm{NaOH} \) to achieve full neutralization as needed.Transferable ions provide the fundamental understanding necessary for analyzing chemical reactions efficiently and are central to quantification in chemistry.