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

All given statements are correct based on the described reaction steps.

Step 1: Identify the Reaction

The problem describes a chemical reaction between phosphoric acid \( \mathrm{H}_{3}\mathrm{PO}_{4} \) and a generic base \( \mathrm{X(OH)}_{2} \). In this reaction, \( \mathrm{H}_{3} \mathrm{PO}_{4} \) donates protons (H⁺ ions). This results in the formation of \( \mathrm{XHPO}_{4} \) and water as products.

Step 2: Determine Equivalent Weight of \( \mathrm{H}_{3} \mathrm{PO}_{4} \)

Equivalent weight is calculated as \( \text{Molecular mass} / n \), where \( n \) is the number of hydrogens ionizable under the reaction conditions. For \( \mathrm{H}_{3} \mathrm{PO}_{4} \), typically all 3 hydrogens are ionizable. Its molar mass is 98 g/mol. Therefore, its equivalent weight is \( \frac{98}{3} = 32.67 \) g/equiv.

Step 3: Determine Equivalent Weight of \( \mathrm{X(OH)}_{2} \)

The equivalent weight of a base is calculated as the molecular mass divided by the number of ionizable hydroxide ions \( (OH^{-}) \). Since \( \mathrm{X(OH)}_{2} \) releases 2 \( OH^{-} \) ions, the equivalent weight is \( \frac{\text{Molecular mass of } \mathrm{X(OH)}_{2}}{2} \).

Step 4: Analyze Complete Neutralization

After reacting 1 mole each of \( \mathrm{H}_{3}\mathrm{PO}_{4} \) and \( \mathrm{X(OH)}_{2} \), the resulting \( \mathrm{XHPO}_{4} \) can still react with hydroxide ions because one hydrogen remains. Thus, 1 more mole of \( \mathrm{X(OH)}_{2} \) is needed for full neutralization of \( \mathrm{XHPO}_{4} \).

Step 5: Determine NaOH Requirement for Neutralization

Similarly, because \( \mathrm{XHPO}_{4} \) has 1 remaining reactive hydrogen, 1 mole of \( \mathrm{NaOH} \) would be required for complete neutralization of \( \mathrm{XHPO}_{4} \) to \( \mathrm{XPO}_{4} \).

Step 6: Conclusion: Verify the Statements

(a) The equivalent weight of \( \mathrm{H}_{3} \mathrm{PO}_{4} \) being \( \frac{98}{3} \) is correct. (b) The equivalent weight of the base is \( \frac{\text{Molecular mass}}{2} \), which is also correct. (c) An additional mole of \( \mathrm{X(OH)}_{2} \) is needed, which is true. (d) 1 mole of \( \mathrm{NaOH} \) is required for complete neutralization, so this is true as well.

Key Concepts

Equivalent Weight

The concept of equivalent weight is essential in understanding chemical reactions, particularly when acids and bases are involved. Equivalent weight refers to the mass of a substance that reacts with or supplies one mole of hydrogen ions (H⁺) or hydroxide ions (OH^-) in a reaction. It is determined by dividing the molecular mass of the compound by the number of moles of ionizable hydrogen or hydroxide ions.
For example, in the case of phosphoric acid, \[\mathrm{H}_{3}\mathrm{PO}_{4},\]with a molar mass of 98 g/mol, the equivalent weight is calculated as follows: Since all three hydrogen ions can typically be ionized, the calculation is\[\frac{98}{3} = 32.67 \text{ g/equiv}.\]This means that 32.67 grams of phosphoric acid will produce one mole of hydrogen ions in a reaction.

Neutralization

Neutralization is a type of chemical reaction in which an acid and a base react to form water and a salt, essentially neutralizing each other's properties. In this specific reaction involving \[\mathrm{H}_{3}\mathrm{PO}_{4}\]and\[\mathrm{X(OH)}_{2},\]the two reactants neutralize each other, resulting in the formation of \[\mathrm{XHPO}_{4}\]and water. After the initial reaction, the remaining \[\mathrm{XHPO}_{4}\]can further react.

• One mole of \[\mathrm{X(OH)}_{2}\]reacts with phosphoric acid to partially neutralize the solution.
• The remaining hydrogen in \[\mathrm{XHPO}_{4}\]indicates that full neutralization hasn't occurred.
• Full neutralization is achieved when another mole of \[\mathrm{X(OH)}_{2},\]or a strong base like \[\mathrm{NaOH},\]is added to react with the remaining hydrogen ion in the solution.

Acid-Base Reactions

Acid-base reactions are fundamental in chemistry, and understanding this concept helps in predicting the result of such interactions. These reactions typically involve proton transfer between the acid and the base. In the reaction discussed, \[\mathrm{H}_{3}\mathrm{PO}_{4}\]utsed its potential as an acid by donating hydrogen ions, while \[\mathrm{X(OH)}_{2}\]as a base provided hydroxide ions for neutralization.

• An acid is a substance that can donate a proton (H⁺), while a base can accept a proton or donate hydroxide ions (OH^-).
• In the equation, one mole of phosphoric acid reacts with one mole of the base, allowing the formation of the intermediate \[\mathrm{XHPO}_{4}.\]
• This reaction leaves a hydrogen ion that can still be neutralized by adding more of the base \[\mathrm{X(OH)}_{2}\]or by using another strong base such as \[\mathrm{NaOH}.\]

Understanding how acids and bases interact allows chemists to manipulate and predict changes in pH, a crucial aspect in many practical applications.