Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The first and second ionisation enthalpies of a metal are 496 and 4560 kJ \(\mathrm{mol}^{-1}\), respectively. How many moles of \(\mathrm{HCl}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\), respectively, will be needed to react completely with 1 mole of the metal hydroxide? (a) 1 and 1 (b) 2 and \(0.5\) (c) 1 and 2 (d) 1 and \(0.5\)

Step-by-Step Solution

Answer

The answer is (d): 1 and 0.5.

Step 1: Understand Ionisation Enthalpies

The first ionisation enthalpy is the energy required to remove the first electron from a neutral atom, and the second ionisation enthalpy is the energy required to remove a second electron after the first has been removed. Given that the second ionisation enthalpy is significantly higher than the first, it indicates that the metal likely forms +1 ions under standard conditions.

Step 2: Determine Metal Hydroxide Composition

Since the metal most likely forms +1 ions, the metal hydroxide formula will be \( ext{MOH}\). This is because it will combine with one hydroxide ion \( ext{OH}^-\) to form a neutral compound.

Step 3: Reaction with HCl

The metal hydroxide \( ext{MOH}\) will react with hydrochloric acid \( ext{HCl}\) to form salt \( ext{MCl}\) and water through a neutralization reaction: \[ ext{MOH} + ext{HCl} ightarrow ext{MCl} + ext{H}_2 ext{O}\]. Each \( ext{MOH}\) molecule requires one \( ext{HCl}\) molecule to react completely, thus 1 mole of \( ext{HCl}\) will react with 1 mole of \( ext{MOH}\).

Step 4: Reaction with H2SO4

The metal hydroxide \( ext{MOH}\) can also react with sulfuric acid \( ext{H}_2 ext{SO}_4\) to form a salt and water: \[2 ext{MOH} + ext{H}_2 ext{SO}_4 ightarrow ext{M}_2 ext{SO}_4 + 2 ext{H}_2 ext{O}\]. This equation shows that 2 moles of \( ext{MOH}\) react with each mole of \( ext{H}_2 ext{SO}_4\), so 1 mole of \( ext{MOH}\) needs 0.5 moles of \( ext{H}_2 ext{SO}_4\).

Step 5: Compare with Given Options

Based on the stoichiometry from steps 3 and 4, reacting 1 mole of the metal hydroxide requires 1 mole of \( ext{HCl}\) and 0.5 moles of \( ext{H}_2 ext{SO}_4\). This matches option (d): 1 and 0.5.

Key Concepts

Metal Hydroxide Reactions

Metal hydroxide reactions involve compounds where metal cations and hydroxide ions form metal hydroxides, like \( \text{MOH} \) in the given exercise. Such reactions are key in understanding how metals interact with other compounds.

These compounds are typically formed when metals react with water, where the metal donates electrons to oxygen, and hydroxide ions \( \text{OH}^-\) are generated. The metal hydroxide is important in neutralization reactions because it can react with acids to form salts and water.

Understanding the nature of the metal helps predict the formula of the hydroxide it forms. For instance, if a metal forms \(+1 \) ions, the resulting hydroxide will have a one-to-one ratio of metal ions to hydroxide ions, as seen in the formula \( \text{MOH} \).

• Metal hydroxides react with acids to produce salts in a process known as a neutralization reaction.
• Prediction of the product formed in these reactions can be made based on the charge of the metal ion.
• For a metal forming +1 ions, it will form hydroxide \( \text{MOH} \).

Neutralization Reaction

A neutralization reaction is a chemical process where an acid and a base react to form water and a salt. These reactions are fundamental across chemistry, especially when dealing with reactions like between \( \text{MOH} \) and an acid such as hydrochloric acid (HCl) or sulfuric acid (H₂SO₄).

In the context of metal hydroxides, when they react with an acid:

• The base (metal hydroxide) reacts with an acid to produce water and a corresponding salt.
• For example, when \( \text{MOH} \) reacts with \( \text{HCl} \), the equation \( \text{MOH} + \text{HCl} \rightarrow \text{MCl} + \text{H}_2\text{O}\) describes the formation of water and salt \( \text{MCl} \).
• The presence of water and a salt as the only products signifies a complete neutralization has occurred.

These reactions regulate pH and are crucial in many industrial and biological processes. Notably, water molecules form from the combination of hydrogen ions from the acid and hydroxide ions from the base.

Stoichiometry of Acids and Bases

Stoichiometry is crucial in predicting how much of each reactant is required in a chemical reaction and what products will result. With acids and bases, stoichiometry helps in balancing chemical equations and determining the precise amounts of substances needed for complete reaction.

Referring to our exercise, the reaction of \( \text{MOH} \) with \( \text{HCl} \) and \( \text{H}_2\text{SO}_4 \) requires specific molar proportions:

• For the reaction with \( \text{HCl} \), the stoichiometry is simple: 1 mole of \( \text{MOH} \) requires 1 mole of \( \text{HCl} \). This 1:1 ratio is straightforward because each hydroxide ion reacts with one hydronium ion from the acid.
• For \( \text{H}_2\text{SO}_4 \), however, 2 moles of \( \text{MOH} \) are required to react with 1 mole of \( \text{H}_2\text{SO}_4 \). This is due to \( \text{H}_2\text{SO}_4 \) being diprotic (yielding two protons per molecule), so the stoichiometry shows a 2:1 ratio between base and acid.

Studying these stoichiometric principles ensures a correct balance of chemical equations and determines reactant usage efficiently, which is vital for both theoretical and practical chemical applications.