Problem 173 - A Complete Resource Book in Chemistry for JEE Main

Question

The reaction, \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}\) (aq) \(\longrightarrow 2 \mathrm{Al}^{3+}\) (aq) $$ \begin{gathered} +6 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g}) \\ \text { [2007] } \end{gathered} $$ (a) \(33.6 \mathrm{~L} \mathrm{H}_{2}(\mathrm{~g})\) is produced regardless of temperature and pressure for every mole of \(\mathrm{Al}\) that reacts (b) \(67.2 \mathrm{~L} \mathrm{H}_{2}(\mathrm{~g})\) at STP is produced for every mole of Al that reacts (c) \(11.2 \mathrm{~L} \mathrm{H}_{2}(\mathrm{~g})\) at STP is produced for every mole of \(\mathrm{HCl}\) (aq) consumed (d) \(6 \mathrm{~L} \mathrm{HCl}\) (aq) is consumed for every \(3 \mathrm{~L} \mathrm{H}_{2}(\mathrm{~g})\) produced

Step-by-Step Solution

Answer

(c) is correct; 11.2 L of H2 at STP per mole of HCl is true.

Step 1: Understand the reaction

The reaction is between aluminum and hydrochloric acid to produce aluminum ions, chloride ions, and hydrogen gas. The balanced chemical equation is: \[2 \text{Al}(s) + 6 \text{HCl}(aq) \rightarrow 2 \text{Al}^{3+}(aq) + 6 \text{Cl}^{-}(aq) + 3 \text{H}_2(g)\] This indicates that 2 moles of aluminum react with 6 moles of hydrochloric acid to produce 3 moles of hydrogen gas.

Step 2: Analyze each statement

Each statement will be analyzed based on the stoichiometry of the balanced equation.

Step 3: Evaluate statement (a)

Statement (a) suggests that 33.6 L of hydrogen gas is produced for every mole of Al. The reaction shows that 2 moles Al produce 3 moles H2. At STP, each mole of gas occupies 22.4 L. Therefore, for 1 mole of Al, \((1 \text{ mole Al} / 2) \times 3 \times 22.4\) = 33.6 L H2 can be true only at STP. Thus, (a) is not always true if it applies regardless of conditions.

Step 4: Evaluate statement (b)

Statement (b) claims 67.2 L of hydrogen at STP is produced per mole of Al reacted. From the equation, 2 moles Al produce 3 moles H2. Thus, each mole of Al produces \((1/2) \times 3 \times 22.4\) = 33.6 L per mole. Hence, (b) is false.

Step 5: Evaluate statement (c)

Statement (c) proposes 11.2 L of H2 at STP per mole of HCl consumed. The balanced equation shows 6 moles of HCl produce 3 moles of H2, or per mole of HCl, \((3/6) \times 22.4 = 11.2\) L of H2, which is true.

Step 6: Evaluate statement (d)

Statement (d) suggests a 6 L consumption of HCl per 3 L of H2 produced. Let’s check: 6 moles of HCl produce 3 moles of H2, so the volume ratio is really \(6 \times 22.4 : 3 \times 22.4 = 2:1\), contradicting the statement's exact terms, making (d) false.

Key Concepts

balanced chemical equation

In chemistry, it is crucial that chemical equations accurately represent what occurs in a reaction. A balanced chemical equation has equal numbers of each type of atom on both sides of the equation. This ensures that mass is conserved during the reaction. For the given reaction:

• \(2 \text{Al}(s) + 6 \text{HCl}(aq) \rightarrow 2 \text{Al}^{3+}(aq) + 6 \text{Cl}^{-}(aq) + 3 \text{H}_2(g)\)

We see that it is balanced because:

• There are 2 aluminum atoms and 6 hydrogen chloride molecules on the reactant side.
• On the product side, there are 2 aluminum ions, 6 chloride ions, and 3 molecules of hydrogen gas.

Each atom and charge is balanced. This equation shows us the stoichiometric relationships, like how many moles of reactants are needed and how many moles of products are formed. Understanding and balancing chemical equations is a fundamental skill in stoichiometry.

mole concept

The mole is a pivotal concept in chemistry that bridges the atomic and macroscopic worlds. Defined as Avogadro's number (\(6.022 \times 10^{23}\)particles), it allows chemists to count atoms, ions, and molecules by weighing them. In our reaction:

• 2 moles of aluminum (\(\text{Al}\)) react with 6 moles of hydrochloric acid (\(\text{HCl}\)).
• This ratio allows for the production of 3 moles of hydrogen gas (\(\text{H}_2\)).

Understanding the mole concept helps us to convert between the mass of substances and the amount of substance, using molar mass as the conversion factor. This is crucial for reaction calculations and analyzing how much of each substance is needed or produced.

gas laws

Gas laws describe how gases behave under different conditions of pressure, volume, and temperature. The Ideal Gas Law, \(PV = nRT\), is one of the most common formulations. Here, \(P\) represents pressure, \(V\) volume, \(n\) the number of moles, \(R\) the gas constant, and \(T\) temperature in Kelvin.
In the problem, statements referring to standard temperature and pressure (STP) use these principles, noting that 1 mole of any ideal gas occupies 22.4 L at STP. Thus:

• For aluminum reacting with HCl to produce hydrogen gas, understanding that 2 moles of aluminum will yield 3 moles of \(\text{H}_2\) helps predict the volume of gas formed in different conditions.

Applying these gas laws allows predictions of gas behaviors and adjustments for real-world non-STP situations.

reaction analysis

Reaction analysis involves evaluating all aspects of a chemical reaction, including reactants, products, and conditions to determine the feasibility and efficiency of the reaction. In this example, the focus is on the stoichiometric relationships and the volume of gases produced.

• By inspecting the reaction and the balanced equation, we conclude that certain statements about volumes and conditions can be true while others cannot.
• For instance, statement (c) correctly predicts the volume of hydrogen gas produced from hydrochloric acid at STP, demonstrating a clear understanding of the equation's stoichiometry.

This kind of analysis is not only vital for understanding and predicting outcomes but also for designing experiments and industrial processes that rely on chemical reactions.