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

Question

The reaction, \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq})\) $$ \begin{gathered} +6 \mathrm{Cl}^{-}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g}) \\ \\\ \text { [2007] } \end{gathered} $$ (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 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

Correct options: (a) and (c). Incorrect options: (b) and (d).

Step 1: Write the Balanced Equation

The balanced chemical equation for the reaction is already given: \( 2 \mathrm{Al}(\mathrm{s}) + 6 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{Al}^{3+}(\mathrm{aq}) + 6 \mathrm{Cl}^{-}(\mathrm{aq}) + 3 \mathrm{H}_{2}(\mathrm{~g}) \). This equation shows us that 2 moles of \( \mathrm{Al} \) react with 6 moles of \( \mathrm{HCl} \) to produce 3 moles of \( \mathrm{H}_{2} \).

Step 2: Analyze Option (a)

Option (a) states that 33.6 L \( \mathrm{H}_{2} \) is produced for each mole of \( \mathrm{Al} \). Since the balanced equation shows 2 moles of \( \mathrm{Al} \) produce 3 moles of \( \mathrm{H}_{2} \), 1 mole of \( \mathrm{Al} \) produces 1.5 moles of \( \mathrm{H}_{2} \). At STP, 1 mole of any gas is 22.4 L, so 1.5 moles of \( \mathrm{H}_{2} \) should be 33.6 L.

Step 3: Analyze Option (b)

Option (b) states that 67.2 L \( \mathrm{H}_{2} \) is produced for every mole of \( \mathrm{Al} \). According to the calculations in the previous step, 1 mole of \( \mathrm{Al} \) should produce 33.6 L \( \mathrm{H}_{2} \). Therefore, option (b) is incorrect.

Step 4: Analyze Option (c)

Option (c) states 11.2 L \( \mathrm{H}_{2} \) is produced for each mole of \( \mathrm{HCl} \). From the balanced equation, 6 moles of \( \mathrm{HCl} \) produce 3 \( \mathrm{H}_{2} \) (3 moles or 67.2 L at STP). Therefore, 1 mole \( \mathrm{HCl} \) produces 1/2 mole \( \mathrm{H}_{2} \), which is 11.2 L at STP. This is correct.

Step 5: Analyze Option (d)

Option (d) states 6 L \( \mathrm{HCl} \) is consumed for every 3 L \( \mathrm{H}_{2} \). Knowing 6 moles of \( \mathrm{HCl} \) produce 3 moles of \( \mathrm{H}_{2} \), the stoichiometry shows it's a 2:1 mole ratio. At STP, this means 6 L \( \mathrm{HCl} \) for every 3 L \( \mathrm{H}_{2} \) is incorrect since it should be 12 L \( \mathrm{HCl} \).

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is a cornerstone in chemistry that ensures the conservation of mass and defines the proportions of reactants and products in a chemical reaction. In the given reaction \(2 \text{Al(s)} + 6 \text{HCl(aq)} \rightarrow 2 \text{Al}^{3+}(\text{aq}) + 6 \text{Cl}^{-}(\text{aq}) + 3 \text{H}_2(\text{g})\), the equation is balanced because it has equal numbers of each type of atom on both sides. This maintains the atomic theory's stipulation that atoms are neither created nor destroyed in chemical reactions.

Balancing an equation involves adding coefficients in front of reactants or products to ensure that the same number of each atom is present on both sides. This particular equation tells us that 2 moles of aluminum react with 6 moles of hydrochloric acid to produce 3 moles of hydrogen gas and other products.

Understanding balanced chemical equations helps predict how much product is formed from a set amount of reactants and is a vital skill for solving stoichiometry problems.

Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the atomic scale and the macroscopic scale, allowing chemists to quantify substances. One mole is defined as \(6.022 \times 10^{23}\) of any chemical unit, whether it be atoms, molecules, ions, etc. This is known as Avogadro's number.

In the context of our example, the balanced equation indicates that 2 moles of aluminum react with 6 moles of hydrochloric acid to form 3 moles of hydrogen gas. By interpreting this equation through the lens of the mole concept, we understand that the quantities of reactants and products are expressed in moles, which allows us to apply mathematical calculations to quantify the substances involved in the reaction.

Using the mole concept, you can calculate how many liters of hydrogen gas are produced. At Standard Temperature and Pressure (STP), which is 0°C and 1 atm, 1 mole of any gas occupies 22.4 liters. This is why 1.5 moles of \(\text{H}_2\) equals 33.6 liters.

Ideal Gas Law

The Ideal Gas Law is a crucial equation in chemistry used to relate the pressure, volume, temperature, and number of moles of a gas. The formula for the Ideal Gas Law is \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin.

This law assumes that gases behave ideally which means their particles have no volume and do not interact with each other. While this is an approximation, it works well under many conditions, especially at high temperatures and low pressures. In our exercise, we focus on hydrogen gas, \(\text{H}_2\). The reaction states that at STP, or standard temperature and pressure, the Ideal Gas Law simplifies to show that 22.4 liters of gas is occupied by 1 mole of any ideal gas.

Whether at STP or not, you can use the Ideal Gas Law to calculate unknown properties of gases in any chemical reaction. This concept allows chemists to predict the behavior of gases accurately, enhancing our understanding of their roles in chemical reactions.