Problem 83 - A Complete Resource Book in Chemistry for JEE Main

Question

\(2 \mathrm{~g}\) of aluminium is treated separately with excess of dilute \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and excess of \(\mathrm{NaOH}\). The ratio of the volumes of hydrogen evolved is (a) \(1: 1\) (b) \(1: 2\) (c) \(2: 1\) (d) \(2: 3\)

Step-by-Step Solution

Answer

The ratio of the volumes of hydrogen evolved is 1:1.

Step 1: Understand the Reactions

When aluminium reacts with dilute sulfuric acid (\(\text{H}_2\text{SO}_4\)) and sodium hydroxide (\(\text{NaOH}\)), it produces hydrogen gas. The balanced chemical equations are: \[2\text{Al} + 3\text{H}_2\text{SO}_4 \rightarrow \text{Al}_2\text{(SO}_4\text{)}_3 + 3\text{H}_2\] for sulfuric acid and \[2\text{Al} + 6\text{NaOH} \rightarrow 2\text{NaAlO}_2 + 3\text{H}_2\] for sodium hydroxide.

Step 2: Calculate Moles of Aluminium

The molar mass of aluminium (\(\text{Al}\)) is 27 g/mol. For 2 g of aluminium, the moles are calculated as follows: \[\text{Moles of Al} = \frac{2 \text{ g}}{27 \text{ g/mol}} \approx 0.074 \text{ moles}\] of aluminium.

Step 3: Hydrogen Evolved with H2SO4

From the first reaction, 3 moles of hydrogen gas are evolved for every 2 moles of aluminium. Therefore, the moles of hydrogen gas evolved are: \[\text{Moles of } \text{H}_2 = \frac{3}{2} \times 0.074 \approx 0.111 \text{ moles} \].

Step 4: Hydrogen Evolved with NaOH

From the second reaction, 3 moles of hydrogen gas are evolved for every 2 moles of aluminium. Therefore, the moles of hydrogen gas evolved are: \[\text{Moles of } \text{H}_2 = \frac{3}{2} \times 0.074 \approx 0.111 \text{ moles} \].

Step 5: Calculate Ratio of Hydrogen Evolved

Since both reactions produce the same amount of hydrogen gas, the ratio of the volumes of hydrogen evolved is \(1:1\) (or option (a)).

Key Concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry that deals with the calculation of reactants and products in chemical reactions. It acts as the bridge between the quantities of substances involved in a reaction. Imagine following a recipe where each ingredient needs to be measured accurately to achieve the desired result. Similarly, stoichiometry ensures that the correct amount of reactants is used to produce the expected amount of product.

In the case of our problem, stoichiometry tells us how many moles of hydrogen gas are produced when 2 grams of aluminium react with excess sulfuric acid or sodium hydroxide. Since 2 moles of aluminium produce 3 moles of hydrogen gas in both reactions, stoichiometry allows us to calculate the actual amount of gas released, ensuring precise and reliable predictions.

To practice stoichiometry effectively, always focus on:

• Balancing chemical equations.
• Using molar ratios to connect reactants and products.
• Calculating moles accurately using molar masses.

Understanding stoichiometry is pivotal for solving a variety of chemistry problems, especially when dealing with chemical reactions and moles.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds, leading to the formation of new products. In our given problem, aluminium reacts with two different chemicals: sulfuric acid (\( \text{H}_2\text{SO}_4 \)) and sodium hydroxide (\( \text{NaOH} \)). Each of these reactions results in the generation of hydrogen gas, a common product due to the presence of aluminium.

The balanced equations for these reactions are:

• With sulfuric acid: \[ 2 \text{Al} + 3 \text{H}_2\text{SO}_4 \rightarrow \text{Al}_2(\text{SO}_4)_3 + 3 \text{H}_2 \]
• With sodium hydroxide: \[ 2 \text{Al} + 6 \text{NaOH} \rightarrow 2 \text{NaAlO}_2 + 3 \text{H}_2 \]

Each reaction has a unique balanced chemical equation, which is crucial for predicting the reaction's outcome.

Chemical reactions aren't just events on paper; they happen around us constantly, driving everything from the fuel in our cars to the metabolic processes in our bodies. By understanding how to balance these reactions, we can predict the amount of products and reactants consumed, making sense of the chemical world.

Moles Calculation

A mole is a fundamental unit in chemistry that provides a bridge between the atomic scale and the macroscopic scale. It's used to quantify the amount of a substance. In chemical calculations, the concept of a mole allows you to calculate how much of a substance is involved in a reaction. For instance, in our exercise, we need to determine how many moles of aluminium are present to find out the amount of hydrogen gas produced.

Here's how that works: The molar mass of aluminium is 27 g/mol. This means one mole of aluminium weighs 27 grams. Thus, for 2 grams of aluminium, we calculate the moles using the formula: \[ \text{Moles of Al} = \frac{2 \text{ grams}}{27 \text{ g/mol}} \approx 0.074 \text{ moles} \]Understanding and calculating moles is essential because the quantities in chemical reactions are derived from moles. Many students find it helpful to link these calculations to real-world examples to solidify the concept.

To enhance comprehension, regularly practice:

• Converting grams to moles using molar mass.
• Relating moles to coefficients in balanced equations.
• Visualizing mole relationships in a reaction.

By mastering moles calculations, you gain a powerful tool for tackling a wide range of chemical problems.