Problem 64 - A Complete Resource Book in Chemistry for JEE Main

Question

In the reaction \(\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g})\), when \(100 \mathrm{~mL}\) of \(\mathrm{N}_{2}\) has reacted, the volumes of \(\mathrm{H}_{2}\) and \(\mathrm{NH}_{3}\) are (a) \(300 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) and \(300 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) (b) \(100 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) and \(200 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) (c) \(300 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) and \(200 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\) (d) \(100 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) and \(100 \mathrm{~mL}\) of \(\mathrm{NH}_{3}\)

Step-by-Step Solution

Answer

(c) 300 mL of H₂ and 200 mL of NH₃.

Step 1: Understand the Balanced Chemical Equation

The given reaction is \( \mathrm{N}_{2} + 3 \mathrm{H}_{2} \rightleftharpoons 2 \mathrm{NH}_{3} \). The stoichiometry of the reaction shows that 1 mole of \( \mathrm{N}_{2} \) reacts with 3 moles of \( \mathrm{H}_{2} \) to produce 2 moles of \( \mathrm{NH}_{3} \).

Step 2: Determine Volume Ratios

According to Gay-Lussac's law, for gases under the same conditions of temperature and pressure, their volumes are proportional to the number of moles. Thus, 1 volume of \( \mathrm{N}_{2} \) reacts with 3 volumes of \( \mathrm{H}_{2} \) to produce 2 volumes of \( \mathrm{NH}_{3} \).

Step 3: Calculate Volumes of Each Gas

Given that 100 mL of \( \mathrm{N}_{2} \) has reacted, it follows that \( 3 \times 100 = 300 \) mL of \( \mathrm{H}_{2} \) is required. During this reaction, \( 2 \times 100 = 200 \) mL of \( \mathrm{NH}_{3} \) is produced.

Step 4: Conclusion Based on Calculations

The calculated volumes show that \( 300 \) mL of \( \mathrm{H}_{2} \) and \( 200 \) mL of \( \mathrm{NH}_{3} \) are formed when 100 mL of \( \mathrm{N}_{2} \) reacts. Therefore, the correct choice is (c).

Key Concepts

Chemical Reactions

In chemistry, reactions occur when substances, known as reactants, transform into different substances, called products. This transformation is driven by the breaking and forming of chemical bonds.
A chemical reaction involves a change in energy and is often categorized by the type of substances involved and the energy change.

• Reactants: These are substances consumed during the reaction.
• Products: These are substances that form as a result of the reaction.
• Energy Change: Reactions can be exothermic (release energy) or endothermic (absorb energy).

Understanding chemical reactions is fundamental as they are at the heart of both industrial processes and biological functions.

Volume Ratios

Volume ratios in gases are related to the quantities of gas reactants and products measured by volume under certain conditions. Through their behavior, gases can share a simple relationship between their volume and amount in moles when temperature and pressure remain constant.
When gases react, the volume ratios of reactants to products can be derived from their stoichiometry.

• The volume ratio is directly proportional to the stoichiometry of the balanced chemical equation.
• For example, in the reaction of nitrogen with hydrogen to form ammonia, the volume ratio reflects the stoichiometric coefficients: 1 volume of nitrogen reacts with 3 volumes of hydrogen to yield 2 volumes of ammonia.

Appreciating the volume relationship helps when predicting the outcome of gas reactions in practical scenarios.

Gay-Lussac's Law

Gay-Lussac's law is essential when studying gases during chemical reactions. It states that volumes of gases reacting at constant temperature and pressure have simple whole-number ratios.
This observation aligns with what we see in balanced chemical equations when describing reactions involving gases.

• This law shows that gases' behavior is predictable, enabling scientists to calculate unknown quantities from known reactants or products.
• For example, if you know that 1 volume of nitrogen reacts with 3 volumes of hydrogen, you can predict the volumes necessary to produce a certain amount of ammonia, assuming temperature and pressure remain constant.

Understanding Gay-Lussac's law helps to solve problems regarding the volume of gases in chemistry applications.

Balanced Chemical Equations

Balanced chemical equations are critical for expressing chemical reactions accurately and following the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system.
Balancing an equation involves ensuring the same number of each type of atom appears on both sides of the reaction.

• Coefficients in the formula represent the proportionate amounts of reactants and products.
• For instance, in the equation \(\mathrm{N}_{2} + 3 \mathrm{H}_{2} \rightarrow 2 \mathrm{NH}_{3}\), 1 nitrogen molecule reacts with 3 hydrogen molecules to produce 2 ammonia molecules.

Utilizing balanced chemical equations enables one to predict the outcomes and optimize conditions for chemical reactions.