Problem 144 - A Complete Resource Book in Chemistry for JEE Main

Question

If a mixture of 3 mole of \(\mathrm{H}_{2}\) and 1 mole of \(\mathrm{N}_{2}\) is completely converted into \(\mathrm{NH}_{3}\), what would be the ratio of the initial and final volume at same temperature and pressure?

Step-by-Step Solution

Answer

The initial to final volume ratio is 2:1.

Step 1: Write the Balanced Chemical Equation

The balanced chemical equation for the reaction between hydrogen \((\mathrm{H}_2)\) and nitrogen \((\mathrm{N}_2)\) to form ammonia \((\mathrm{NH}_3)\) is given by:\[ \mathrm{N}_2 + 3\mathrm{H}_2 \rightarrow 2\mathrm{NH}_3 \]

Step 2: Determine the Initial Moles of Reactants and Products

Initially, we have 3 moles of \( \mathrm{H}_2 \) and 1 mole of \( \mathrm{N}_2 \). According to the reaction stoichiometry (from Step 1), from 1 mole of \( \mathrm{N}_2 \), we fully react with 3 moles of \( \mathrm{H}_2 \) to produce 2 moles of \( \mathrm{NH}_3 \). Initial moles:- \( \mathrm{H}_2 \): 3 moles- \( \mathrm{N}_2 \): 1 moleFinal moles (when fully converted):- \( \mathrm{NH}_3 \): 2 moles

Step 3: Determine the Initial and Final Volume Ratios

According to Avogadro's law, the volume ratio of gases at the same temperature and pressure is equal to the mole ratio. Thus, we calculate the mole ratio:- **Initial moles:** Total = 3 (\( \mathrm{H}_2 \)) + 1 (\( \mathrm{N}_2 \)) = 4 moles- **Final moles:** Total = 2 (\( \mathrm{NH}_3 \)) = 2 molesThe volume ratio of initial to final moles is 4:2, which simplifies to 2:1.

Key Concepts

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions. It allows us to understand the exact proportions of reactants and products in a given chemical reaction. In a balanced chemical equation, stoichiometry helps determine how much of each substance is needed to react completely without any leftover reactants.
In our exercise, we use stoichiometry to calculate the relationship between moles of reactants and products. By examining the equation \( \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \), stoichiometry tells us that 1 mole of \( \text{N}_2 \) requires 3 moles of \( \text{H}_2 \) to produce 2 moles of \( \text{NH}_3 \). This relationship is critical to predicting outcomes and quantities in chemical processes.

• Enables precise measurements and calculations.
• Keeps chemical reactions balanced and efficient.
• Essential for calculating the needed amounts of reactants and expected amounts of products.

Avogadro's Law

Avogadro's Law is a fundamental principle in chemistry that states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This means that the volume of gas is directly proportional to the number of moles present, assuming constant temperature and pressure.
For our problem, Avogadro's Law helps us determine that the total initial volume related to the total initial moles compares to the total final volume relating to the total final moles. Given the initial 4 moles of reactants \( (3\text{H}_2 + 1\text{N}_2) \) and 2 moles of the product \( (2\text{NH}_3) \), the initial to final volume ratio can be determined as 4:2.

• Assists in comparing volumes of gases in reactions.
• Explains the effect of mole quantities on gas volumes.
• Useful for understanding gas behavior under various conditions.

Balanced Chemical Equation

A balanced chemical equation is essential as it represents the conservation of mass in a chemical reaction. It shows the exact number of atoms and molecules involved in reactants and products, ensuring that no atoms are lost or created in the process.
For the reaction \( \text{N}_2 + 3\text{H}_2 \rightarrow 2\text{NH}_3 \), balance is achieved by ensuring that nitrogen and hydrogen atoms are equal on both sides. This indicates that we start with 3 molecules of hydrogen and 1 molecule of nitrogen to yield 2 molecules of ammonia.

• Ensures the correctness of chemical equations.
• Allows for the accurate application of stoichiometry.
• Keeps chemical reactions efficient and reliable.

Without a balanced equation, understanding the proportions and results of reactions would be impossible, leading to incorrect predictions and miscalculations.