Problem 65 - A Complete Resource Book in Chemistry for JEE Main

Question

If a mixture containing 3 moles of hydrogen and 1 mole of nitrogen is converted completely into ammonia, the ratio of volumes of reactants and products at the same temperature and pressure would be (a) \(2: 1\) (b) \(1: 2\) (c) \(1: 3\) (d) \(3: 1\)

Step-by-Step Solution

Answer

The ratio of volumes of reactants to products is \(2:1\).

Step 1: Understand the Reaction

The chemical reaction for the formation of ammonia from hydrogen and nitrogen is represented by the balanced equation: \[ N_2 + 3H_2 \rightarrow 2NH_3 \] This equation shows that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia.

Step 2: Identify the Moles of Reactants

According to the problem, we have 3 moles of hydrogen and 1 mole of nitrogen. This aligns perfectly with the stoichiometry of the balanced equation, as 3 moles of hydrogen are needed for every 1 mole of nitrogen.

Step 3: Calculate Total Moles of Reactants

Based on the reaction equation, the total moles of reactants are the sum of moles of hydrogen and nitrogen: \(3 + 1 = 4\) moles.

Step 4: Calculate Total Moles of Products

The balanced equation shows that from 3 moles of hydrogen and 1 mole of nitrogen, we get 2 moles of ammonia \(NH_3\). Thus, the total moles of product is 2.

Step 5: Compute Ratio of Volumes

At the same temperature and pressure, the volume of gases is directly proportional to the number of moles (according to Avogadro's law). Hence, the ratio of the volumes of the reactants to the products is the same as the ratio of moles: \[\text{Ratio} = \frac{4}{2} = 2:1\]

Key Concepts

Stoichiometry

In chemistry, stoichiometry is a fundamental concept that deals with the proportions of reactants and products in chemical reactions. It is critical in predicting how much of each substance is consumed and formed. The balanced chemical equation for the formation of ammonia is a perfect example: \[ N_2 + 3H_2 \rightarrow 2NH_3 \] This equation indicates strict stoichiometric ratios—1 mole of nitrogen reacts with 3 moles of hydrogen to form 2 moles of ammonia. These numbers, called coefficients, show the precise amount of reactants needed and the amount of products formed.

• Coefficients in a chemical equation tell us the relative number of moles of each substance involved.
• They help in calculating how much of a reactant is needed or how much of a product will be produced.

In essence, stoichiometry is the bridge between the reactants and products, ensuring that the law of conservation of mass is maintained.

Chemical Reactions

A chemical reaction describes the process by which substances, known as reactants, undergo reorganization of atoms to form new substances, termed products. In the ammonia formation reaction, hydrogen and nitrogen gases interact to yield ammonia.

• The reactants are hydrogen gas \( H_2 \) and nitrogen gas \( N_2 \).
• The product is ammonia \( NH_3 \).
• The reaction is: \[ N_2 + 3H_2 \rightarrow 2NH_3 \]

During this transformation, bonds between the atoms of hydrogen and nitrogen are broken, and new bonds are formed in the resulting ammonia. This chemical rearrangement involves the following key characteristics:

• Reactants and products differ in composition.
• The process involves changes at the molecular level.
• The reaction is carried out under certain conditions, often requiring heat or a catalyst.

Avogadro's Law

Avogadro's Law is a crucial principle in understanding gas behavior. It states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules or moles. This principle is crucial in predicting the volumes of gases involved in the ammonia formation reaction.Considering the balanced equation: \[ N_2 + 3H_2 \rightarrow 2NH_3 \], Avogadro's Law implies that the volume ratio of gases is the same as their mole ratio.

• If you have a total of 4 moles of reactant gases (1 mole of \( N_2 \) and 3 moles of \( H_2 \)), their combined volume will be 4 units of gas.
• The product, \( NH_3 \), is formed in 2 moles, hence its volume would be 2 units.
• Therefore, the ratio of the volume of the reactants to products is \(2:1\), precisely reflecting the mole ratio due to Avogadro's principle.

In practice, Avogadro's Law allows chemists to predict the behavior of gases in reactions, assuming ideal gas conditions.