Problem 106 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{aHNO}_{3}+\mathrm{bH}_{2} \mathrm{~S} \longrightarrow \mathrm{cNO}+\mathrm{d} \mathrm{H}_{2} \mathrm{O}+3 \mathrm{~S}\). What are the values of \(\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d} ?\) (a) \(2,3,2,2\) (b) \(2,3,2,4\) (c) \(3,3,2,4\) (d) \(4,3,1,2\)

Step-by-Step Solution

Answer

The values are (b) 2, 3, 2, 4.

Step 1: Count Atoms on Each Side

First, we'll compare the number of atoms for each element on both sides of the chemical equation. We have N, H, O, and S involved in this reaction.

Step 2: Balance Nitrogen (N)

The reactant side has \(a\) molecules of \(\mathrm{HNO}_3\) providing \(a\) nitrogen atoms. The product side has \(c\) molecules of NO, each containing one nitrogen atom. Set \(a = c\) to balance nitrogen atoms.

Step 3: Balance Sulfur (S)

Look at sulfur. There are \(b\) \(\mathrm{H}_2\mathrm{S}\) molecules on the reactant side providing \(b\) sulfur atoms. The product side contains \(3\) sulfur atoms, implying \(b = 3\).

Step 4: Balance Hydrogen (H)

For hydrogen, the reactant side has \(a + 2b\) hydrogen atoms from \(a\) \(\mathrm{HNO}_3\) and \(b\) \(\mathrm{H}_2\mathrm{S}\). The product side has \(2d\) hydrogen atoms from water, \(\mathrm{H}_2\mathrm{O}\). Set \(a + 2b = 2d\).

Step 5: Balance Oxygen (O)

The oxygen atoms come from \(a\) \(\mathrm{HNO}_3\), each contributing \(3\) oxygen atoms, giving \(3a\) oxygen atoms on the reactant side. \(c\) NO molecules and \(d\) water molecules have \(c + d\) oxygen atoms on the product side. Set \(3a = c + d\).

Step 6: Solve the Equations

Consider the equations derived: \(a = c\), \(b = 3\), \(a + 2b = 2d\), \(3a = c + d\). Substitute \(b = 3\) and solve:- Since \(d = 4\) satisfies \(a + 2b = 2d\) when \(a = c = 2\), check the options.

Step 7: Verify the Balanced Equation

Substitute the values: \(a=2\), \(b=3\), \(c=2\), \(d=4\). Verify with the equation: \[2\mathrm{HNO}_{3} + 3\mathrm{H}_{2}\mathrm{S} \rightarrow 2\mathrm{NO} + 4\mathrm{H}_{2}\mathrm{O} + 3\mathrm{S}\]Now check if every atom is balanced on both sides.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental aspect of chemistry that involves the calculation of reactants and products in chemical reactions. It allows chemists to predict the quantities of substances consumed and produced in reactions.
To grasp stoichiometry, it's important to understand a few key ideas:

• **Molar Ratios:** These are derived from the coefficients in a balanced chemical equation. They indicate the ratio in which reactants combine and products form. For example, the equation given: \[2\mathrm{HNO}_{3} + 3\mathrm{H}_{2}\mathrm{S} \rightarrow 2\mathrm{NO} + 4\mathrm{H}_{2}\mathrm{O} + 3\mathrm{S}\] means that two moles of nitric acid react with three moles of hydrogen sulfide to produce two moles of nitrogen monoxide, four moles of water, and three moles of sulfur.
• **Balancing Equations:** It's crucial because it ensures that the same number of each type of atom is present on both sides of the reaction. This follows the law of conservation of mass.
• **Using Ratios to Calculate Amounts:** Once an equation is balanced, these ratios can be used to calculate how much of each substance is needed or produced.

Understanding stoichiometry is essential for solving problems related to chemical reactions and for practical applications such as chemical engineering and laboratory experiments.

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. This transformation involves the breaking and forming of chemical bonds, leading to changes in the substances involved.
Here’s what you need to know about chemical reactions:

• **Reactants and Products:** In any chemical reaction, the starting materials are called reactants, and the substances formed are called products. For the given formula: \[\mathrm{HNO}_{3} + \mathrm{H}_{2}\mathrm{~S} \rightarrow \mathrm{NO} + \mathrm{H}_{2}\mathrm{O} + \mathrm{S}\] \(\mathrm{HNO}_{3}\) and \(\mathrm{H}_{2}\mathrm{S}\) are the reactants, and \(\mathrm{NO}, \mathrm{H}_{2}\mathrm{O}\), and sulfur (\mathrm{S}) are the products.
• **Balancing Reactions:** A balanced reaction means that the number of each type of atom is equal on both sides of the equation, indicating that mass is conserved during the reaction.
• **Types of Chemical Reactions:** These can be classified into various types, such as synthesis, decomposition, and oxidation-reduction, which are based on the nature of the reactants and products.

Chemical reactions are not just theoretical; they happen all around us and are fundamental to many scientific and industrial processes. Mastery of chemical reactions allows chemists to manipulate matter in beneficial ways.

Oxidation-Reduction Reactions

Oxidation-reduction reactions, or redox reactions, are a type of chemical reaction involving the transfer of electrons between two species. These reactions are essential for numerous natural and industrial processes.Redox reactions are characterized by changes in oxidation states of the reactants. Here's how it works:

• **Oxidation:** This involves the loss of electrons. The substance that loses electrons is said to be oxidized. In our equation, notice that sulfur in \(\mathrm{H}_2\mathrm{S}\) is oxidized as it turns into elemental sulfur.
• **Reduction:** This involves the gain of electrons. The substance that gains electrons is reduced. For example, the nitrogen in \(\mathrm{HNO}_3\) is reduced to form \(\mathrm{NO}\).
• **Oxidizing and Reducing Agents:** The oxidizing agent is the compound that is reduced, and conversely, the reducing agent is the compound that is oxidized.

Understanding redox reactions is vital for explaining energy generation in batteries, metal extraction, and even biological processes like respiration. Learning to identify changes in oxidation states is a key skill in mastering chemistry.