Problem 67 - A Complete Resource Book in Chemistry for JEE Main

Question

In the redox reaction \(\mathrm{xMnO}+\mathrm{yPbO}_{2}+\mathrm{zHNO}_{3} \longrightarrow \mathrm{HMnO}_{4}\) \(+\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{H}_{2} \mathrm{O}\) (a) \(\mathrm{x}=2, \mathrm{y}=5, \mathrm{z}=10\) (b) \(x=10, y=2, z=5\) (c) \(x=3, y=7, z=6\) (d) \(x=5, y=2, z=10\)

Step-by-Step Solution

Answer

The balanced equation is best represented by option (d), with coefficients x=5, y=2, z=10.

Step 1: Balance Manganese

To determine the correct coefficients in the redox reaction, first balance the number of manganese atoms. In the products, there is one manganese in \(\mathrm{HMnO}_{4}\), so ensure the coefficient before \(\mathrm{MnO}\) on the reactants matches. Look into each answer choice and focus on how the manganese atoms are consistent with this need.

Step 2: Balance Lead

Next, we need to balance lead atoms. Ensure the coefficients allow for consistent lead atoms from reactants \(\mathrm{PbO}_{2}\) going to \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\). "\(y\)" in the reactants should match with the production of lead in the nitrate form.

Step 3: Balance Oxygen

Now, check that the overall oxygen count is the same on both sides. Involves counting oxygen in both water and nitrate products as well. Notice the discrepancy in options which ensures correct application of coefficients.

Step 4: Balance Nitrogen

The presence of \(\mathrm{HNO}_{3}\) indicates nitrogen needs attention. Verify your choice ensures each nitrogen from \(\mathrm{HNO}_{3}\) matches those found in \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\).

Step 5: Final Balance with Hydrogen

With coefficients thus decided for all the atoms, ensure hydrogens from both the nitrate and water terms result in balanced hydrogen atom counts in the sum.

Step 6: Verify and Select

Ensure all steps agreed upon criteria and values. This holistic check guarantees all balancing reflects appropriateness for the balanced equation. The right coefficients should ensure each atom count per element is maintained accurately between reactants and products.

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry that ensures that a reaction obeys the law of conservation of mass. This law states that matter cannot be created or destroyed in an isolated system. As a result, the number of each type of atom must be the same on both sides of the equation.

To balance an equation, you need to adjust the coefficients, which are the numbers in front of molecules or atoms in the equation. Here's a step-by-step approach to balancing equations:

• Identify the reactants and products. List all the elements involved.
• Count the number of atoms of each element in the reactants and in the products.
• Use coefficients to balance the heaviest elements (those found in fewer compounds) first. Leave elements like hydrogen and oxygen for last, as they are commonly found in multiple molecules in reactions.
• Iterate the previous step until all elements are balanced.
• Double-check your equation to verify the same number of each type of atom appears on both sides of the equation.

Mastering this procedure ensures accuracy and reinforces the fundamental principle of mass conservation in chemical reactions.

Oxidation-Reduction

Oxidation-reduction reactions, or redox reactions, are chemical reactions involving the transfer of electrons between two substances. Understanding redox is key for many areas of chemistry, from biochemistry to industrial processes.

During a redox process:

• Oxidation refers to the loss of electrons in a substance. The substance that gives away electrons gets oxidized. Often, you can identify the oxidized substance by an increase in oxidation state.
• Reduction is the gain of electrons. The substance receiving the electrons gets reduced, often marked by a decrease in its oxidation state.

A mnemonic to remember this is "OIL RIG"—Oxidation Is Loss, Reduction Is Gain.

Balancing redox reactions often involves two parallel processes:

• Half-reaction method, where the reaction is split into two parts, each representing oxidation or reduction.
• Electrons are balanced separately in each half-reaction, ensuring no electrons are lost or gained across the entire chemical equation.
• Finally, the half-reactions are combined, ensuring that the electrons cancel out, helping to maintain neutrality and mass balance.

Understanding and executing redox transfers is vital, as they underpin a vast number of natural and synthetic processes.

Chemical Stoichiometry

Chemical stoichiometry is the calculation of reactants and products in chemical reactions. It uses balanced chemical equations to determine the amounts of substances needed or produced. This concept is crucial for laboratory and industrial settings where precise chemical measurements are vital.

To effectively use stoichiometry:

• Begin with a balanced chemical equation, which dictates the quantitative relationship between reactants and products.
• Use molar ratios from the balanced equation to calculate moles of different substances. The coefficients in the equation provide this conversion metric.
• Convert between units of moles, mass, and volume, using molar masses and the ideal gas law as appropriate. This step allows real-world application of theoretical chemistry.
• Consistency is critical – always ensure the units are consistent across your calculations to avoid errors.

Practicing stoichiometry helps in predicting the outcomes of reactions under various conditions and is essential for advancements in chemical manufacturing and research.