Problem 160 - A Complete Resource Book in Chemistry for JEE Main

Question

Consider the reaction, \(3 \mathrm{Br}_{2}+6 \mathrm{NaOH} \longrightarrow 5 \mathrm{NaBr}+\) \(\mathrm{NaBrO}_{3}+3 \mathrm{H}_{2} \mathrm{O}\). If \(\mathrm{E}\) and A represent equivalent weight and atomic weight of bromine, then \(5 \mathrm{E}=\mathrm{x} \mathrm{A}\). The value of \(x\) is

Step-by-Step Solution

Answer

The value of \( x \) is 1.

Step 1: Understand the Reaction

The given reaction is a redox reaction involving bromine and sodium hydroxide, resulting in the formation of sodium bromide, sodium bromate, and water.

Step 2: Analyze Oxidation States

Determine the change in oxidation states of bromine in the reaction. In Br2, bromine is in the 0 oxidation state. In NaBrO3, bromine is in +5 oxidation state, while in NaBr, bromine is in -1 oxidation state.

Step 3: Calculate Changes in Electrons

Calculate the number of electrons gained and lost. NaBrO3 gets +5 oxidation state from 0, losing 5 electrons per Br atom (thus for 1 mole, it is 5 equivalents), and each NaBr is formed by gaining 1 electron per Br.

Step 4: Evaluate Reaction Equivalents

According to the reaction, 3Br2 (6 Br atoms) turns to form 5 molecules of NaBr and 1 NaBrO3. Therefore, to compare equivalents, those forming NaBr contribute -5 equivalents and those for NaBrO3 are +5.

Step 5: Relate Equivals to Atomic Weight

The equivalent weight (E) is defined per equivalent of change, corresponding to weights involved in electron movements. In this case, calculate how 5 equivalents translate to x times the atomic weight: 5E = xA.

Step 6: Solve for x

5E refers to 5 equivalents of change. Atomic weight used per equivalent change ( in x) works with gauging electron transfer in pairs adequately, so 5E = 5A.

Key Concepts

Oxidation States

To understand redox reactions, grasping the concept of oxidation states is essential. Oxidation states, also known as oxidation numbers, help keep track of electrons as they are gained or lost in a chemical reaction.
They are assigned to elements based on certain rules. For example, in diatomic molecules like \( ext{Br}_2\), bromine is neutral, and thus the oxidation state is 0. But, in compounds like sodium bromide (NaBr), bromine takes on an oxidation state of -1 due to gaining an electron.

In our sample reaction, bromine undergoes two distinct changes in its oxidation state:

• From \(0\) in \( ext{Br}_2\) to \(+5\) in sodium bromate \( ext{NaBrO}_3\). This indicates a loss of electrons, and thus, oxidation.
• From \(0\) in \( ext{Br}_2\) to \(-1\) in \( ext{NaBr}\), which corresponds to a gain of electrons, hence reduction.

This dual change is crucial in understanding the redox nature of such reactions, where one substance gets oxidized and another gets reduced simultaneously.

Equivalent Weight

Equivalent weight is a fundamental concept in understanding reactions involving electron transfer, such as redox reactions. It is defined as the mass of a substance that gains or loses one mole of electrons in a redox reaction.
For bromine in our reaction, the equivalent weight corresponds to its weight per electron exchanged. Since equivalent weight (E) is linked to molar mass and the number of electrons, it can be used to relate to atomic weight (A).

In the given reaction, we have:

• Each Br in NaBr loses 1 electron, contributing to \( -5 \) equivalents, as 5 of such forms exist.
• Br in \( ext{NaBrO}_3\) undergoes a shift from \(0\) to \(+5\) oxidation state, contributing to \(+5\) equivalents as one such form exists.

The calculation of equivalents aids in determining how many atomic weights () compose 5 equivalents (), allowing us to find that 5E is equivalent to 5A.

Electron Transfer

Electron transfer is the backbone of redox reactions, where electrons shift from one species to another. This transfer dictates the changes in oxidation states and helps balance the reaction.
Remember, in redox reactions, one species will lose electrons (oxidation) while another gains them (reduction). In our example:

• Electrons are lost by the bromine molecules transforming into \( ext{NaBrO}_3\), where each bromine loses 5 electrons.
• Conversely, bromine atoms in \( ext{NaBr}\) gain electrons to achieve an oxidation state of -1, each receiving 1 electron.

This balance of electron transfer is pivotal to understanding how substances interact at the atomic level during redox reactions. By calculating the total number of electrons shifted, you ensure the reaction is balanced correctly, maintaining the principle that electrons lost equal electrons gained.