Problem 28 - A Complete Resource Book in Chemistry for JEE Main

Question

\(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}+6 \mathrm{I}^{-}+14 \mathrm{H}^{+} \longrightarrow 2 \mathrm{Cr}^{3+}+7 \mathrm{H}_{2} \mathrm{O}+3 \mathrm{I}_{2}\) Equivalent weight of \(\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}\) is (a) \(\mathrm{M} / 3\) (b) \(\mathrm{M} / 6\) (c) \(\mathrm{M} / 2\) (d) none of these

Step-by-Step Solution

Answer

The equivalent weight of \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) is \(\mathrm{M} / 6\). Option (b) is correct.

Step 1: Identify the redox changes in the reaction

In the given reaction, the dichromate ion (\(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\)) is reduced to \(\mathrm{Cr}^{3+}\), and \(\mathrm{I}^{-}\) is oxidized to \(\mathrm{I}_{2}\). We need to determine the change in oxidation states for these elements.

Step 2: Determine oxidation states

For \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\), each \(\mathrm{Cr}\) has an oxidation state of +6 (since oxygen is -2), and each \(\mathrm{Cr}^{3+}\) has an oxidation state of +3. The change per chromium atom is +6 to +3, a change of 3 units.

Step 3: Calculate total electron exchange for Cr

There are 2 \(\mathrm{Cr}\) atoms in \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\), so the total change in oxidation state for the entire ion is \(2 \times 3 = 6\) electrons gained.

Step 4: Determine equivalent weight formula

The equivalent weight of a species involved in a redox reaction is given by \(\frac{\text{Molar mass of the species}}{\text{n-factor}}\), where the n-factor is the total change in oxidation states of the element being reduced or oxidized. Here, the n-factor is 6, because \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\) gains six electrons in total.

Step 5: Solve for equivalent weight of \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\)

The equivalent weight of\(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\)is \(\frac{\mathrm{M}}{6}\), where \(\mathrm{M}\) is the molar mass of \(\mathrm{Cr}_{2}\mathrm{O}_{7}^{2-}\).

Step 6: Choose the correct answer

Based on the calculation, the correct answer from the options given is (b) \(\mathrm{M} / 6\).

Key Concepts

Redox Reactions

Redox reactions are fundamental chemical reactions that involve the transfer of electrons between two substances. The term "redox" comes from the two processes occurring simultaneously: reduction and oxidation. In simple terms, a reduction involves the gain of electrons, while oxidation is the loss of electrons. In the context of our reaction, we can see these processes at work. The dichromate ion ( Cr_{2}O_{7}^{2-} ) is reduced, meaning it gains electrons to become Cr^{3+} ions. Meanwhile, the iodide ions ( I^{-} ) are oxidized, meaning they lose electrons and form diatomic iodine ( I_{2} ). Understanding redox reactions is crucial because they are involved in many key processes, from metabolism to industrial chemical reactions.
Here are some important points about redox reactions:

• They involve the transfer of electrons between chemical species.
• Redox reactions are characterized by changes in oxidation states of the reactants.
• These reactions are often balanced by adjusting the electrons transferred to ensure mass and charge conservation.

Oxidation States

Oxidation states, also known as oxidation numbers, indicate the degree of oxidation of an atom in a chemical compound. They are critical for understanding redox reactions because they help determine how electrons are transferred between reactants. The oxidation state is assigned based on certain rules that account for known charges and the structure of molecules.
In the exercise, we have dichromate ion ( Cr_{2}O_{7}^{2-} ), where each chromium atom has an oxidation state of +6. After the reaction, in which they are reduced to Cr^{3+} , each chromium's oxidation state drops to +3, indicating a gain of electrons. Similarly, I^{-} ions start with an oxidation state of -1 and are oxidized to form I_{2} , with each iodine atom reaching an oxidation state of 0.
Remember these points about oxidation states:

• They are theoretical charges assigned to atoms to help track electron flow in reactions.
• Changes in oxidation states help identify which components are oxidized or reduced in a reaction.
• Balancing redox reactions often involves using oxidation states to ensure the reaction is consistent in terms of mass and charge.

Dichromate Ion

The dichromate ion ( Cr_{2}O_{7}^{2-} ) is a common oxidizing agent in chemical reactions. It is known for its bright orange color and is commonly encountered in solution as a part of the chromium-based compounds. The dichromate ion's structure consists of two chromium atoms linked through oxygen atoms, forming a bridged structure that is key to its chemical properties.
When participating in redox reactions, the dichromate ion accepts electrons, which accounts for its oxidizing ability. In the provided exercise, it can reduce from its +6 oxidation state to a +3 oxidation state by gaining electrons. This change is essential for calculating the equivalent weight in redox reactions.
Key aspects of dichromate ions include:

• They often serve as oxidizing agents due to their high oxidation state.
• Its reduction potential is utilized in titrations and other chemical processes.
• The color change associated with its redox activity helps indicate reaction progress in experiments.

Electron Exchange

Electron exchange is a central component of redox reactions, reflecting the movement of electrons from one atom to another. This transfer is what drives the change in oxidation states and allows for the effective balancing of chemical reactions. In the exercise, the dichromate ion system ( Cr_{2}O_{7}^{2-} ) undergoes electron exchange to become Cr^{3+} , while the I^{-} turns into I_{2} .
Understanding electron exchange involves knowing how electrons are conserved and transferred. For the equation provided, each chromium atom has an oxidation state change that corresponds to an overall gain of six electrons for the dichromate ion. These electrons are provided by iodide ions, which lose six electrons in total when forming iodine.
Key concepts about electron exchange include:

• It is essential for calculating the equivalent weight of substances in a reaction.
• Electron exchange ensures that the reaction remains balanced in terms of charge and mass.
• Tracking electron exchange helps in comprehending the efficiency and direction of chemical reactions.