Question

In acidic medium, dichromate ion oxidize ferrous ion to ferric ion. If the gram molecular weight of potassium dichromate is \(294 \mathrm{~g}\), its equivalent weight is: (a) 19 (b) 49 (c) 99 (d) 294

Short answer

The equivalent weight of potassium dichromate is 49 g.

Step-by-step solution

Understanding the Reaction

In acidic medium, the reaction can be represented as: \[ \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6\text{Fe}^{2+} \rightarrow 2\text{Cr}^{3+} + 6\text{Fe}^{3+} + 7\text{H}_2\text{O} \] Here, the dichromate ion (\(\text{Cr}_2\text{O}_7^{2-}\)) oxidizes ferrous ion (\(\text{Fe}^{2+}\)) to ferric ion (\(\text{Fe}^{3+}\)).

Calculating Change in Oxidation State

In this redox reaction, one molecule of \(\text{Cr}_2\text{O}_7^{2-}\) contains two chromium atoms that each undergo a change in oxidation state from +6 to +3, which means a total change of 6 electrons (from +12 to +6 combined over the two chromium atoms).

Applying the Equivalent Weight Formula

The equivalent weight of a substance in a redox reaction is given by \( \text{Equivalent Weight} = \frac{\text{Molar mass}}{n} \), where \( n \) is the number of electrons exchanged per molecule of compound undergoing oxidation or reduction. Here, potassium dichromate (\(\text{K}_2\text{Cr}_2\text{O}_7\)), which has a molar mass of 294 g/mol, exchanges 6 electrons.

Calculating Equivalent Weight

Using the formula: \[ \text{Equivalent Weight} = \frac{294}{6} \approx 49 \] Therefore, the equivalent weight for potassium dichromate in this reaction is 49 g/eq.

Key concepts

Redox Reaction

A redox reaction is a chemical process where the oxidation states of atoms change. These reactions involve two simultaneous processes: reduction and oxidation.

• Reduction is the gain of electrons or a decrease in oxidation state by a molecule, atom, or ion.
• Oxidation is the loss of electrons or an increase in oxidation state.

In the given reaction, dichromate ions play the role of the oxidizing agent, meaning they accept electrons. Concurrently, ferrous ions (\( ext{Fe}^{2+}\)) act as the reducing agent by donating electrons to be transformed into ferric ions (\( ext{Fe}^{3+}\)). The balance of these processes defines the redox equilibrium.

Dichromate Ion

The dichromate ion, represented as \( ext{Cr}_2 ext{O}_7^{2-}\), is a potent oxidizing agent often used in redox reactions. It plays a significant role in analytical chemistry and industrial processes due to its stability and ability to induce oxidation.

• Dichromate ions contain two chromium atoms bonded to seven oxygen atoms.
• Each chromium atom within the dichromate ion initially holds an oxidation state of +6.
• In acidic conditions, dichromate ions can induce changes to the oxidation state of other substances, which makes them useful in diverse chemical reactions.

In the provided exercise, these ions transform from a +6 to a +3 oxidation state while oxidizing the ferrous ions.

Oxidation State Change

Oxidation states are integers used to describe the degree of oxidation of an atom in a chemical compound. Changes in oxidation state are central to understanding redox reactions.

• An increase in oxidation state indicates oxidation (loss of electrons).
• A decrease in oxidation state signifies reduction (gain of electrons).

In the exercise's reaction, chromium atoms in the dichromate ion undergo a change in oxidation state from +6 to +3. This corresponds to a gain of electrons, illustrating a reduction process. Monitoring these changes helps determine the number of electrons exchanged during the reaction  crucial for calculating equivalent weight.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is found by summing the atomic masses of all atoms in a molecule.

• For potassium dichromate, \( ext{K}_2 ext{Cr}_2 ext{O}_7\), the molar mass is given as 294 g/mol.
• This molar mass is crucial for determining the equivalent weight in redox reactions by the formula \( \text{Equivalent Weight} = \frac{\text{Molar mass}}{n} \).

In the specific redox reaction, it is important to calculate the equivalent weight accurately since it considers both the molar mass and the number of electrons exchanged, which is six for dichromate ions.