Question

In the standardization of \(\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}\) using \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) by iodometry, the equivalent weight of \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) is: (a) Same as mol. wt. (b) \(\frac{\text { Mol. wt }}{2}\) (c) \(\frac{\text { Mol. wt. }}{4}\) (d) \(\frac{\text { Mol. wt. }}{6}\)

Short answer

The equivalent weight of \( K_2Cr_2O_7 \) is \( \frac{\text{Mol. wt.}}{6} \), so the answer is (d).

Step-by-step solution

Understanding Equivalent Weight

Equivalent weight is calculated by dividing the molecular weight by the number of electrons transferred in the balanced redox reaction. In this problem, we are dealing with a redox reaction where potassium dichromate (K_2Cr_2O_7) serves as an oxidizing agent.

Balancing the Redox Reaction

The balanced half-reaction for K_2Cr_2O_7 acting as an oxidizing agent is: \[ Cr_2O_7^{2-} + 14H^+ + 6e^- \rightarrow 2Cr^{3+} + 7H_2O \] From this reaction, we see that 6 electrons (6e^-) are involved in the redox process.

Calculating Equivalent Weight

To find the equivalent weight of K_2Cr_2O_7, use the formula: \[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{\text{Number of Electrons Transferred}} \] Since 6 electrons are transferred, the equivalent weight becomes: \[ \frac{\text{Mol. wt.}}{6} \]

Selecting the Correct Option

Given the equivalent weight calculation, the correct answer from the provided options is \(\frac{\text{Mol. wt.}}{6}\). This corresponds to option (d).

Key concepts

Understanding Redox Reactions

Redox reactions are a type of chemical reaction where oxidation and reduction processes occur simultaneously. In these processes, electrons are transferred between reactants. Redox is short for reduction-oxidation reaction.

• Oxidation: Here, a substance loses electrons and typically increases in oxidation state.
• Reduction: This involves the gain of electrons, resulting in a decrease in oxidation state.

Potassium dichromate ( K_2Cr_2O_7 ) is an example of a powerful oxidizing agent. This means it tends to gain electrons in a redox reaction, thereby causing another substance to lose electrons, or be oxidized. In a balanced redox reaction involving K_2Cr_2O_7 , chromium changes from a higher oxidation state (from +6 to +3), indicating that it gains electrons (gets reduced). These behaviors are essential when performing titrations, especially in iodometry, a method that uses iodine in the presence of oxidizing agents to determine concentration levels of substances.

Calculating Equivalent Weight

The concept of equivalent weight is crucial for understanding stoichiometry in redox reactions. Equivalent weight can be defined as the mass of a compound that combines with or displaces 1 mole of hydrogen ions (or electrons in redox reactions). It's computed by dividing the molecular weight of the substance by the number of electrons transferred per molecule or formula unit in the reaction.
For potassium dichromate (K_2Cr_2O_7), in a standard redox reaction, 6 electrons are exchanged. Thus, the equivalent weight of K_2Cr_2O_7 is: \[ \text{Equivalent Weight} = \frac{\text{Molecular Weight}}{6} \]
Understanding and calculating equivalent weight is important for performing accurate titrations and preparing solutions of known concentration, especially when using K_2Cr_2O_7 in analytical chemistry tasks.

Role of Potassium Dichromate in Titrations

Potassium dichromate is often used in analytical chemistry due to its stable and strong oxidizing properties. It's a primary standard in titrations because of its high purity and consistency. During the iodometry process, K_2Cr_2O_7 acts as an oxidizer, converting iodide ions ( I^- ) to iodine ( I_2 ), which can then be titrated using sodium thiosulfate ( Na_2S_2O_3 ). This type of titration is used to determine the concentration of reducing agents.
When performing these titrations, the following properties make K_2Cr_2O_7 highly valued:

• Precision: Its known reaction stoichiometry allows for precise calculations of concentration.
• Color change: Provides clear endpoint detection due to the color shift of iodine.
• Stability: It remains stable and does not easily decompose over time.

Understanding these qualities and how K_2Cr_2O_7 interacts in redox titrations helps in accurately determining chemical concentrations in various samples.