Concept:
Potassium dichromate (\(\text{K}_2\text{Cr}_2\text{O}_7\)) is an important industrial reagent and laboratory standard in volumetric titrations.
Its properties include pH-dependent equilibria between chromate and dichromate, an \(n\)-factor of \(6\) in acid, and a bridged tetrahedral structure with a characteristic bond angle.
Step 1: Evaluation of Statement (A):
Potassium dichromate is widely utilized as an oxidizing agent in organic chemistry, specifically in the dye industry for preparing azo dyes and intermediates.
Hence, statement (A) is correct.
Step 2: Evaluation of Statement (B):
In aqueous solution, chromate (\(\text{CrO}_4^{2-}\), yellow) and dichromate (\(\text{Cr}_2\text{O}_7^{2-}\), orange) exist in a pH-dependent equilibrium:
\[
2\text{CrO}_4^{2-} + 2\text{H}^+ \rightleftharpoons \text{Cr}_2\text{O}_7^{2-} + \text{H}_2\text{O}
\]
When the pH decreases (acidic medium, high \([\text{H}^+]\)), Le Chatelier's principle shifts the equilibrium to the right, converting chromates into dichromates.
Conversely, increasing pH (alkaline conditions) shifts the equilibrium to the left, converting dichromate into chromate.
Statement (B) states that decreasing pH converts dichromate to chromate, which is incorrect.
Step 3: Evaluation of Statement (C):
In acidic solution, the reduction half-reaction of dichromate is:
\[
\text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \rightarrow 2\text{Cr}^{3+} + 7\text{H}_2\text{O}
\]
Because each mole of dichromate accepts \(6\) electrons, the \(n\)-factor is \(6\).
The equivalent weight is therefore:
\[
\text{Equivalent Weight} = \frac{\text{Molar Mass}}{6} = \frac{M}{6}
\]
Statement (C) claims the equivalent weight is \(M/5\), which is incorrect (this value applies to \(\text{KMnO}_4\) in acid).
Step 4: Evaluation of Statement (D):
The dichromate ion consists of two tetrahedral \(\text{CrO}_4\) units sharing a central bridging oxygen atom.
The \(\text{Cr}-\text{O}-\text{Cr}\) bond angle in the dichromate ion is \(126^\circ\).
Hence, statement (D) is correct.
Final Answer:
The correct statements are (A) and (D) only, corresponding to option (C).