Step 1: Understanding the Concept:
Dichromates are powerful oxidizing agents in acidic media. Their chemical properties involve pH-dependent equilibria and specific structural parameters in the solid state.
Step 2: Key Formula or Approach:
1. Reaction: $Cr_2O_7^{2-} + 14H^+ + 6Fe^{2+} \to 2Cr^{3+} + 6Fe^{3+} + 7H_2O$.
2. Equilibrium: $2CrO_4^{2-} + 2H^+ \rightleftharpoons Cr_2O_7^{2-} + H_2O$.
Step 3: Detailed Explanation:
1. Statement A analysis: $K_2Cr_2O_7$ is a well-known oxidant in acidic medium and converts $Fe^{2+}$ (ferrous) to $Fe^{3+}$ (ferric). This is true.
2. Statement B analysis: Sodium dichromate ($Na_2Cr_2O_7$) is hygroscopic (absorbs moisture), which prevents it from being a primary standard. Potassium dichromate is used instead because it is non-hygroscopic. This is false.
3. Statement C analysis: Chromate ($CrO_4^{2-}$, yellow) and dichromate ($Cr_2O_7^{2-}$, orange) exist in equilibrium. Low pH (acidic) favors dichromate; high pH (basic) favors chromate. This is true.
4. Statement D analysis: The dichromate ion consists of two $CrO_4$ tetrahedra sharing an oxygen atom, with a $Cr-O-Cr$ bond angle of 126°. This is true.
Step 4: Final Answer:
Statements A, C, and D are correct.