Step 1: Statement I.
- Cr(III) = low solubility, low mobility.
- Cr(VI) = high solubility, highly mobile.
Hence, Statement I is correct.
Step 2: Statement II.
- Reaction with zero-valent iron reduces hexavalent chromium (Cr VI) → trivalent chromium (Cr III).
- It does not produce Cr(VI).
Hence, Statement II is incorrect.
Step 3: Statement III.
- Cr(VI) is highly toxic and a known carcinogen.
Hence, Statement III is correct.
Step 4: Statement IV.
- Cr(III) is an essential trace element, less toxic.
- Cr(VI) is far more toxic.
Hence, Statement IV is incorrect.
Step 5: Conclusion.
Correct statements = I and III → Option (C).
Final Answer:
\[
\boxed{\text{(C) I and III are correct; II and IV are incorrect}}
\]