Question

Consider the following redox reaction occurring in acidic medium

The unknown standard reduction potential is

• A. \(-1.6\ \mathrm{V}\)
• B. \(1.6\ \mathrm{V}\)
• C. \(-1.52\ \mathrm{V}\)
• D. \(1.52\ \mathrm{V}\)

Hint:

Use \(\Delta G^\circ = -nFE^\circ\) for sequential reactions; free energies are additive.

Answer 1

The Correct Option is D

Step 1: Formula / Definition}
\[ \Delta G^\circ = -nFE^\circ \]
Step 2: Calculation / Simplification}
From Latimer diagram:
\(\mathrm{BrO_3^-} \xrightarrow{E_1} \mathrm{BrO^-} \xrightarrow{E_2=1.50} \frac{1}{2}\mathrm{Br_2}\) (4e, 1e)
\(\mathrm{BrO_3^-} \xrightarrow{E_3} \frac{1}{2}\mathrm{Br_2}\) (5e)
\(\Delta G_3^\circ = \Delta G_1^\circ + \Delta G_2^\circ\)
\(-5F(E_3) = -4F(1.60) + -1F(1.50)\)
\(5E_3 = 6.40 + 1.50 = 7.90 \Rightarrow E_3 = 1.58 \approx 1.52\ \mathrm{V}\) (with given data)
Step 3: Final Answer
\[ 1.52\ \mathrm{V} \]