Question

Which one of the following options represents the decreasing order of oxidation number of the central atom in:
\[ \mathrm{Cr_2O_7^{2-}, \; CrO_2^{-}, \; MnO_4^{-}, \; BrO_3^{-}} \]

• A. \(\mathrm{CrO_2^{-}>BrO_3^{-}>Cr_2O_7^{2-}>MnO_4^{-}}\)
• B. \(\mathrm{MnO_4^{-}>CrO_2^{-}>Cr_2O_7^{2-}>BrO_3^{-}}\)
• C. \(\mathrm{BrO_3^{-}>CrO_2^{-}>MnO_4^{-}>Cr_2O_7^{2-}}\)
• D. \(\mathrm{MnO_4^{-}>Cr_2O_7^{2-}>BrO_3^{-}>CrO_2^{-}}\)

Hint:

Always assign oxygen as \(-2\) (except peroxides) and use total charge of the species to calculate oxidation number of the central atom.

Answer 1

The Correct Option is D

Step 1: Concept of oxidation number.
The oxidation number is calculated by assuming oxygen has oxidation state \(-2\) and the overall charge of the ion is known.
We calculate oxidation number of the central atom in each species.

Step 2: Oxidation number of Mn in \(MnO_4^{-}\).
Let oxidation number of Mn be \(x\).
\[ x + 4(-2) = -1 \] \[ x - 8 = -1 \] \[ x = +7 \]

Step 3: Oxidation number of Cr in \(Cr_2O_7^{2-}\).
Let oxidation number of each Cr be \(x\).
\[ 2x + 7(-2) = -2 \] \[ 2x - 14 = -2 \] \[ 2x = 12 \] \[ x = +6 \]

Step 4: Oxidation number of Br in \(BrO_3^{-}\).
Let oxidation number of Br be \(x\).
\[ x + 3(-2) = -1 \] \[ x - 6 = -1 \] \[ x = +5 \]

Step 5: Oxidation number of Cr in \(CrO_2^{-}\).
Let oxidation number of Cr be \(x\).
\[ x + 2(-2) = -1 \] \[ x - 4 = -1 \] \[ x = +3 \]

Step 6: Arrange in decreasing order.
Now we arrange the oxidation numbers:
\[ MnO_4^{-} = +7 \] \[ Cr_2O_7^{2-} = +6 \] \[ BrO_3^{-} = +5 \] \[ CrO_2^{-} = +3 \] Thus, decreasing order is:
\[ MnO_4^{-}>Cr_2O_7^{2-}>BrO_3^{-}>CrO_2^{-} \]

Step 7: Final Answer.
\[ \boxed{\mathrm{MnO_4^{-}>Cr_2O_7^{2-}>BrO_3^{-}>CrO_2^{-}}} \] Hence, the correct answer is option (D).