Step 1: Understanding the Concept:
The oxidation state of an atom is the charge it would carry if all bonds to it were completely ionic.
The sum of oxidation states of all atoms in a neutral molecule must equal zero.
Step 2: Key Formula or Approach:
The chemical formula $HOBrO_2$ can be rewritten as $HBrO_3$ (Bromic acid).
Let the oxidation state of Bromine ($Br$) be $x$.
Standard oxidation states:
Hydrogen ($H$) = $+1$
Oxygen ($O$) = $-2$
Step 3: Detailed Explanation:
Applying the rule for the neutral molecule \( HBrO_3 \):
\[ (+1) \times 1 + (x) \times 1 + (-2) \times 3 = 0 \]
\[ 1 + x - 6 = 0 \]
\[ x - 5 = 0 \]
\[ x = +5 \]
Step 4: Final Answer:
The oxidation state of bromine in $HOBrO_2$ is +5.