Question

In the equation, $\text{BiO}_{3}^{-}+6\text{H}^{+}+xe^{-}\rightarrow \text{Bi}^{3+}+3\text{H}_{2}\text{O}$ What is the value of x?

• A. 2
• B. 3
• C. 4
• D. 6

Hint:

Using oxidation states is the fastest way to find the number of electrons in a half-reaction. Bismuth goes from +5 to +3; since $5 - 3 = 2$, it requires 2 electrons!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We are given a redox half-reaction equation containing an unknown coefficient '$x$' for the electrons. We must determine the value of $x$ required to balance the equation perfectly.

Step 2: Detailed Explanation:
An ionic equation must be balanced in terms of both mass (atoms) and electrical charge.
Let's check the mass balance first:
Left side: 1 Bi, 3 O, 6 H
Right side: 1 Bi, 3 O, 6 H
Mass is already perfectly balanced.
Now, we balance the electrical charges. The total net charge on the reactant side must exactly equal the total net charge on the product side.
Total charge on the Left Side:
Charge from $\text{BiO}_3^-$ = -1
Charge from $6\text{H}^+$ = $6 \times (+1) = +6$
Charge from $x$ electrons = $x \times (-1) = -x$
Net Left Charge = $-1 + 6 - x = +5 - x$
Total charge on the Right Side:
Charge from $\text{Bi}^{3+}$ = +3
Charge from $3\text{H}_2\text{O}$ = 0 (neutral molecule)
Net Right Charge = +3
Equating the charges from both sides:
$5 - x = +3$
$x = 5 - 3$
$x = 2$
Alternative Method (Oxidation States):
Determine the oxidation state of Bismuth on both sides.
In $\text{BiO}_3^-$, let the oxidation state of Bi be $y$.
$y + 3(-2) = -1 \implies y - 6 = -1 \implies y = +5$.
In the products, Bi is a bare ion, so its oxidation state is $+3$.
To go from an oxidation state of $+5$ down to $+3$, the Bismuth atom must gain exactly 2 electrons.
Thus, $x = 2$.

Step 3: Final Answer:
The value of x is 2, matching option (a).