Question

In the redox reaction, taking place in acidic medium: $\text{X MnO}_4^-(aq) + \text{Y SO}_2(g) \rightarrow \text{Mn}^{+2}(aq) + \text{HSO}_4^-(aq)$,} the ratio of X:Y in a stoichiometrically balanced equation will be:

• A. $5:2$
• B. $1:2$
• C. $2:3$
• D. $2:5$

Hint:

You can find the stoichiometric coefficients quickly by cross-multiplying the changes in oxidation states! Since $\text{Mn}$ changes by $5$ and $\text{S}$ changes by $2$, the coefficients must invert to balance the electrons, giving a ratio of $2:5$ immediately.

Answer 1

The Correct Option is D

Understanding the Concept: A redox equation can be balanced by equating the total number of electrons lost during oxidation with the total number of electrons gained during reduction (ion-electron or oxidation number methods).
Step 1: Analyze the reduction half-reaction and electron gain.
In the conversion of permanganate ($\text{MnO}_4^-$) to manganese(II) ions ($\text{Mn}^{2+}$):
Oxidation state of $\text{Mn}$ in $\text{MnO}_4^-$: $x + 4(-2) = -1 \implies x = +7$
Oxidation state of $\text{Mn}$ in product: $+2$
The net change in oxidation state represents a gain of 5 electrons per manganese atom: \[ \text{Mn}^{+7} + 5e^- \rightarrow \text{Mn}^{+2} \quad \cdots (\text{Reduction}) \]
Step 2: Analyze the oxidation half-reaction and electron loss.
In the conversion of sulfur dioxide ($\text{SO}_2$) to bisulfate ions ($\text{HSO}_4^-$):
Oxidation state of $\text{S}$ in $\text{SO}_2$: $y + 2(-2) = 0 \implies y = +4$
Oxidation state of $\text{S}$ in $\text{HSO}_4^-$: $1 + y + 4(-2) = -1 \implies y = +6$
The net change in oxidation state represents a loss of 2 electrons per sulfur atom: \[ \text{S}^{+4} \rightarrow \text{S}^{+6} + 2e^- \quad \cdots (\text{Oxidation}) \end{center}
Step 3: Equate electron transfer to find the stoichiometric coefficients X and Y.
To balance the total electron flow, multiply the reduction half-reaction by 2 and the oxidation half-reaction by 5: \[ \text{Total electrons exchanged} = 2 \times 5e^- = 5 \times 2e^- = 10e^- \] This assigns a stoichiometric coefficient of $\text{X} = 2$ to $\text{MnO}_4^-$ and $\text{Y} = 5$ to $\text{SO}_2$. Therefore, the balanced ratio is $\text{X}:\text{Y} = 2:5$.