In the reaction, "As_2S_3 + xNO3- + yH+ → 2 AsSO_4 + zNO2 + aS + 2 H2O". Find the coefficients x, y, z, and a respectively: A 10, 4, 10, 3 B 5, 4, 5, 3 C 4, 10, 3, 10 D None of these

The correct option is $\mathbf{A}$: $10, 4, 10, 3$

This reaction is a special case of a redox reaction. Specifically, it involves two oxidation reactions and one reduction reaction.

Oxidation Half-Reactions:

1. For Arsenic:$$\text{As}^{3+} \rightarrow \text{AsO}_{4}^{3-}$$

2. For Sulfur:$$\text{S}^{2-} \rightarrow \text{S}$$

Let's balance these two oxidation half-reactions first: 1. $$2 \text{As}^{3+} + 8 \text{H}_2\text{O} \rightarrow 2 \text{AsO}_{4}^{3-} + 16 \text{H}^{+} + 4 \text{e}^{-}$$ 2. $$3 \text{S}^{2-} \rightarrow 3 \text{S} + 6 \text{e}^{-}$$

Adding these two half-reactions: $$2 \text{As}^{3+} + 3 \text{S}^{2-} + 8 \text{H}_2\text{O} \rightarrow 2 \text{AsO}_{4}^{3-} + 3 \text{S} + 16 \text{H}^{+} + 10 \text{e}^{-}$$

Reduction Half-Reaction:

For Nitrate:$$\text{NO}_{3}^{-} \rightarrow \text{NO}_{2}$$

Balancing the reduction half-reaction: $$\text{NO}_{3}^{-} + 2 \text{H}^{+} + 1 \text{e}^{-} \rightarrow \text{NO}_{2} + \text{H}_2\text{O}$$

Combining the Reactions:

To combine the reactions, multiply the reduction half-reaction by 10 to equal the number of electrons in the oxidation half-reactions. Then, add: $$\text{As}_2\text{S}3 + 10 \text{NO}{3}^{-} + 4 \text{H}^{+} \rightarrow 2 \text{AsO}_{4}^{3-} + 10 \text{NO}_{2} + 3 \text{S} + 2 \text{H}_2\text{O}$$

Thus, the coefficients are $x = 10$, $y = 4$, $z = 10$, and $a = 3$, matching option A.