Sulphide ion reacts with solid sulphur
`S_((aq))^(2-) +S_((s)) hArr S_(2(aq))^(2-), k_1= 10`
`S_((aq))^(2-)+2S_((s)) hArr S_(3(aq))^(2-) k_2=130`
The equilibrium constant for the formation of `S_3^(2-) (aq)` from `S_2^(2-)(aq)` and sulphur is

Options

A. 10
B. 13
C. 130
D. 1300

Answer

To find the equilibrium constant for the formation of \( S_3^{2-} (aq) \) from \( S_2^{2-} (aq) \) and solid sulfur, we will use the given reactions and their equilibrium constants.

### Given Reactions:
1. \( S^{2-} (aq) + S (s) \rightleftharpoons S_2^{2-} (aq), \quad K_1 = 10 \)
2. \( S^{2-} (aq) + 2S (s) \rightleftharpoons S_3^{2-} (aq), \quad K_2 = 130 \)

### Step 1: Write the Reactions
We have two reactions. The first reaction produces \( S_2^{2-} \) from \( S^{2-} \) and solid sulfur, and the second reaction produces \( S_3^{2-} \) from \( S^{2-} \) and two moles of solid sulfur.

### Step 2: Reverse the First Reaction
To find the equilibrium constant for the reaction that we need, we will reverse the first reaction:
\[ S_2^{2-} (aq) \rightleftharpoons S^{2-} (aq) + S (s) \]
When we reverse a reaction, the equilibrium constant becomes the reciprocal:
\[ K_1' = \frac{1}{K_1} = \frac{1}{10} = 0.1 \]

### Step 3: Add the Reversed First Reaction to the Second Reaction
Now we can add the reversed first reaction to the second reaction:
1. Reversed first reaction:
\[ S_2^{2-} (aq) \rightleftharpoons S^{2-} (aq) + S (s) \quad (K_1' = 0.1) \]
2. Second reaction:
\[ S^{2-} (aq) + 2S (s) \rightleftharpoons S_3^{2-} (aq) \quad (K_2 = 130) \]

### Step 4: Combine the Reactions
When we combine these reactions, we get:
\[ S_2^{2-} (aq) + S^{2-} (aq) + 2S (s) \rightleftharpoons S_3^{2-} (aq) + S (s) \]
This simplifies to:
\[ S_2^{2-} (aq) + S (s) \rightleftharpoons S_3^{2-} (aq) \]

### Step 5: Calculate the Overall Equilibrium Constant
The overall equilibrium constant \( K \) for the combined reaction is the product of the equilibrium constants of the individual reactions:
\[ K = K_1' \times K_2 = 0.1 \times 130 = 13 \]

### Final Answer:
The equilibrium constant for the formation of \( S_3^{2-} (aq) \) from \( S_2^{2-} (aq) \) and solid sulfur is \( K = 13 \).

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