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. \( S^{2-} (aq) + S_{(s)} \rightleftharpoons S_2^{2-} (aq) \) with \( K_1 = 10 \)
2. \( S^{2-} (aq) + 2S_{(s)} \rightleftharpoons S_3^{2-} (aq) \) with \( K_2 = 130 \)

### Step 1: Reverse the first reaction
To find the equilibrium constant for the formation of \( S_3^{2-} \) from \( S_2^{2-} \) and sulfur, we first need to 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:

\[ K' = \frac{1}{K_1} = \frac{1}{10} \]

### Step 2: Write the second reaction
The second reaction remains as is:

\[ S^{2-} (aq) + 2S_{(s)} \rightleftharpoons S_3^{2-} (aq) \]

### Step 3: Add the two reactions
Now, we can add the reversed first reaction and the second reaction:

1. \( S_2^{2-} (aq) \rightleftharpoons S^{2-} (aq) + S_{(s)} \) (from Step 1)
2. \( S^{2-} (aq) + 2S_{(s)} \rightleftharpoons S_3^{2-} (aq) \) (from Step 2)

Adding these reactions gives:

\[ S_2^{2-} (aq) + S^{2-} (aq) + 2S_{(s)} \rightleftharpoons S_3^{2-} (aq) + S_{(s)} \]

### Step 4: Simplify the equation
Notice that the \( S^{2-} (aq) \) and one \( S_{(s)} \) cancels out:

\[ S_2^{2-} (aq) + S_{(s)} \rightleftharpoons S_3^{2-} (aq) \]

### Step 5: Calculate the equilibrium constant for the overall reaction
The overall equilibrium constant \( K \) for the combined reaction is the product of the equilibrium constants of the individual reactions:

\[ K = K' \times K_2 = \left(\frac{1}{10}\right) \times 130 = \frac{130}{10} = 13 \]

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

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