The reaction of sulphur in alkaline medium is given below: $S_8(s) + a OH^-(aq) \to b S^{2-}(aq) + c S_2O_3^{2-}(aq) + d H_2O(l)$ The value of 'a' is __________. (Integer answer)
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Sulfur, Phosphorus ($P_4$), and Halogens ($Cl_2$) all undergo disproportionation in concentrated alkali.
To solve the problem of finding the value of 'a' for the reaction: \( S_8(s) + a \, OH^-(aq) \to b \, S^{2-}(aq) + c \, S_2O_3^{2-}(aq) + d \, H_2O(l) \), we will balance the redox reaction step-by-step.
Step 1: Analyze Oxidation and Reduction In the reaction, sulfur (\(S_8\)) is transformed into sulfide ions (\(S^{2-}\)) and thiosulfate (\(S_2O_3^{2-}\)).
Oxidation change: \( S_8 \) to \( S^{2-} \)
Reduction change: \( S_8 \) to \( S_2O_3^{2-} \)
Step 2: Assign Oxidation Numbers The oxidation number of sulfur in \( S_8 \) is 0.
For \( S^{2-} \), oxidation number = -2
In \( S_2O_3^{2-} \), average oxidation number of sulfur = +2.
Step 3: Balance the Change in Oxidation Number - From \( S_8 \) to \( S^{2-} \): Change = 0 - (-2) = +2 per sulfur, totaling 8 changes. - From \( S_8 \) to \( S_2O_3^{2-} \): Change for two sulfur atoms = 0 - (+4) = -4. Need to multiply by coefficients to balance.
Step 4: Balancing the Equation For 8 sulfur atoms in \( S_8 \):
4 go to form \( S^{2-} \), which needs \( b=16 \) \( S^{2-} \) ions (as \((4 \times +2)\)).
4 go to form \( S_2O_3^{2-} \) needing \( 2c=2 \) thiosulfate ions.
Step 5: Balance Oxygen and Hydrogen Considering each \( S_2O_3^{2-} \) contributes 3 oxygens that require hydroxide ions (\( OH^- \)):
React each \( OH^- \) with \( S_8 \) producing water. Total \( a = b + 6c = 16 + 6 \times 2 = 28 \) OH⁻.
Step 6: Check the Calculation The total number of moles of water creates \( d=12 \).
Therefore, the integer value of 'a' is \( 28 \), calculated correctly and verified through redox balance and aligns within the provided value range.
