Sulphide ions in alkaline solution react with solid sulphur to form polyvalent sulphide ions. The equilibrium constant for the formation of `S_(2)^(2-)` and `S_(3)^(2-)` from `S` and `S^(2-)` ions is `1.7` and `5.3` respectively. Calculate equilibrium constant for the formation of `S_(3)^(2-)` from `S_(2)^(2-)` and `S`.

Options

A. `1.33`
B. `3.11`
C. `4.21`
D. `1.63`

Explanation

`{:("Given",S_((s)),+,S^(2-),hArr,S_(2)^(2-),, ,K_(c_(1))=1.7),(,2S_((s)),+,S^(2-),hArr,S_(3)^(2-),, ,K_(c_(2))=5.3):}`
`:. K_(c_(1))=([S_(2)^(2-)])/([S^(2-)])=1.7` ….(`1`)
`K_(c_(2))=([S_(3)^(2-)])/([S^(2-)])=5.3` ….(`2`)
Nor for `S_(2)^(2-)+S_((s))hArrS_(3)^(2-)`
`K_(c)=([S_(3)^(2-)])/([S_(2)^(2-)])`
`:.` By eqs. (`2`) and (`1`) ,
`(K_(c_(2)))/(K_(c_(1)))=([S_(3)^(2-)])/([S_(2)^(2-)])=K_(c)`
`:. K_(c)=3.11`