Question

Sulphide ion in alkaline solution reacts with solid sulphur to form polysulphide ions having formula , $S _{2}^{2-}, S _{3}^{2-}, S _{4}^{2-}$, etc. if $K _{1}=12$ for $S + S ^{2} \rightleftharpoons S _{2}^{2-}$ and $K _{2}=132$ for $2 S + S ^{2} \rightleftharpoons S _{3}^{2-}$, calculate $K _{3}$ for $S + S _{2}^{2-} \rightleftharpoons S _{3}^{2-}$ Give your answer by dividing $5.5$

Answer 1

$S + S ^{2} \rightleftharpoons S _{2}^{2-} K _{1}=12\,\,\, ...(1)$
$2 S + S ^{2-} \rightleftharpoons S _{3}^{2-} K _{2}=132\,\,\,...(2)$
$S + S _{2}^{2-} \rightleftharpoons S _{3}^{2-} K _{3}=?$
$K _{1}=\frac{\left( S _{2}{ }^{2-}\right)}{( S ) \times\left( S ^{2-}\right)}$
equation $( II \div I )$
$=\frac{ K _{2}}{ K _{1}}=\frac{\left( S _{3}{ }^{2-}\right)}{( S )^{2} \times\left( S ^{2-}\right)} \times \frac{( S )\left( S ^{2-}\right)}{\left( S _{2}{ }^{2-}\right)}$
$K _{3}=\frac{\left( S _{3}{ }^{2-}\right)}{( S ) \times\left( S _{2}^{2-}\right)}=\frac{ K _{2}}{ K _{1}}=\frac{\left( S _{3}{ }^{2-}\right)}{( S ) \times\left( S _{2}^{2-}\right)}$
$K _{3}=\frac{\left( S _{3}{ }^{2-}\right)}{( S ) \times\left( S _{2}{ }^{2-}\right)}=\frac{132}{12}$
$=11$