## Relation entre solubilité et produit de solubilité

### - Cas d'un électrolyte simple

CA . ( s ) ⇔ CA . ( aq ) ⇔ C + . . ( aq ) + A − . . ( aq ) CA {color white.}_(s) dlrarrow CA {color white.}_(aq) dlrarrow C^{+ color white.} {color white.}_(aq)+A^{- color white.} {color white.}_(aq)
K s = [ C + . ] [ A − . ] K_s=[C^+ {color white.}][A^- {color white.}]
S = [ C + . ] = [ A − . ] → K s = S 2 → S = ( K s ) 1 / 2 S=[C^+ {color white.}]=[A^- {color white.}] toward K_s=S^2 toward S=( K_s ) ^{1/2}

### - Cas général

C m A n . ( s ) ⇔ C m A n . ( aq ) ⇔ mC n + . . ( aq ) + nA m − . . ( aq ) {C_m A_n} {color white.}_(s) dlrarrow {C_m A_n} {color white.}_(aq) dlrarrow mC ^{n+ color white.} {color white.}_(aq) + nA ^{m-color white.}{color white.} _(aq)
K s = [ C n + . ] m [ A m − . ] n K_s = [C ^{n+ color white.}]^m[ A ^{m- color white.} ]^n
S = 1 / m [ C n + . ] = 1 / n [ A m − . ] S = 1/m [C ^{n+ color white.} ] = 1/n[ A ^{m- color white.}]

Soit

[ C n + . ] = mS ..... et ..... [ A m − . ] = nS → Ks = ( mS ) m ( nS ) n = ( m m ) ( n n ) ( S m + n ) → S = ( Ks / m m n n ) 1 / ( m + n ) [C ^{n+ color white.}]= mS {color white.....} et{color white.....} [ A ^{m- color white.} ]=nS toward Ks=( mS )^m ( nS )^n=( m^m)(n^n)(S^{m+n}) toward S=( Ks/m^m n^n)^{1/(m+n)}