Solubility product

Solubility product of a salt at a given temperature is equal to the product of the concentrations of its ions in the saturated solution, with each concentration term raised to the power equal to the number of moles of ions produced on dissociation of one mole of the substance.



Relationship between solubility (S) and solubility product (K_sp)

Consider M_qA_r a sparingly soluble salt.
Where
q = Number of cations (M^r+) and
r = Number of anions (A^q-)

That is we have in dissolved state


M_qA_r ↔ qM^r+ + r A^q-


Then

K_sp = [M^r+]^q [A^q-]^r

If solubility is S, according to the definition of solubility product

We have
[M^r+]^q = q.S mol/dm³
[A^q-]^r = r.S mol/dm³

Hence K_sp = [q.S] ^q [r.S] ^r

= S^q+r. q^q.r^r


For example for the salt, calcium Phophate, Ca₃(PO₄)₂


Ca₃(PO₄)₂ ↔ 3Ca_aq²⁺ + 2PO_4(aq)^3-


K_sp = [Ca²⁺] ³ [PO₄^3-]²

= S³⁺².3³.2²
= 108S⁵

Past JEE Question

For a sparingly soluble salt A_pB_q, the relationship of its solubility product (K_sp) with its solubility (s) is

a. K_sp = s^p+q.p^p.q^q
b. K_sp = s^p+q.p^q.q^p
c. K_sp = s^pq.p^p.q^q
d. K_sp = s^pq.(pq)^p+q)

(2001)

Answer: a