Vapour pressure of a saturated solution of a sparingly soluble salt A_(2)B_(3) is 31.8 mm of Hg at 40^(@)C. If vapour pressure of pure water is 31.9mm of Hg at 40^(@)C, calculate the solubility product of A_(2)B_(3)at 40^(@)C.

Vapour pressure of a saturated solution of a sparingly soluble salt A_

1.	Vapour pressure of a saturated solution of a sparingly soluble salt A_(2)B_(3) is 31.8 mm of Hg at 40^(@)C. If vapour pressure of pure water is 31.9mm of Hg at 40^(@)C, calculate the solubility product of A_(2)B_(3)at 40^(@)C.
Answer» <P> Solution :As `A_(2)B_(3)` is an electrolyte which ionizes to gives 5 ions, I = 5. Applying the relation `(p^(@)-p_(s))/(p^(@))=i=(n_(2))/(n_(1))=(i n_(2))/(w_(1)//M_(1))` If `w_(1)=1000g, n_(2)` = molality (m) of the solution `therefore""(31.9-31.8)/(31.9)=(5xxm)/(1000//18)"or"m=(0.1)/(31.9)xx(1000)/(18)xx(1)/(5)=0.035` As solution is dilute, molarity = molality `=0.035" mol L"^(-1)` i.e., solubility (s) of the salt = `"0.035 mol L"^(-1)` Now, `""{:(A_(2)B_(3)rarr2A^(3+)+3B^(2-)),("s2s3s"),(K_(sp)=(2S)^(2)(3s)^(3)=108s^(5)=108xx(0.035)^(5)=5.672xx10^(-6)):}`