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Calculate the simultaneous solubility of AgCNS and AgBr ina solution of water. K_(sp) of AgCNS=1xx10^(-12)and AgBr=5xx10^(-13). |
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Answer» Solution :SUPPOSE the simultaneous solubility of AgCNS and AgBr in water are a and b respectively. `{:(AgCNS hArr Ag^(+) + CNS^(-) , AgBr hArr Ag^(+) + Br^(-)),("aa","bb"):}` Thus, `[Ag^(+)] = a+b , [ CNS^(-)] = a, [Br^(-) ] = b ` `K_(sp) ` of AgCNS `= [Ag^(+)] [ CNS^(-)]= a (a+b)` `:. a(a+b) = 5 xx 10^(-12) " " ...(i)` `K_(sp) "of" AgBr = [Ag^(+)][Br^(-)]=b (a+b)` `:. b(a+b) = 5 xx 10^(-13) " " ...(ii)` DIVIDING EQN.(i) by (ii), we get `(a)/(b) = (10^(-12))/(5xx10^(-13))=2 or a = 2b` PUTTING this valuein eqn. (i) `2b(2b+b) = 10^(-12) or 6B^(2) = 10^(-12) or b^(2) = 1/6 xx 10^(-12)` or, `b= 4.08xx10^(-7) "mol" L^(-1) ` `a=2b=2xx4.08xx10^(-7) "mol" L^(-1) = 8.16xx10^(-7) "mol " L^(-1)`. |
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