Answer to Question #27035 in Chemistry for sam

Question

will a precipitate occur if 250 ml of 1.5 x 10^.3 M NaCl is mixed with 250 mL of 2.0 x 10^.7 M AgNO3? Ksp of AgCl = 1.6 x 10^-10

Answer 1

The equation for the chemical reaction is

NaCl(aq) + AgNO₃(aq) = AgCl(s) + NaNO₃(aq)

K_sp = [Ag⁺] x [Cl^-] = 1.6 x 10^-10
From the equation for K_sp:
[Ag⁺] = [Cl^-] = (1.6 x 10^-10) ^0.5 = 1.3 x 10^-5 M

The amount of NaCl is
n(NaCl) = C(NaCl) x V(L) = 1.5 x 10^-3 x 0.25 = 3.75 x 10^-4 mol

The amount of AgNO₃ is
n(AgNO₃) = C(AgNO₃) x V(L) = 2.0 x 10^-7 x 0.25 = 5.0 x 10^-8 mol

The precipitate will occur if the product of [Ag⁺] and [Cl^-] will be more or equal to K_sp:
[Ag⁺] = n(Ag⁺) / V(of new solution) = 5.0 x 10^-8 / (0.25 + 0.25) = 1.0 x 10^-7 M
[Cl^-] = n(Cl^-)/V(of new solution) = 3.75 x 10^-4 / (0.25 + 0.25) = 7.5 x 10^-4 M
[Ag⁺] x [Cl^-] = 1.0 x 10^-7 x 7.5 x 10^-4 = 7.5 x 10^-11 it is less than K_sp, that's why the precipitate will not occur

Answer: The precipitate won't occur.