InterviewSolution
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InterviewSolution
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The following solutions are mixed: `500mL of 0.01 M AgNO_(3)` and `500mL` solution that was both `0.01M` in `NaCI` and `0.01M` in `NaBr`. Given `K_(sp) AGCI = 10^(-10), K_(sp) AgBr = 5 xx 10^(-13)`. Calculate the `[CI^(Theta)]` in the equilibrium solution.A. `5 xx 10^(-5)M`B. `2.5 xx 10^(-5)`C. `5 xx 10^(-3)M`D. `2.5 xx 10^(-3)M` |
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Answer» Correct Answer - C i. On dilution (equal volume) and if there were no precipitation. `[NO_(3)^(Theta)] = [Ag^(o+)] = [CI^(Theta)] = [Br^(Theta)] = (0.01)/(2) = 0.005 M = 5.0 xx 10^(-3) M`. `AgBr` is the more soluble salt (less `Ksp` means more soluble)and would take precendence in the precipitating reaction. ii. Assume `AgCI` does not precipitate. In this case `Ag^(o+)` and `Br^(Theta)` would be removed by precipitation and the concentration of these two ions in solution would remain eqial to each other. iii. `[Ag^(o+)] [Br^(Theta)] = sqrt(K_(sp) AgBr) = (5.0 xx 10^(-13))^((1)/(2)) = 7.1 xx 10^(-7)M`. iv. `Q_(sp)` or I.P. of `AgCI = [Ag^(o+)] [CI^(Theta)]` `= (7.1 xx 10^(-7)) (5.0 xx 10^(-3)M) = 3.5 xx 10^(-9)` `Q_(sp)` of `AgCI gt K_(sp)` of AgCI.(`because` Some `AgCI` most also precipitate) Hence the assumption in (ii) is wrong. v. Since both holides precipitate, it is a case of simultaneous solubilities. vi. By electronutrality `[Na^(o+)] + [Ag^(o+)] = [CI^(Theta)] + [Br^(Theta)] + [NO_(3)^(Theta)]` `0.01 + [Ag^(o+)] = [CI^(Theta)] +[Br^(Theta)] = 0.005` or `[CI^(Theta)] + [Br^(Theta)] - [Ag^(o+)] = 0.005 ...(1)` vii. `[Ag^(o+)] [CI^(Theta)] = 10^(-10) ...(2)` `[Ag^(o+)] [Br^(Theta)] = 5 xx 10^(-13).. (3)` viii. Divide (2) by (3), `([CI^(Theta)])/([Br^(Theta)]) = 200` This shows `Br^(Theta)` plays a significant role in the total anion concentration of the solution. xi. Moreover, `[Ag^(o+)]` must be negligible in (1) because of ionsolubility of two silver salts. x. Therefore assume in (1) that `[CI^(Theta)] = 0.005 = 5 xx 10^(-3)`. `[CI^(Theta)] = 5 xx 10^(-3)` xi. From (2), `[Ag^(o+)] = (10^(-10))/([CI^(Theta)]) = (10^(-10))/(0.005) = 2.0 xx 10^(-8)` |
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