Calculate the equilibrium constants of each of the indicated species necessary to reduce an initial `0.2M Zn^(2+)` solution to `1.0 xx 10^(-4)Zn^(2+)`. a. `Nh_(3)` and `Zn(NH_(3))_(4)^(2+)` (assume no partial complexation) b. `overset(Theta)OH` in equilibrium with `Zn(OH)_(2)(s)`. c. `overset(Theta)OH` and `Zn(OH)_(4)^(2-)`. d. Calculate `[overset(Theta)OH]` which would be produced by each equilibrium concentration of `NH_(3)` in part (a). Predict whether `Zn(OH)_(2)` or `Zn(OH)_(4)^(2-)` would form in preference to `Zn(NH_(3))_(4)^(2+)` upon addition of suficient `NH_(3)` to produce the equilibrium concentration calculated in part(a). e. Explain what would be observeed if concentrated `NH_(3)` solution were added slowely to `0.2M` solution of `Zn^(2+)`. Given. `K_(f)Zn(NH_(3))_(4)^(2+) = 5 xx 10^(8)`. `K_(sp)ZN(OH)_(2) = 1.8 xx 10^(-14)`. `K_(f)Zn(OH)_(4)^(2-) = 5 xx 10^(14)`. `K_(b) NH_(4)OH = 1.8 xx 10^(-5)`.

Calculate the equilibrium constants of each of the indicated species n

1.	Calculate the equilibrium constants of each of the indicated species necessary to reduce an initial `0.2M Zn^(2+)` solution to `1.0 xx 10^(-4)Zn^(2+)`. a. `Nh_(3)` and `Zn(NH_(3))_(4)^(2+)` (assume no partial complexation) b. `overset(Theta)OH` in equilibrium with `Zn(OH)_(2)(s)`. c. `overset(Theta)OH` and `Zn(OH)_(4)^(2-)`. d. Calculate `[overset(Theta)OH]` which would be produced by each equilibrium concentration of `NH_(3)` in part (a). Predict whether `Zn(OH)_(2)` or `Zn(OH)_(4)^(2-)` would form in preference to `Zn(NH_(3))_(4)^(2+)` upon addition of suficient `NH_(3)` to produce the equilibrium concentration calculated in part(a). e. Explain what would be observeed if concentrated `NH_(3)` solution were added slowely to `0.2M` solution of `Zn^(2+)`. Given. `K_(f)Zn(NH_(3))_(4)^(2+) = 5 xx 10^(8)`. `K_(sp)ZN(OH)_(2) = 1.8 xx 10^(-14)`. `K_(f)Zn(OH)_(4)^(2-) = 5 xx 10^(14)`. `K_(b) NH_(4)OH = 1.8 xx 10^(-5)`.
Answer» d. `[Zn^(2+)]` final `=1 xx 10^(-4)M` `[Zn(NH_(3))_(4)^(2+)]aq = 0.2 - 10^(-4) ~~ 0.2` `Zn^(2+) + 4NH_(3) hArr Zn(NH_(3))_(4)^(2+)` `K_(f) = ([Zn(NH_(3))_(4)^(2+)])/([Zn^(2+)][NH_(3)]^(4))` `5 xx 10^(8) =(0.2)/((10^(-4))[NH_(3)]^(4))` `(NH_(3))^(4) = 4 xx 10^(-6) = 400 xx 10^(-8)` `(NH_(3)) = 4.5 xx 10^(-2)M` b. `Zn(OH)_(2) rarr Zn^(2+) +2 overset(Theta)OH` `K_(sp) = (1.8 xx 10^(-14))/(10^(-4)) = 1.8 xx 10^(-10)` `[overset(Theta)OH] = 1.3 xx 10^(-5)M` c. `Zn^(2+) + 4overset(Theta)OH rarr Zn(OH)_(4)^(2-)` `K_(f) - ([Zn(OH)_(4)^(2-)])/([Zn^(2+)][overset(Theta)OH]^(4))` `5 xx 10^(4) = (0.2)/((10^(-4))[overset(Theta)OH]^(4))` `rArr [overset(Theta)OH]^(4) = 4 xx 10^(-12), [overset(Theta(O)H] = 1.4 xx 10^(-3)` d. The concentration of `overset(Theta)OH` in equilibrium with the `NH_(3)` concentration of part (a) is given by, `NH_(3) + H_(2)O hArr overset(o+)NH_(4) + overset(Theta)OH`, (Let `x = [overset(o+)NH_(4)] = [overset(Theta)OH]` `K_(b) = ([overset(o+)NH_(4)][overset(Theta)OH])/([NH_(3)])` `1.8 xx 10^(-5) = (x^(2))/(4.5 xx 10^(-2))` `rArr x^(2) = 8.1 xx 10^(-7) rArr x = [overset(Theta)OH] = 9.0 xx 10^(-4)M`. `[overset(Theta)OH] (9.0 xx 10^(-4)M)` from the `4.5 xx 10^(-2)M NH_(3)` is sufficient precipitate `Zn(OH)_(2)` [part (b)] but not sufficient to from `Zn(OH_(4)^(2-))` [part (c)] e. On addition of `Nh_(3)` solution to `Zn^(2+)` solution, a precipitate of `Zn(OH)_(2)` will form, which will later dissolve to yield a clear solution containing `[Zn(NH_(3))_(4)]^(2+)`

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