Answer:
1.2x10⁻²³M = [Ag⁺]
Step-by-step explanation:
The Kf of Ag(CN)₂⁻ is:
Ag⁺(aq) + 2CN⁻ → Ag(CN)₂⁻(aq)
Kf = 1.0x10²¹ = [Ag(CN)₂⁻] / [Ag⁺] [CN⁻]²
Where [] are equilibrium concentrations.
The initial concentrations of the reactants are:
[Ag⁺] = 3.0x10⁻³M * (130mL / 355mL) = 1.10x10⁻³M
335mL is the total volume of the solution
[CN⁻] = 0.14M * (225mL / 355mL) = 0.089M
In equilibrium, the concentrations are:
[Ag⁺] = 1.10x10⁻³M - X
[CN⁻] = 0.089M - 2X
Ag(CN)₂ = X
Replacing in Kf expression:
1.0x10²¹ = [Ag(CN)₂⁻] / [Ag⁺] [CN⁻]²
1.0x10²¹ = [X] / [1.10x10⁻³ - X] [0.089 - 2X ]²
1.0x10²¹ = [X] / 8.7131×10⁻⁶ - 0.0083126 X + 0.3604 X² - 4 X³
8.7131×10¹⁵ - 8.3126×10¹⁸ X + 3.604×10^20 X² - 4x10²¹ X³ = X
8.7131×10¹⁵ - 8.3126×10¹⁸ X + 3.604×10^20 X² - 4x10²¹ X³ = 0
X = 0.0011M → Right solution.
X = 0.0445M → False solution. Produce negative concentrations
Replacing:
[Ag⁺] = 0
[CN⁻] = 0.0868M
Ag(CN)₂ = 0.0011M
The equilibrium will shift to the left just a little bit until produce a determined amount of Ag⁺ that we can write as:
[Ag⁺] = X
Thus:
1.0x10²¹ = [0.0011] / [X] [0.0868M ]²
1.2x10⁻²³M = [Ag⁺]