Calculate Ka for the cation and Kb for the anion in an aqueous NH4CN solution. Is the solution acidic, basic, or neutral?

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Identify the ions present in the solution: NH4CN dissociates into NH4+ (ammonium ion) and CN- (cyanide ion).

Determine the acid-base nature of each ion: NH4+ is a weak acid, and CN- is a weak base.

Use the known Ka value for NH4+ to calculate its acidic strength: NH4+ + H2O ⇌ NH3 + H3O+. The Ka expression is Ka = [NH3][H3O+]/[NH4+].

Use the known Kb value for CN- to calculate its basic strength: CN- + H2O ⇌ HCN + OH-. The Kb expression is Kb = [HCN][OH-]/[CN-].

Compare the Ka of NH4+ and the Kb of CN- to determine the nature of the solution: If Ka > Kb, the solution is acidic; if Kb > Ka, the solution is basic; if Ka = Kb, the solution is neutral.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Acid-Base Equilibria

Acid-base equilibria involve the transfer of protons (H+) between species in a solution. The strength of an acid is quantified by its acid dissociation constant (Ka), while the strength of a base is measured by its base dissociation constant (Kb). In the context of NH4CN, NH4+ acts as a weak acid and CN- as a weak base, influencing the overall pH of the solution.

Dissociation Constants (Ka and Kb)

Ka and Kb are equilibrium constants that describe the extent to which an acid or base dissociates in water. For NH4+, the Ka value indicates how readily it donates protons, while for CN-, the Kb value shows its ability to accept protons. The relationship between Ka and Kb for conjugate acid-base pairs is given by the equation Kw = Ka × Kb, where Kw is the ion product of water.

pH and Solution Classification

The pH of a solution determines whether it is acidic, basic, or neutral. A pH less than 7 indicates an acidic solution, a pH of 7 is neutral, and a pH greater than 7 is basic. By calculating the Ka for NH4+ and Kb for CN-, one can determine the dominant species in solution and thus predict the overall pH, allowing for classification of the solution.

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