Final answer:
The most acidic hydrated metal ion at equal molar concentration in water is Al³⁺ due to its favorable charge-to-radius ratio, which increases the acidity of water molecules coordinated to it, as evidenced by its pK1 value of 5.0.
Step-by-step explanation:
The acidic strength of hydrated metal ions in water can be determined by the charge-to-radius ratio of the metal ion. When considering the options given (Al³⁺, Ba²⁺, K⁺, Zn²⁺, and Ag⁺), the Al³⁺ ion exhibits the highest charge density due to its small size and high charge.
This makes the hydration shell around aluminum more acidic.
[Al(H2O)6]³⁺ is the most acidic among the provided options because it promotes acid ionization to a greater extent when dissolved in water.
The aluminum ion tends to attract electron density from the water molecules, weakening their O-H bonds and increasing the ease with which the H2O ligands can release H⁺ ions, forming H3O⁺ and the hydroxy complex [Al(H2O)5OH]²⁺.
The pK1 value of 5.0 for the hydrated aluminum ion further validates its relatively strong acidity.