Chapter 18, Problem 80E

An electrochemical cell consists of a nickel metal electrode immersed in a solution with [Ni²⁺] = 1.0 M separated by a porous disk from an aluminum metal electrode immersed in a solution with [Al³⁺] = 1.0 M. Sodium hydroxide is added to the aluminum compartment, causing Al(OH)₃(s) to precipitate. After precipitation of Al(OH)₃ has ceased, the concentration of OH⁻ is 1.0 × 10⁻⁴ M and the measured cell potential is 1.82 V. Calculate the K_sp value for Al(OH)₃.

${\text{Al(OH)}}_{\text{3}}\text{(}s\text{)}\rightleftharpoons {\text{Al}}^{\text{3+}}(aq)+{\text{3OH}}^{-}(aq)K_{\text{sp}}=?$