A weak base, like ammonia, is a Brønsted base that accepts a proton from water to produce the hydroxide ion. Weak bases react partially with water according to their base dissociation constant, K_b, which is 1.76 × 10⁻⁵ for ammonia.

The K_b for ammonia can be expressed as the ammonium ion concentration times the hydroxide ion concentration divided by the concentration of ammonia at equilibrium.

K_b can be used to determine the hydroxide ion concentration in a weak base solution and consequently, the pOH and pH of the solution.

The hydroxide ion concentration and pH of 0.23 M of ammonia solution can be determined using its base dissociation constant and by preparing an ICE table containing the initial and equilibrium values of the ammonia, ammonium ions, and hydroxide ions.

Substituting equilibrium concentrations in the K_b expression, K_b equals x times x divided by 0.23 minus x. As weak bases show partial dissociation, 0.23 minus x can be considered to be approximately 0.23.

When the equation is solved, x equals 2 × 10⁻³ M.

The approximation 0.23 minus x is equal to 0.23 is valid here as the hydroxide ion concentration is only 0.86% of 0.23 molar.

To calculate the pH of this solution, first determine the pOH by taking the negative log of the hydroxide ion concentration, which equals 2.70. The pH can be determined using the formula: pH plus pOH is equal to 14 and calculated to be 11.30.

The K_b for a weak base solution can be calculated if the pH of the weak base solution is known.

Methylamine is a weak base that partially dissociates in water into methylammonium ions and hydroxide ions.

The K_b for methylamine can be expressed as the methylammonium ion concentration times the hydroxide ion concentration divided by the concentration of methylamine at equilibrium.

To calculate the K_b of a 0.040 M methylamine solution with pH 11.6, first the pOH needs to be calculated followed by its hydroxide ion concentration. As the pH is 11.60, the pOH is 2.40, and its hydroxide ion concentration is 4.0 × 10⁻³. 

The ICE table can be constructed from the initial and the equilibrium concentrations of methylamine, methylammonium, and hydroxide.

Substituting equilibrium concentrations in the expression for the K_b yields value for K_b, which is 4.4 × 10⁻⁴.