Answer:

The pH of a 0.15 M solution of ammonium bromide is approximately 5.74.

Step-by-step explanation:

To calculate the pH of a solution of ammonium bromide (NH4Br), we need to consider the dissociation of NH4Br and the equilibrium reaction with water.

The dissociation reaction of NH4Br in water can be represented as follows:

NH4Br (aq) ↔ NH4+ (aq) + Br- (aq)

NH4+ is the conjugate acid, and it can react with water as follows:

NH4+ (aq) + H2O (l) ↔ NH3 (aq) + H3O+ (aq)

The Kb value provided represents the equilibrium constant for the reaction of NH4+ with water to form NH3 and H3O+.

To calculate the pH, we can use the fact that the concentration of H3O+ is equal to the concentration of NH4+ in the solution at equilibrium.

Given that the concentration of NH4Br is 0.15 M, we can assume that the concentration of NH4+ is also 0.15 M.

Now, let's set up the equation to calculate the concentration of H3O+:

Kb = [NH3][H3O+] / [NH4+]

Since [NH4+] = 0.15 M and the concentration of NH3 can be assumed negligible, we can simplify the equation to:

Kb = [H3O+]

Plugging in the value of Kb (1.8 x 10^5), we find:

[H3O+] = 1.8 x 10^5

The pH of a solution is calculated using the formula:

pH = -log[H3O+]

Taking the negative logarithm of 1.8 x 10^5, we get:

pH = -log(1.8 x 10^5) ≈ -5.74

Therefore, the pH of a 0.15 M solution of ammonium bromide is approximately 5.74.