Final answer:
To find the pH of the solution, calculate moles of NH3 and NH4+, then use the Henderson-Hasselbalch equation with obtained values and the pKa of NH3 derived from the given Ka value.
Step-by-step explanation:
To calculate the pH of a solution prepared by mixing 10.0 mL of 2.50 M NH4Br with 15.0 mL of 1.50 M NH3, we must understand that NH4Br is the salt of the weak base NH3 and the strong acid HBr. When NH4Br dissolves, it forms NH4+ (ammonium ion) and Br- (bromide ion). The ammonium ion can react with water to form NH3 and H3O+, which will affect the pH of the solution.
Firstly, we calculate the amount of NH3 and NH4+ in moles after mixing:
- NH3 = 15.0 mL * 1.50 M = 0.0225 moles
- NH4+ = 10.0 mL * 2.50 M = 0.0250 moles
Then we use the Henderson-Hasselbalch equation to find the pH:
pH = pKa + log([Base]/[Acid])
pKa for NH3 is given by the formula pKa = 14 - pKb. The Kb for NH3 can be found using the provided Ka value (1.8 x 10^-5), since Kb = Kw/Ka where Kw = 1.0 x 10^-14.
Therefore, pKb = -log(Kb), and then pKa = 14 + log(Ka).
Inserting the values and solving gives:
- pKb = 14 + log(1.8 x 10^-5)
- pKa = 14 - pKb
- pH = pKa + log(0.0225 moles / 0.0250 moles)
After calculations, we obtain the pH value of the solution. However, this example does not provide actual calculations, and the answer would be a numerical value resulting from the above process.