Final answer:
The pH of the solution before HBr is added is 1. At the point when 1 mL of HBr is added to neutralize the solution, the pH is 2.53. When the solution is titrated 1 mL past neutralization, the pH is 0.82.
Step-by-step explanation:
a. What is the pH of the solution before HBr is added?
Before HBr is added, the solution contains 0.1M Ca(OH)2. Calcium hydroxide is a strong base, so it completely dissociates in water to form hydroxide ions (OH-) and calcium ions (Ca2+). The concentration of hydroxide ions is therefore 0.1M.
The pH of a solution can be calculated using the formula pH = -log[H+], where [H+] is the concentration of hydrogen ions. In this case, the concentration of hydrogen ions is equal to the concentration of hydroxide ions, so the pH is equal to -log(0.1) = 1.
b. What is the pH of the solution at the point when it needs 1 mL of HBr to neutralize the solution?
When 1 mL of HBr is added to the solution, it reacts with the hydroxide ions present in the solution to form water. This reaction reduces the concentration of hydroxide ions and increases the concentration of hydrogen ions. Therefore, the pH of the solution decreases.
To calculate the new pH, we need to determine the concentration of hydrogen ions after the neutralization reaction. Since 1 mL of a 0.15M HBr solution is added to the 50 mL Ca(OH)2 solution, the moles of HBr added can be calculated as (0.001 L) * (0.15M) = 1.5 x 10^-4 mol.
Assuming no additional OH- or H+ ions are present in the solution before the titration, the final volume of the solution is 51 mL (50 mL Ca(OH)2 + 1 mL HBr).
Therefore, the concentration of hydrogen ions in the solution can be calculated as (1.5 x 10^-4 mol)/(0.051 L) = 2.94 x 10^-3M.
Using the formula pH = -log[H+], the pH of the solution after adding 1 mL of HBr is -log(2.94 x 10^-3) = 2.53.
c. What is the pH of the solution when it is titrated 1 mL past neutralization?
When 1 mL of HBr is added to the solution, it reacts with all of the hydroxide ions present, leaving only HBr in the solution. Since HBr is a strong acid, it completely dissociates in water to form hydrogen ions (H+) and bromide ions (Br-).
Since the concentration of HBr in the solution is 0.15M (given in the question), the concentration of hydrogen ions is also 0.15M.
The pH of the solution can be calculated as -log(0.15) = 0.82.