Which of the following statements is (are) true? Correct the false statements. a. When a base is dissolved in water, the lowest possible pH of the solution is \(7.0 .\) b. When an acid is dissolved in water, the lowest possible pH is \(0 .\) c. A strong acid solution will have a lower pH than a weak acid solution. d. A \(0.0010-M \mathrm{Ba}(\mathrm{OH})_{2}\) solution has a pOH that is twice the pOH value of a \(0.0010-M \mathrm{KOH}\) solution.

A base dissolved in water will always lead to a pH greater than 7. A pH of 7 indicates a neutral pH, where the concentrations of hydrogen ions (H+) and hydroxide ions (OH-) are equal. Adding a base to water will increase the OH- concentration, leading to a higher pH. Therefore, the lowest possible pH for a base dissolved in water cannot be 7.0. Corrected Statement a: When a base is dissolved in water, the lowest possible pH of the solution is 7.0. (False)

When an acid is dissolved in water, depending on the strength of the acid, the resulting pH value will be lower than 7. The strongest possible acid will have the highest H+ concentration, resulting in the lowest pH value. If the concentration of hydrogen ions is \(10^{0} \mathrm{M}\) then the pH will be 0 (since pH = -log[H+]). Therefore, when an acid is dissolved in water, the lowest possible pH is 0. Statement b: When an acid is dissolved in water, the lowest possible pH is 0. (True)

A strong acid completely dissociates in water, thus releasing more hydrogen ions (H+) and having a lower pH than a weak acid, which partially dissociates in water. Therefore, a strong acid solution will have a lower pH than a weak acid solution. Statement c: A strong acid solution will have a lower pH than a weak acid solution. (True)

First, we need to understand that when a base is added to water, it increases the concentration of OH- ions. In this case, Ba(OH)2 is a strong base, and it has two OH- ions for each molecule. So, when 0.0010 M Ba(OH)2 is added to water, it produces 2 × 0.0010 M = 0.0020 M of OH- ions. The pOH is defined as -log[OH-]. The pOH for 0.0020 M of OH- ions is -log(0.002) ≈ 2.7. Now, for the KOH solution which also has 0.0010 M concentration, it has only one OH- ion for each molecule. Therefore, the pOH of this solution would be -log(0.0010) ≈ 3.0. Comparing the pOH values, it is not true that the pOH of the Ba(OH)2 solution is twice the pOH value of the KOH solution. They are different by around 0.3 pOH units. So, the statement is false. Corrected statement d: A 0.0010 M Ba(OH)2 solution has a pOH value that is slightly lower compared to the pOH value of a 0.0010 M KOH solution. (False)