Answer :

To determine the pH of a 0.0040 M solution of calcium hydroxide, [tex]\( \text{Ca(OH)}_2 \)[/tex], follow the steps below:

1. Understand the dissociation of calcium hydroxide in water:
[tex]\[ \text{Ca(OH)}_2 \rightarrow \text{Ca}^{2+} + 2 \text{OH}^- \][/tex]
Each molecule of [tex]\( \text{Ca(OH)}_2 \)[/tex] dissociates into one calcium ion ([tex]\( \text{Ca}^{2+} \)[/tex]) and two hydroxide ions ([tex]\( \text{OH}^- \)[/tex]).

2. Calculate the concentration of hydroxide ions ([tex]\( \text{OH}^- \)[/tex]):
Given the concentration of [tex]\( \text{Ca(OH)}_2 \)[/tex] is 0.0040 M, and knowing that each formula unit dissociates to produce two [tex]\( \text{OH}^- \)[/tex] ions, we can find the concentration of [tex]\( \text{OH}^- \)[/tex] as follows:
[tex]\[ \text{Concentration of } \text{OH}^- = 0.0040 \times 2 = 0.008 \text{ M} \][/tex]

3. Calculate the pOH of the solution:
The pOH is related to the concentration of [tex]\( \text{OH}^- \)[/tex] ions and is calculated using the formula:
[tex]\[ \text{pOH} = -\log[\text{OH}^-] \][/tex]
Substituting the concentration of [tex]\( \text{OH}^- \)[/tex]:
[tex]\[ \text{pOH} = -\log(0.008) \approx 2.097 \][/tex]

4. Determine the pH of the solution:
The pH and pOH are related by the equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Therefore, we can calculate the pH as follows:
[tex]\[ \text{pH} = 14 - \text{pOH} \][/tex]
Substituting the value found for pOH:
[tex]\[ \text{pH} = 14 - 2.097 \approx 11.903 \][/tex]

Hence, the pH of the 0.0040 M solution of [tex]\( \text{Ca(OH)}_2 \)[/tex] is approximately 11.903.