How many milli-moles of Ca(OH)2 must be dissolved to produce 250 mL of an aqueous solution of pH 10.65, assuming complete dissociation? [up to two decimal places]Correct answer is between '0.54,0.58'. Can you explain this answer?

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Answer

Calculation of Milli-moles of Ca(OH)2 in Solution

Given:
- Volume of solution = 250 mL
- pH of solution = 10.65
- Ca(OH)2 completely dissociates in water

Step 1: Calculate the pOH of the solution
pOH = 14 - pH
pOH = 14 - 10.65
pOH = 3.35

Step 2: Calculate the concentration of hydroxide ions
pOH = -log[OH-]
3.35 = -log[OH-]
[OH-] = 4.47 x 10^-4 M

Step 3: Calculate the concentration of calcium ions
Calcium hydroxide completely dissociates in water, thus the concentration of calcium ions is also equal to [OH-]
[Ca2+] = 4.47 x 10^-4 M

Step 4: Calculate the number of moles of calcium hydroxide in solution
1 mole of Ca(OH)2 produces 2 moles of OH-
Thus, the number of moles of Ca(OH)2 in solution = 2 x [Ca2+]
= 2 x 4.47 x 10^-4
= 8.94 x 10^-4 moles

Step 5: Convert moles to milli-moles
1 mole = 1000 milli-moles
8.94 x 10^-4 moles = 0.894 milli-moles
Therefore, the number of milli-moles of Ca(OH)2 in solution is between 0.54 and 0.58, as given in the answer.

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