Question

Millimoles of calcium hydroxide required to produce 100 mL of the aqueous solution of pH 12 is \(x \times 10^{-1}\). The value of \(x\) is — (Nearest integer).

Hint:

For pH-based calculations:
• Use the relationship pH + pOH = 14 to find OH− concentration.
• Consider the stoichiometry of the dissociation reaction to relate hydroxide
ion concentration to the base concentration.
• Calculate millimoles using the formula Molarity × Volume (in mL).

Answer 1

Correct Answer: 5

To determine the millimoles of calcium hydroxide required to produce 100 mL of an aqueous solution with a pH of 12, we need to calculate the concentration of hydroxide ions, [OH^-], in the solution.

Since pH + pOH = 14, for a pH of 12, the pOH is 2.

The concentration of hydroxide ions is given by [OH^-] = 10^-pOH = 10^-2 mol/L.

Calcium hydroxide, Ca(OH)₂, dissociates in water to form one Ca²⁺ ion and two OH^- ions:

Ca(OH)₂ → Ca²⁺ + 2OH^-

Therefore, for each mole of Ca(OH)₂, 2 moles of OH^- are produced. Thus, the concentration of Ca(OH)₂ needed is half the concentration of OH^- ions:

[Ca(OH)₂] = [OH^-] / 2 = 10^-2 / 2 = 0.005 mol/L.

For 100 mL (0.1 L) of solution, the moles of Ca(OH)₂ needed is:

0.005 mol/L × 0.1 L = 0.0005 mol.

Converting to millimoles (1 mol = 1000 mmol):

0.0005 mol × 1000 = 0.5 mmol.

Hence, \(x = 5\), and this value is within the given range of 5 to 5.