The pH of a solution of Ba(OH)₂ is 10.66 at 25 ℃. What is the hydroxide ion concentration in the solution? If the solution volume is 125 mL, what mass of Ba(OH)₂ must have been dissolved?

Interpretation:

hydroxide ion concentration in the solution has to be calculated and mass of Ba(OH)2 must be dissolved in 125 mL solution also to be calculated.

Concept introduction:

The pH is a measure of hydrogen ion concentration. The expression for pH is,

pH=−log[H+]                                                                                                       (1)

The sum of pH and pOH is equal to 14 at 25 °C.

pH+pOH=14                                                                                                         (2)

Molarity (M) is the concentration of solution expressed as the number of moles of solute per litre of solution.

M=n(mol)V(L)                                                                                                            (3)

Number of moles (n) is calculated as,

n=m(g)Mw(g⋅mol−1)                                                                                                   (4)

Here, (m) is the mass of the substance and (Mw) is the molar mass of the substance.

Barium hydroxide is a strong base, it completely dissociates into ions in an aquoeous solution as follows:

  Ba(OH)2⇌Ba+2+2OH−

Given:

The pH of solution is 10.66.

The volume (V) of solution is 0.125 L.

Substitute the value of pH in equation (1) to calculate pOH.

14=10.66+pOHpOH=3.34

Now substitute the value of pOH in equation (2).

3.34=−log[OH−][OH−]=4.57×10−4 M

Since, barium hydroxide after dissociation gives two moles of hydroxide ions. Therefore the concentration of barium hydroxide is half of the concentration of hydroxide ion in the solution.

[Ba(OH)2]=4