The correct answer is: pH = 12.73
Explanation:
The neutralization reaction between HCl and KOH is given by the following chemical equation:
HCl + KOH ⇒ KCl + H₂O
Since HCl is a strong acid and KOH is a strong base, HCl is completely dissociated into H⁺ and Cl⁻ ions, whereas KOH is dissociated completely into K⁺ and OH⁻ ions.
For acids, the number of equivalents is given by the moles of H⁺ ions (in this case: 1 equivalent per mol of HCl). For bases, the number of equivalents is given by the moles of OH⁻ ions (in this case: 1 equivalent per mol of KOH).
The H⁺ ions from HCl will react with OH⁻ ions of KOH to give H₂O. The pH is calculated from the difference between the equivalents of H⁺ and OH⁻:
equivalents of H⁺= volume HCl x Molarity HCl
= (15.0 mL x 1 L/1000 mL) x 0.100 mol/L
= 1.5 x 10⁻³ eq H⁺
equivalents of OH⁻= volume KOH x Molarity KOH
= (50.0 mL x 1 L/1000 mL) X 0.100 mol/L
= 5 x 10⁻³ eq OH⁻
There are more OH⁻ ions than H⁺ ions. The excess of OH⁻ (that did not react with H⁺ ions) is calculated as follows:
OH⁻ ions= (5 x 10⁻³ eq OH⁻) - (1.5 x 10⁻³ eq H⁺) = 3.5 x 10⁻³ eq OH⁻= 3.5 x 10⁻³ moles OH⁻
As the volumes of the solutions are additive, the total volume of the solution is:
V= 15.0 mL + 50.0 mL = 65.0 mL= 0.065 L
So, the concentration of OH⁻ ions in the solution is given by:
[OH⁻] = moles OH⁻/V= (3.5 x 10⁻³ moles OH⁻)/0.065 L = 0.054 mol/L = 0.054 M
From [OH⁻], we can calculate pOH:
pOH = -log [OH⁻] = -log (0.054) = 1.27
Finally, we know that pH + pOH= 14; so we calculate pH:
pH= 14 - pOH = 14 - 1,27 = 12.73
