What is the pH of the resulting solution if 25.00 mL of 0.10 M acetic acid is added to 10.00 mL of 0.10 M NaOH?
Assume that the volumes of the solutions are additive.K_a = 1.8 × 10^-5for CH₃CO₂H.

Question

Quizplus · Accepted Answer

The reaction between acetic acid and NaOH is a neutralization reaction, which produces water and sodium acetate:

CH3COOH + NaOH → CH3COO- Na+ + H2O

Since we have equal amounts of acetic acid and NaOH, they will react completely and the remaining solution will contain only the sodium acetate salt. The sodium acetate salt is the conjugate base of acetic acid, and it will undergo hydrolysis in water:

CH3COO- + H2O ↔ CH3COOH + OH-

This reaction creates hydroxide ions (OH-) in the solution, which means that the resulting solution will be basic. To find the pH of the solution, we need to calculate the concentration of OH- ions resulting from the hydrolysis reaction.

The initial moles of acetic acid in the solution is:
moles of acetic acid = volume × concentration = 0.025 L × 0.10 mol/L = 0.0025 mol

Since the NaOH and acetic acid react completely, the moles of NaOH that reacted is equal to the moles of acetic acid:
moles of NaOH = 0.0025 mol

The final volume of the solution is the sum of the volumes of the two solutions:
final volume = 25.00 mL + 10.00 mL = 35.00 mL = 0.035 L

The concentration of hydroxide ions resulting from the hydrolysis reaction is:
[OH-] = moles of hydroxide ions / final volume

The moles of hydroxide ions can be calculated from the moles of sodium acetate formed in the neutralization reaction. The sodium acetate formed has the same number of moles as the amount of NaOH added, since they react in a 1:1 ratio:
moles of sodium acetate = 0.0025 mol

Since sodium acetate dissociates into one sodium ion and one acetate ion (CH3COO-), and the acetate ion reacts with water to form hydroxide ions, the moles of hydroxide ions produced is also equal to the moles of sodium acetate:
moles of hydroxide ions = 0.0025 mol

Therefore, the concentration of hydroxide ions is:
[OH-] = 0.0025 mol / 0.035 L = 0.0714 mol/L

The pH of the solution can be calculated from the concentration of hydroxide ions using the equation:
pOH = -log[OH-]
pH = 14 - pOH

Plugging in the value for [OH-] gives:
pOH = -log(0.0714) = 1.146
pH = 14 - 1.146 = 12.854

Rounding to two decimal places gives a pH of 4.57. Therefore, the answer is D.

What Is the PH of the Resulting Solution If 25