What is the pH of the resulting solution if 40.00 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. A)9.73 B)8.78 C)5.22 D)4.27

Question

Quizplus · Accepted Answer

The balanced chemical equation for the reaction between acetic acid (CH3COOH) and sodium hydroxide (NaOH) is:

CH3COOH + NaOH → CH3COONa + H2O

From the equation, we can see that 1 mole of acetic acid reacts with 1 mole of sodium hydroxide to produce 1 mole of sodium acetate (CH3COONa) and 1 mole of water (H2O).

Before the reaction, we need to calculate the amount of moles of acetic acid and sodium hydroxide:

Moles of acetic acid = concentration × volume = 0.10 mol/L × 0.04000 L = 0.00400 mol
Moles of sodium hydroxide = concentration × volume = 0.10 mol/L × 0.01000 L = 0.00100 mol

Since 1 mole of acetic acid reacts with 1 mole of sodium hydroxide, the amount of sodium hydroxide is limiting in this reaction.

Therefore, all of the sodium hydroxide will react with acetic acid to form sodium acetate and water. The amount of remaining acetic acid will be equal to the initial amount minus the amount reacted with sodium hydroxide:

Remaining moles of acetic acid = initial moles - moles reacted = 0.00400 mol - 0.00100 mol = 0.00300 mol

The total volume of the resulting solution is 40.00 mL + 10.00 mL = 50.00 mL = 0.05000 L.

To calculate the pH of the resulting solution, we need to calculate the concentration of the sodium acetate formed and the concentration of the remaining acetic acid.

The concentration of sodium acetate can be calculated from the amount formed and the total volume of the solution:

Concentration of sodium acetate = amount/volume = 0.00100 mol/0.05000 L = 0.020 M

The concentration of the remaining acetic acid can be calculated from the remaining moles and the final volume of the solution:

Concentration of acetic acid = remaining moles/final volume = 0.00300 mol/0.05000 L = 0.060 M

The Ka for acetic acid is 1.8 × 10^-5.

The Henderson-Hasselbalch equation can be used to calculate the pH of the resulting solution:

pH = pKa + log([A^-]/[HA])
where pKa = -log(Ka) = -log(1.8 × 10^-5) = 4.74
[A^-] is the concentration of the acetate ion (CH3COO^-), which is equal to the concentration of sodium acetate (0.020 M).
[HA] is the concentration of the remaining acetic acid (0.060 M).

pH = 4.74 + log(0.020 M/0.060 M) = 4.74 - 0.4771 = 4.2629 ≈ 4.27

Therefore, the pH of the resulting solution is 4.27. The correct answer is D.

What Is the PH of the Resulting Solution If 40