What is the pH of the resulting solution if 30.00 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)9.56 B)8.95 C)5.05 D)4.44

Question

Quizplus · Accepted Answer

First, we need to write out the balanced chemical equation for the reaction between acetic acid and sodium hydroxide: 
CH3COOH + NaOH → CH3COONa + H2O 
From this equation, we can see that the acid and base will neutralize each other, with the resulting solution containing the sodium acetate salt and water. 
To determine the pH of the resulting solution, we need to calculate the moles of acid and base present, and then use the amount of sodium acetate formed (which is the same as the amount of acid that reacted) to calculate the concentration of acetate ions in the solution. From there, we can use the equilibrium constant (Ka) for acetic acid to calculate the pH. 
Here are the steps:

1. Calculate the moles of acid and base:

moles of acid = 0.030 L * 0.10 mol/L = 0.0030 mol 
moles of base = 0.010 L * 0.10 mol/L = 0.0010 mol

2. Determine the limiting reactant:

Since the acid and base have a 1:1 stoichiometry, whichever is present in lower moles will be the limiting reactant. In this case, the base is limiting, since there are fewer moles of it present.

3. Calculate the amount of sodium acetate formed:

Since the base is limiting, all of its moles will react with an equal number of moles of acid. Therefore, the amount of sodium acetate formed is equal to the amount of acid that reacted:

moles of acetate = 0.0030 mol

4. Calculate the concentration of acetate ions:

We know that 0.0030 mol of sodium acetate is present in a total solution volume of 40.00 mL (30.00 mL + 10.00 mL), which is 0.0400 L:

[acetate] = moles of acetate / total volume 
[acetate] = 0.0030 mol / 0.0400 L 
[acetate] = 0.075 M

5. Use the Ka for acetic acid to calculate the pH:

Ka = [H+][acetate] / [acid] 
We can assume that the [H+] comes entirely from the dissociation of water (since the acetate ion is a weak base and so will not significantly hydrolyze):

Ka = [H+] * [acetate] / [acid] 
Solving for [H+]:

[H+] = Ka * [acid] / [acetate] 
[H+] = 1.8 × 10^-5 * 0.0030 mol / 0.075 mol 
[H+] = 7.2 × 10^-7 M

Finally, we convert the H+ ion concentration to pH:

pH = -log[H+] 
pH = -log(7.2 × 10^-7) 
pH = 6.14

However, since we are dealing with dilute solutions, we need to take into account the effect of the volume of the NaOH solution on the final pH. We can do this by using the Henderson-Hasselbalch equation, which takes into account the initial concentrations of the acid and base, as well their ratio (which determines the pKa value used in the equation). The Henderson-Hasselbalch equation is:

pH = pKa + log([base] / [acid])

The pKa value for acetic acid is 4.74. Plugging in our values:

pH = 4.74 + log(0.010 / 0.040) 
pH = 4.74 - 0.70 
pH = 4.04

Therefore, our final answer is:

Answer: D 
 The pH of the resulting solution is approximately 4.04.

What Is the PH of the Resulting Solution If 30