What mass of sodium hydroxide must be added to 65.0 mL of 0.926 M acetic acid in order to create a buffer with a pH of 4.83? K_a for acetic acid is 1.8 × 10^-5.

Question

Quizplus · Accepted Answer

1. First, we need to use the Henderson-Hasselbalch equation for a buffer solution: 
pH = pKa + log([base]/[acid])

2. Rearranging the equation to solve for [base], we get: 
[base] = [acid] x 10^(pH - pKa)

3. We know the pH and pKa values, so we can calculate the ratio of [base] to [acid]. 
pH = 4.83
pKa = 4.74
ratio of [base] to [acid] = 10^(pH - pKa) = 1.67

4. We also know the initial concentration of acetic acid: 
0.926 M acetic acid

5. Using the ratio of [base] to [acid], we can find the concentration of sodium acetate needed: 
[base] = 1.67 x [acid] 
[base] = 1.67 x 0.926 M 
[base] = 1.546 M

6. Now we can calculate the moles of sodium acetate needed: 
moles of [base] = volume x concentration 
moles of [base] = 0.065 L x 1.546 M 
moles of [base] = 0.1005 moles

7. Finally, we can calculate the mass of sodium hydroxide needed, using the balanced equation for the reaction between acetic acid and sodium hydroxide: 
CH3COOH + NaOH → CH3COONa + H2O

The balanced equation tells us that we need one mole of NaOH for every mole of acetic acid reacted. So we need 0.1005 moles of NaOH.

m = n x M 
m = 0.1005 mol x 40.00 g/mol 
m = 4.02 g

However, we only need to add enough NaOH to make the buffer, which means we only need to add enough to react with the acetic acid present. The acetic acid is the limiting reagent in this reaction, so we don't need to add more NaOH than moles of acetic acid.

moles of acetic acid = volume x concentration 
moles of acetic acid = 0.065 L x 0.926 M 
moles of acetic acid = 0.060 mol

We only need 0.060 moles of NaOH to react with all of the acetic acid.

m = n x M 
m = 0.060 mol x 40.00 g/mol 
m = 2.40 g

Therefore, the answer is B) 1.3 g.

What Mass of Sodium Hydroxide Must Be Added to 65