Answer :
Final answer:
The pH after 27.5 mL of base have been added is approximately 3.97.
Explanation:
In this titration, acetic acid (CH3COOH) is being titrated with sodium hydroxide (NaOH). Acetic acid is a weak acid, and sodium hydroxide is a strong base. The reaction between them is as follows:
CH3COOH + NaOH -> CH3COONa + H2O
Before the titration, we have a 39.4 mL sample of a 0.486 M acetic acid solution. This means that there are 0.486 moles of acetic acid in 1 liter of solution. To calculate the number of moles of acetic acid in the 39.4 mL sample, we can use the formula:
moles = concentration x volume
moles = 0.486 M x 0.0394 L = 0.0191 moles
During the titration, 27.5 mL of a 0.485 M sodium hydroxide solution is added. This means that there are 0.485 moles of sodium hydroxide in 1 liter of solution. To calculate the number of moles of sodium hydroxide added, we can use the formula:
moles = concentration x volume
moles = 0.485 M x 0.0275 L = 0.0133 moles
Since acetic acid and sodium hydroxide react in a 1:1 ratio, the number of moles of acetic acid remaining after the titration is:
moles remaining = initial moles - moles added
moles remaining = 0.0191 moles - 0.0133 moles = 0.0058 moles
To calculate the concentration of acetic acid after the titration, we divide the number of moles remaining by the total volume of the solution:
concentration = moles remaining / total volume
total volume = initial volume + volume added
total volume = 39.4 mL + 27.5 mL = 66.9 mL = 0.0669 L
concentration = 0.0058 moles / 0.0669 L = 0.0866 M
Now, we can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log([A-]/[HA])
The pKa value for acetic acid is 4.76. Since acetic acid is a weak acid, we can assume that most of it has dissociated into acetate ions (A-) and hydrogen ions (H+). Therefore, [A-] is approximately equal to the concentration of acetic acid after the titration, which is 0.0866 M. [HA] is the concentration of acetic acid before the titration, which is 0.486 M.
pH = 4.76 + log(0.0866/0.486) = 4.76 - 0.79 = 3.97
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