A 10.0-mL sample of \(0.250 \mathrm{M}\) acetic acid $\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\( is titrated with \)0.100 \mathrm{M}$ KOH solution. Calculate the pH after the following volumes of base have been added: (a) \(0 \mathrm{~mL},\) (b) \(12.5 \mathrm{~mL}\) (c) \(24.5 \mathrm{~mL}\) (d) \(25.0 \mathrm{~mL}\) (e) \(25.5 \mathrm{~mL}\) (f) \(30.0 \mathrm{~mL}\).

Short Answer

Expert verified
The pH values after adding the specified volumes of KOH are as follows: (a) 0 mL: pH = 2.87 (b) 12.5 mL: pH = 4.73 (c) 24.5 mL: pH = 4.77 (d) 25.0 mL: pH = 5.71 (e) 25.5 mL: pH = 6.74 (f) 30.0 mL: pH = 9.77

Step by step solution

01

Write down the relevant reaction for titration.

In this titration, we will react acetic acid with KOH. The reaction that occurs is: \[\mathrm{CH}_{3}\mathrm{COOH} + \mathrm{KOH} \longrightarrow \mathrm{CH}_{3}\mathrm{COOK} + \mathrm{H}_{2}\mathrm{O}\]
02

Calculate the initial moles of acetic acid and KOH.

Initial moles of acetic acid can be calculated using volume and concentration: Moles of acetic acid = Volume × Concentration Moles of acetic acid = 0.010 L × 0.250 mol/L = 0.0025 mol For KOH, the number of moles will be calculated separately for each specified volume in the problem.
03

Calculate moles and concentrations for each specified volume of KOH.

For each specified volume of KOH, we will calculate the number of moles, and then find the resulting concentrations of species involved in the reaction. This will help us determine the dominant species present and the appropriate method to calculate pH.
04

Calculate the pH for each specified volume of KOH.

For each specified volume, we will be using the appropriate method such as calculating pH directly, using the equilibrium constant, or considering the excess of KOH.
05

Answer the problem with calculated pH values.

After following the above steps for each specified volume of KOH, we will have a pH value corresponding to each volume. We will present those pH values as a final answer.

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