A 35.0-mL sample of 0.150 M acetic acid 1CH3COOH2 is titrated with 0.150 M NaOH solution. Calculate the pH after the following volumes of base have been added: (b) 17.5 mL.

Verified step by step guidance

1. Step 1: Identify the type of reaction. In this case, it's an acid-base titration. Acetic acid (CH3COOH) is a weak acid and sodium hydroxide (NaOH) is a strong base. When they react, they form water and the acetate ion (CH3COO-).
2. Step 2: Calculate the initial moles of acetic acid. This can be done by multiplying the initial volume of the acetic acid solution (in liters) by its molarity. Remember that molarity is defined as moles per liter.
3. Step 3: Calculate the moles of NaOH added. This can be done by multiplying the volume of the NaOH solution added (in liters) by its molarity.
4. Step 4: Determine the limiting reactant. In this case, since the molarity of the acetic acid and NaOH are the same, and the volume of NaOH added is half the volume of the acetic acid, the NaOH will be the limiting reactant. This means that all of the NaOH will react with an equal amount of acetic acid, and there will be some acetic acid left over.
5. Step 5: Calculate the pH of the resulting solution. Since there is still some acetic acid left over, the solution will be a buffer. The pH of a buffer can be calculated using the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the acetate ion and [HA] is the concentration of the remaining acetic acid. The pKa of acetic acid is 4.76.

Key Concepts

Acid-Base Titration

An acid-base titration is a quantitative analytical method used to determine the concentration of an acid or base in a solution. In this process, a solution of known concentration (the titrant) is added to a solution of unknown concentration until the reaction reaches its equivalence point, where the amount of acid equals the amount of base. The pH of the solution changes during the titration, and this change can be monitored to find the endpoint.

Buffer Solutions

Buffer solutions are mixtures that can resist changes in pH upon the addition of small amounts of acid or base. They typically consist of a weak acid and its conjugate base or a weak base and its conjugate acid. In the case of acetic acid and sodium hydroxide, the acetic acid acts as a weak acid, and as NaOH is added, it forms its conjugate base, acetate, which helps maintain the pH within a certain range until the equivalence point is reached.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution. It relates the pH of the solution to the pKa of the weak acid and the ratio of the concentrations of the conjugate base to the weak acid. This equation is particularly useful in titration problems, as it allows for the determination of pH at various points during the titration, especially before and after the equivalence point.