Problem 33 - Chemistry: An Atoms-Focused Approach

Question

What volume of \(0.422 M\) NaOH must be added to \(0.500 \mathrm{L}\) of \(0.300 M\) acetic acid to raise its \(\mathrm{pH}\) to 4.00 at \(25^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Answer: Approximately 0.1407 L (or 140.7 mL) of 0.422 M NaOH should be added.

Step 1: Calculate the weak acid to conjugate base ratio using the Henderson-Hasselbalch equation

To find the ratio of weak acid (acetic acid, CH3COOH) to its conjugate base (acetate ion, CH3COO-), we can use the Henderson-Hasselbalch equation, which relates pH, pKa and the ratio of conjugate base/weak acid: pH = pKa + log (A-/HA) where pH = 4.00 (given), and pKa of acetic acid is 4.74. Plug in the values to find the ratio: 4.00 = 4.74 + log (A-/HA) log (A-/HA) = -0.74 A-/HA = 10^(-0.74)

Step 2: Convert volume and molar concentration of acetic acid into moles

Given that the initial volume of 0.300 M acetic acid solution is 0.500 L, we can find the moles of acetic acid as follows: moles of acetic acid (HA) = molar concentration × volume moles of acetic acid (HA) = 0.300 M × 0.500 L = 0.150 moles

Step 3: Set up an equation to find the moles of NaOH required

Let x be the moles of NaOH needed to achieve the desired pH. The addition of NaOH will convert acetic acid into its conjugate base (acetate ion) while reacting with it, so we will have x moles of acetate ion and (0.150 - x) moles of acetic acid. This will result in the following equation using the ratio calculated in Step 1: 10^(-0.74) = (x) / (0.150 - x) Solve for x (moles of NaOH): x ≈ 0.0594 moles

Step 4: Calculate the volume of 0.422 M NaOH needed

Now, we will use molarity to calculate the required volume of 0.422 M NaOH. Molarity is defined as moles of solute per liter of solution: moles of NaOH = molarity of NaOH × volume of NaOH 0.0594 moles ≈ 0.422 M × volume of NaOH Solve for the volume of NaOH: volume of NaOH ≈ 0.1407 L Therefore, approximately 0.1407 L (or 140.7 mL) of 0.422 M NaOH needs to be added to 0.500 L of 0.300 M acetic acid to raise its pH to 4.00 at 25°C.

Key Concepts

pH Calculation

Understanding pH is crucial for many chemical processes, especially when dealing with acid-base reactions. The pH is a measure of the hydrogen ion concentration in a solution, given by the formula:
\[pH = -\log[H^+]\]For buffer solutions which resist changes in pH, the calculation becomes more involved. Here, the Henderson-Hasselbalch equation becomes quite handy:
\[pH = pKa + \log\left(\frac{[A^-]}{[HA]}\right)\]In this context:

• \(pKa\) is the acid dissociation constant, specific to each weak acid.
• \([A^-]/[HA]\) is the ratio of the conjugate base \(A^-\) to the weak acid \(HA\).

With the help of this equation, you can determine the pH of a buffer solution given the concentrations of the acid and its conjugate base or vice versa. It allows chemists to predict how much of a base needs to be added to achieve a desired pH.

Buffer Solution

A buffer solution is a special type of solution that resists changes in pH upon the addition of small amounts of acids or bases. This property is invaluable in many chemical and biological processes. Buffer solutions are typically made up of a weak acid and its conjugate base, or a weak base and its conjugate acid.
In our context:

• Acetic acid \( (CH_3COOH) \) acts as the weak acid.
• Acetate ion \( (CH_3COO^-) \) is the conjugate base.

When a strong base like \(NaOH\) is added, it reacts with the weak acid, converting it to the conjugate base. This reaction minimizes the change in pH. The capacity of a buffer to maintain a stable pH depends on the ratio and concentrations of the weak acid and its conjugate base. Understanding this is crucial for any work involving acid-base titrations and maintaining conditions for chemical reactions.

Acid-Base Titration

Acid-base titration is an analytical method used to determine the concentration of an acid or base in a solution. This technique involves adding a titrant of known concentration to a solution with an unknown concentration until a reaction reaches completion. In this exercise, a strong base (NaOH) is used as the titrant to determine how much is needed to raise the pH of an acetic acid solution to 4.00.
The titration process goes as follows:

• As NaOH is added, it reacts with the acetic acid, forming water and acetate ions.
• Each mole of NaOH will react with one mole of acetic acid, converting it to its conjugate base.
• The goal is to reach a point where the ratio of acetic acid to acetate ion results in the desired pH of 4.00.

This specific step of the titration can be calculated using the Henderson-Hasselbalch equation to anticipate how much NaOH must be added to shift the pH to the desired level. Performing titrations with accuracy is important for achieving the right solution balance.