Problem 75 - Chemistry: Principles and Reactions

Question

In a titration of \(50.00 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\) with \(1.00 \mathrm{M} \mathrm{NaOH}\), a student used bromcresol green as an indicator \(\left(K_{\mathrm{a}}=1.0 \times 10^{-5}\right)\). About how many milliliters of \(\mathrm{NaOH}\) would it take to reach the end point with this indicator? Is there a better indicator that she could have used for this titration?

Step-by-Step Solution

Answer

If not, suggest a better indicator. Answer: The volume of NaOH required to reach the endpoint in the titration is 50.00 mL. Bromcresol green is not an ideal indicator for this titration due to its color change range of 3.8 – 5.4, which does not include the pH of the equivalence point. A better indicator for this titration would be phenolphthalein, with a pH range of 8.2 – 10.0.

Step 1: Calculate the moles of acetic acid in the solution

To determine the equivalence point in the titration, first calculate the moles of acetic acid in the solution using the given molarity and volume: \(n_{\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}} = \mathrm{M} \times \mathrm{V}\) \(n_{\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}} = 1.00 \mathrm{M} \times 50.00 \mathrm{mL} \times \frac{1 \mathrm{L}}{1000 \mathrm{mL}} = 0.0500 \mathrm{mol}\)

Step 2: Calculate the volume of NaOH required to reach the equivalence point

At the equivalence point, there will be equal moles of NaOH and acetic acid. Use the moles of acetic acid and the molarity of NaOH to calculate the volume of NaOH needed to reach this point: \(V_{\mathrm{NaOH}} = \frac{n_{\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}}}{\mathrm{M}_{\mathrm{NaOH}}}\) \(V_{\mathrm{NaOH}} = \frac{0.0500 \mathrm{mol}}{1.00 \mathrm{M}} = 0.0500 \mathrm{L}\) or \(50.00 \mathrm{mL}\)

Step 3: Analyze the color change of bromcresol green at the pH of the equivalence point

Bromcresol green has a Ka value of \(1.0 \times 10^{-5}\). This means that the pH range of color change for bromcresol green is approximately 3.8 – 5.4. The titration of acetic acid (a weak acid) with NaOH (a strong base) will produce a basic solution at the equivalence point, as the weak acid will be fully neutralized by the strong base. Since the pH of the equivalence point will lie outside the color change range of bromcresol green, it is not the ideal indicator and may give inaccurate results.

Step 4: Determine if a better indicator could be used

For the titration involving a weak acid and a strong base, the preferred indicator should have a pH range that includes the pH of the equivalence point. Phenolphthalein, for example, has a pH range of about 8.2 – 10.0, which includes the pH of the equivalence point for this titration. Therefore, using phenolphthalein as an indicator would provide more accurate results in this titration.

Key Concepts

Equivalence Point Calculation

The equivalence point in a titration is the moment where the amount of titrant added is stoichiometrically equivalent to the amount of substance initially present in the sample. For an acid-base titration, it signifies the point at which the acid has been completely neutralized by the base, or vice versa.

To calculate the equivalence point, you need to know the molarity and volume of both the acid and base solutions. In our exercise, acetic acid (\( \text{HC}_2\text{H}_3\text{O}_2 \)) is the acid with a known concentration and volume, and sodium hydroxide (NaOH) is the titrant. By multiplying the molarity (\( M \)) of acetic acid by its volume in liters (\( V \)), you obtain the moles of acetic acid present. Assuming a 1:1 molar ratio between the acid and the base, which is the case for NaOH reacting with acetic acid, the same number of moles of NaOH would be required to reach the equivalence point. Thus the calculated volume of NaOH would be sufficient to neutralize the acetic acid present.

To assist with understanding, consider this: if you have 0.0500 moles of acetic acid, and you’re using a 1.00M NaOH solution, you would need 0.0500 L (or 50.00 mL) of NaOH to reach the equivalence point, as demonstrated in the step-by-step solution.

Acid-Base Titration

Acid-base titration is a quantitative analytical procedure used to determine the concentration of an acid or base in a solution. The process involves the gradual addition of a known concentration of titrant (in our case, NaOH) to a known volume of the substance being analyzed (acetic acid) until the equivalence point is reached.

An indicator, which changes color at a certain pH range, is often used to visually signal the proximity to or the achievement of the equivalence point. During an acid-base titration, the pH of the solution changes gradually until it spikes at the equivalence point. By carefully monitoring this pH change, one can conclude when the neutralization has occurred.

Understanding titration curves, the graphical representation of a titration, can be especially useful. As the titrant (base) is added to the analyte (acid), the curve begins to rise until it reaches a point of inflection—the equivalence point—where the slope is the steepest, typically indicating that the acid has been neutralized.

Titration Indicators

Titration indicators are substances that exhibit different colors at different pH levels and are used to identify the endpoint of a titration, which closely corresponds to the equivalence point. The choice of indicator is crucial as it must have a color change that falls within the sudden pH change range observed at the equivalence point.

Two common types of acid-base indicators are organic compounds that react with ions in the solution to produce a color, and pH-sensitive electrochemical sensors that change their electrochemical potential with the pH. However, for educational or simple laboratory titrations, organic dye indicators like bromcresol green or phenolphthalein are commonly employed because they provide a clear visual cue through a color change that is easy to observe. It’s essential that the pH range of the indicator’s color change bracket the pH expected at the equivalence point for best results.

Bromcresol Green

Bromcresol green is a dye that is often used as an acid-base indicator in titrations. As described in the problem, it has a pH range for its color change of approximately 3.8 – 5.4, which makes it suitable for titrations that end in this pH range.

For instance, bromcresol green would be appropriate for a strong acid titrated with a weak base, which would have an equivalence point in the acidic pH range. However, in the case of our problem where a weak acid (acetic acid) is being titrated with a strong base (NaOH), the equivalence point would lie in the basic range, typically above pH 7. Therefore, bromcresol green would change color before the actual equivalence point is reached, leading to an early endpoint and inaccurate results. This mismatch emphasizes the need to select an appropriate indicator based on the expected pH at the equivalence point.

Phenolphthalein

Phenolphthalein is another commonly used acid-base indicator that changes color in the pH range of about 8.2 – 10.0, turning from colorless in acidic solutions to pink in basic solutions. This property makes phenolphthalein suitable for detecting the endpoint in titrations involving weak acids and strong bases—as is the case with our acetic acid and NaOH titration.

Since the equivalence point of a weak acid-strong base titration tends to fall within a slightly basic pH range, phenolphthalein provides a more accurate indication of the endpoint. The color change to pink will occur as the pH of the solution surpasses 8.2, which is more aligned with the equivalence point we expect in this titration exercise. Therefore, phenolphthalein would have been a better choice than bromcresol green for the student's titration, offering a clearer and more accurate determination of the equivalence point.