Question

Assume that 30.0 \(\mathrm{mL}\) of a 0.10 \(\mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a 0.10\(M\) solution of the monoprotic strong acid HA. (a) How many moles of HA have been added at the equivalence point? (b) What is the predominant form of B at the equivalence point? (a) Is the pH \(7,\) less than \(7,\) or more than 7 at the equivalence point?\( (\mathbf{d} )\) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

Short answer

(a) At the equivalence point, 0.0030 moles of HA have been added. (b) The predominant form of B at the equivalence point is its conjugate acid (HB+). (c) To find the pH at the equivalence point, calculate the concentration of H$_{3}$O$^{+}$ ions using the equilibrium constant (Ka) of the conjugate acid and the given procedure in Step 3. (d) The better choice of indicator can be determined by comparing the pH at the equivalence point with the pH range of phenolphthalein (8.2 - 10.0) and methyl red (4.4 - 6.2).

Step-by-step solution

Determine the moles of HA at the equivalence point

At the equivalence point, the moles of base B equals the moles of acid HA. We can calculate the moles of base from its concentration and volume. Moles of base B = concentration × volume Moles of base B = 0.10 M × 0.030 L = 0.0030 mol So, there are 0.0030 moles of HA added at the equivalence point.

Find the predominant form of B at the equivalence point

As the weak base B accepts one proton from the strong acid HA, at the equivalence point, the predominant form of B will be its conjugate acid (HB+).

Calculate the pH at the equivalence point

At the equivalence point, all of the added acid (HA) has reacted with the base (B) to form the conjugate acid (HB+). Since the conjugate acid is present in solution, we need to determine the equilibrium constant for the hydrolysis reaction of the conjugate acid: HB+ + H2O <=> H3O+ + B Let the equilibrium constant (Ka) for this reaction be x. Since the moles of HB+ are 0.0030, and the total volume of the solution is 60.0 mL (30.0 mL base + 30.0 mL acid), the concentration of HB+ will be: \[C_{HB^{+}} = \frac{0.0030\: mol}{0.060\: L} = 0.050\; M\] To determine the concentration of H3O+ ions, we can use the equilibrium expression: \[x = \frac{[%\:H_{3}O^{+}][\:B]}{[%\:HB^{+}]}\] Since the moles of HB+ and B are equal, their concentrations can cancel out: \[[\:H_{3}O^{+}] = x \times[\:HB^{+}]\] Once we have the concentration of H3O+ ions, we can calculate the pH: \[pH = -\log([\:H_{3}O^{+}])\]

Choose the appropriate indicator

To choose the right indicator for the titration, we need to compare the pH at the equivalence point with the pH range of color change for the two indicators. Phenolphthalein has a pH range of 8.2 - 10.0, and Methyl Red's range is 4.4 - 6.2. If the pH at the equivalence point is closer to the range of phenolphthalein, it should be the better choice. If the pH is closer to the range of methyl red, that indicator would be more suitable. In summary: a) There are 0.0030 moles of HA added at the equivalence point. b) The predominant form of B at the equivalence point is HB+. c) The pH at the equivalence point can be calculated using the procedure described in Step 3. d) The appropriate indicator for the titration can be determined by comparing the pH at the equivalence point with the pH range of phenolphthalein and methyl red.

Key concepts

Equivalence Point

Understanding the equivalence point is critical for mastering titrations. During an acid-base titration, the equivalence point is the moment when the amount of added titrant (in this case, a strong acid) exactly neutralizes the amount of analyte (the weak base B) in the solution. It’s worth noting that at the equivalence point, the number of moles of the acid equals the number of moles of the base. For example, if you start with 30.0 mL of a 0.10 M solution of a weak base, at the equivalence point, you will have added 0.0030 moles of a strong acid (HA) to completely neutralize it. It is imperative to mention that the equivalence point is not always where the pH equals 7. This common misconception can lead students astray, particularly during titrations involving weak acids or bases. In the case of titrating a weak base with a strong acid, the equivalence point will typically result in a pH less than 7 due to the formation of a weakly acidic solution.

Choosing the correct indicator hinges on having a clear understanding of where the equivalence point lies on the pH scale; thus, learning how to calculate the equivalence point is essential for successful titration analysis.

Weak Base Titration

When titrating a weak base, it’s important to consider the properties of weak bases. They do not dissociate completely in water, which means not every molecule of the base turns into its ion form. Instead, a dynamic equilibrium is established between the base and its conjugate acid. Throughout a weak base titration with a strong acid, the weak base (B) will accept a proton from the strong acid (HA) and transform into its conjugate acid (HB+). In this context, at the equivalence point of the titration, the predominant form present in the solution is the conjugate acid of the base, rather than the base itself. This conversion significantly influences the pH of the solution at the equivalence point and underscores the importance of understanding both the nature of the compound being titrated and the reactivity with its titrant.

Comprehending this interplay is vital to predict the pH changes during the titration process and determine the correct end point of the titration.

pH Calculation

The pH calculation during a titration process involves determining the concentration of hydrogen ions \( H_3O^+ \) in the solution at various points throughout the titration. In the case of our example, where a weak base is titrated with a strong acid, the pH at the equivalence point is not neutral (pH 7), because the conjugate acid (HB+) formed is capable of donating a proton to water to form hydronium ions, resulting in an acidic solution. To calculate the pH at the equivalence point, you will first need the equilibrium constant (Ka) for the conjugate acid's hydrolysis reaction and apply it to calculate the concentration of H3O+ ions using the equilibrium expression. Once the concentration of hydronium ions is known, you can calculate the pH:
\[pH = -\log([H_3O^+])\]
It's crucial to remember to take into account the volume of the solution after the titrant is added, as the dilution effect can impact the concentration of the ions in the solution. Simplification of the calculation by canceling out equal concentrations on both sides of the equilibrium expression is a strategic approach to avoid unnecessary complexity in pH calculations.

Titration Indicators

Titration indicators are substances that show a noticeable color change at a particular pH range. This color change happens due to a structural change in the indicator molecule triggered by the pH alteration in the solution. The point of color change, known as the endpoint, should closely match the titration’s equivalence point for accurate results.

In the exercise example, phenolphthalein and methyl red are given as potential indicators. Phenolphthalein changes color in a basic pH range (approximately 8.2 to 10.0), making it unsuitable for a titration where a weak base is neutralized by a strong acid. On the other hand, methyl red transitions from red to yellow within a pH range of 4.4 to 6.2, which typically aligns better with the acidic conditions expected at the equivalence point in such a titration. Thus, for a weak base-strong acid titration like the one in the exercise, methyl red would likely be the more appropriate choice. The selection of an indicator is a pivotal decision in the titration process because using an indicator with a matching pH range ensures a clear and accurate determination of the endpoint.