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

Short Answer

Expert verified
(a) At the equivalence point, 3.00 mmol of HX will have been added. (b) The predominant form of B at the equivalence point is its conjugate acid BH鈦. (c) The presence of conjugate acid BH鈦, which partially dissociates into B and H鈦, determines the pH at the equivalence point. (d) Methyl red is the better choice for this titration, as it will accurately signal the change in pH close to the acidic equivalence point.

Step by step solution

01

(a) Moles of HX at equivalence point

At the equivalence point, all of the weak base B has reacted with the strong acid HX. This means the moles of B and HX are equal at the equivalence point. Since we know the initial volume and concentration of the base B solution, we can calculate the number of moles of B: Moles of B = Volume 脳 Concentration Moles of B = \(30.0 \times 0.10\) Moles of B = 3.00 mmol At the equivalence point, the moles of HX added must equal the moles of B. Therefore, 3.00 mmol of HX will have been added at the equivalence point.
02

(b) Predominant form of B at the equivalence point

At the equivalence point, all of the weak base has reacted with the strong acid. As a weak base, B accepts a proton when reacting with a strong acid to form its conjugate acid BH鈦. Thus, at the equivalence point, the predominant form of B is its conjugate acid BH鈦.
03

(c) Factor determining pH at equivalence point

Since the pH is determined by the concentration of hydrogen ions (H鈦) in the solution, the factor that determines the pH at the equivalence point is the presence of its conjugate acid BH鈦, which was formed when all the weak base B has reacted with the strong acid HX. The conjugate acid BH鈦 will determine the pH of the solution by partially dissociating into B and H鈦, thus affecting the concentration of H鈦 ions in the solution.
04

(d) Suitable indicator for this titration

To choose a suitable indicator for a titration, we must consider the pH at the equivalence point and compare it with the pH range of different indicators. For a titration between a weak base and a strong acid, the pH at the equivalence point is expected to be below 7 since the resulting solution will be acidic due to the formation of conjugate acid BH鈦 in the solution. Therefore, among the two given indicators: 1. Phenolphthalein: pH range for color change is 8.2鈥10.0 (colorless to pink) 2. Methyl red: pH range for color change is 4.4鈥6.2 (red to yellow) In this case, since the pH at the equivalence point is expected to be below 7, methyl red is likely to be the better choice for this titration, as it will accurately signal the change in pH close to the acidic equivalence point.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Equivalence Point
Understanding the equivalence point is crucial when performing a titration, a method used in chemistry to determine the concentration of a solution. The equivalence point, often the goal of a titration, is the moment in the reaction when the amount of titrant added reacts exactly with the amount of the substance being titrated. In the context of a titration between a weak base and a strong acid, like the titration of base B with acid HX in our example, the equivalence point is reached when the moles of HX equal the moles of B, indicating that all the weak base has been neutralized.

At this point, there is no excess of the base or the acid present. For the titration of a weak base with a strong acid, like our scenario, this is also the point when the pH of the solution will be less than 7 due to the formation of the weak conjugate acid, which slightly dissociates, contributing hydrogen ions to the solution.
Weak Base Titration
In a weak base titration with a strong acid, we should note that the pH will vary significantly throughout the process. A weak base, such as our example base B, does not completely ionize in solution. This distinctive behavior impacts the titration curve, which tracks the pH of the solution as the strong acid is added.

During titration, initially, the pH changes gradually. However, as we approach the equivalence point, the pH decreases more rapidly due to the formation of the conjugate acid, as seen in our exercise with the formation of BH鈦 from base B.
pH Indicator Selection
Selecting the right pH indicator for a titration is fundamental for accurate results. The indicator must change color at a pH that is very close to the equivalence point so that the end of the titration can be accurately determined. For a weak base titration with a strong acid, where the equivalence point pH is below 7, an indicator with a color change in the acidic range is needed.

For our example, methyl red, which changes color between pH 4.4 and 6.2 is more suitable than phenolphthalein, which changes color between pH 8.2 and 10.0. The reason being, at the acidic equivalence point, phenolphthalein would not have a visible color change, whereas methyl red would shift from red to yellow, indicating the endpoint effectively.
Conjugate Acid
In our exercise example, the base B turns into its conjugate acid, BH鈦, upon reaction with the strong acid HX. A conjugate acid is the species formed when a base gains a proton. The strength of this conjugate acid is a key factor in determining the pH of the solution at the equivalence point.

In the weak base titration, the conjugate acid BH鈦 only partially dissociates in water; this partial dissociation is why the pH at the equivalence point does not fall to the same values as it would if a strong acid was being titrated. Understanding the nature of the conjugate acid helps us predict and interpret the titration curve and the pH changes that occur during the titration process.

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Most popular questions from this chapter

The acid-base indicator bromcresol green is a weak acid. The yellow acid and blue base forms of the indicator are present in equal concentrations in a solution when the \(\mathrm{pH}\) is \(4.68 .\) What is the \(\mathrm{pK}_{a}\) for bromcresol green?

A sample of \(0.2140 \mathrm{~g}\) of an unlenown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.0950 \mathrm{M} \mathrm{NaOH}\). The acid required \(27.4 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molar mass of the acid? (b) After \(15.0 \mathrm{~mL}\) of base had been added in the titration, the \(\mathrm{pH}\) was found to be \(6.50 .\) What is the \(K_{a}\) for the unknown acid?

Tooth enamel is composed of hydroxyapatite, whose simplest formula is \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{OH}\), and whose corresponding \(K_{s p}=6.8 \times 10^{-27}\). As discussed in the "Chemistry and Life" box in Section \(17.5\), fluoride in fluorinated water or in toothpaste reacts with hydroxyapatite to form fluoroapatite, \(\mathrm{Ca}_{5}\left(\mathrm{PO}_{4}\right)_{3} \mathrm{~F}\), whose \(K_{s p}=1.0 \times 10^{-60}\) (a) Write the expression for the solubility-constant for hydroxyapatite and for fluoroapatite. (b) Calculate the molar solubility of each of these compounds.

A 20.0-mL sample of \(0.200 \mathrm{M}\) HBr solution is titrated with \(0.200 \mathrm{M} \mathrm{NaOH}\) solution. Calculate the \(\mathrm{pH}\) of the solution after the following volumes of base have been added: (a) \(15.0 \mathrm{~mL}\), (b) \(19.9 \mathrm{~mL}\), (c) \(20.0 \mathrm{~mL}\), (d) \(20.1 \mathrm{~mL}\), (e) \(35.0 \mathrm{~mL}\).

A buffer is prepared by adding \(20.0 \mathrm{~g}\) of acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) and \(20.0 \mathrm{~g}\) of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to enough water to form \(2.00 \mathrm{~L}\) of solution. (a) Determine the \(\mathrm{pH}\) of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of sodium hydroxide solution are added to the buffer.

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