Problem 40 - Chemistry The Central Science

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 \(0.10 \mathrm{M}\) 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 \(\mathrm{B}\) 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?

Step-by-Step Solution

Answer

(a) The moles of HX at the equivalence point is 0.003 moles. (b) The predominant form of B at the equivalence point is its protonated form, BH+. (c) The factor determining pH at the equivalence point is the extent of hydrolysis of the BH+ ions in the solution. (d) Methyl red is the better indicator for this titration, as its color change range (pH 4.4 - 6.3) is more suitable for detecting the acidic pH shift at the equivalence point.

Step 1: Moles of HX at equivalence point

At the equivalence point in a titration, the number of moles of the titrant (in this case, HX) is equal to the number of moles of the analyte (in this case, B). Since we have the volume and concentration of the weak base B, we can calculate the moles of B and, consequently, the moles of HX at the equivalence point: Moles of B = Volume of B × Concentration of B Moles of B = 30.0 mL × 0.10 M \(\) To convert the volume in mL to L, we need to divide by 1000: \( 30.0 \mathrm{~mL} = 30.0 \div 1000 = 0.03 \mathrm{~L} \) So, moles of B = 0.03 L × 0.10 M = 0.003 moles. Then, the moles of HX at the equivalence point is also 0.003 moles. #b) Predominant form of B at equivalence point#

Step 2: Predominant form of B

At the equivalence point, all of the weak base B has reacted with the strong acid HX. The weak base B has accepted one proton from HX, so the predominant form of B at the equivalence point is the protonated form, BH+. #c) Factor determining pH at equivalence point#

Step 3: Determining pH factor

The factor that determines the pH at the equivalence point is the extent of hydrolysis of the BH+ ions in the solution. At the equivalence point, BH+ ions will undergo hydrolysis and produce H3O+ ions, which will influence the pH of the solution. By calculating the concentration of H3O+ ions, we can determine the pH at the equivalence point. In the case of weak base - strong acid titration, the pH at the equivalence point is always less than 7. #d) Choice of indicator#

Step 4: Choosing the Indicator

Phenolphthalein has a color change range of approximately pH 8.2 - 10.0, while methyl red has a color change range of approximately pH 4.4 - 6.3. Since this is a weak base - strong acid titration, we expect the pH at the equivalence point to be less than 7. Therefore, methyl red would be the better indicator for this titration, as its color change range is more suitable to detect the acidic pH shift at the equivalence point.

Key Concepts

Equivalence Point

During a titration, the equivalence point is a pivotal moment. It occurs when the amount of titrant added is exactly enough to react completely with the analyte in the solution. In simpler terms, it marks the stage where all the weak base, such as

• 30.0 mL of weak base B at 0.10 M concentration,

has exactly reacted with the strong acid titrant, like HX at the same concentration.
This reaction demonstrates that the moles of the acid HX are equal to the moles of the base B at the equivalence point. Calculations show us that we have 0.003 moles of HX, which exactly equals the moles of B.
At the equivalence point in a reaction between a weak base and strong acid, the original characteristics of both solutions have changed. Leading to a solution that is typically neutralized in terms of the reacting species, but not necessarily in pH.

Weak Base

A weak base only partially dissociates in the solution. Common examples can include things like ammonia or, in this case, base B. During the titration, the weak base reacts with a strong acid, which in our case is HX.
When we reach the equivalence point, fascinatingly, the weak base has transformed. Instead of B, we find BH+. This is due to B accepting a proton from the strong acid HX.
This protonated form, BH+, demonstrates the conclusion of a complete reaction at the equivalence point. The ion BH+ is the predominant form. Because it results directly from the reaction of B with the acid, it is a critical player in determining the final properties of the solution.

pH Indicator Selection

Choosing the right pH indicator is essential in a titration. Especially considering we are dealing with a weak base-strong acid combination.
The pH indicator should have a color change range that matches where we expect the pH of the solution to be at the equivalence point. Since we anticipate the solution at equivalence to be acidic with a pH less than 7, this guides our choice.
Phenolphthalein changes color in the pH range of 8.2 to 10.0, which makes it unsuitable for detecting equivalence in this titration.

• Conversely, methyl red changes color between pH 4.4 and 6.3,

making it ideal for this context. It covers the acidic range, ensuring we detect the equivalence point accurately.