Chapter 3, Problem 1E

The accompanying graph shows the titration curves for two monoprotic acids.
a. Which curve is that of a strong acid?
b. What is the approximate pH at the equivalence point of each titration?
c. 40.0 mL of each acid was titrated with a 0.100 M base. Which acid is more concentrated?
d. Estimate the pK_a of the weak acid.

Interpretation Introduction

To identify: The curve that corresponds to a strong acid.

Answer to Problem 1E

Solution: The curve that corresponds to a strong acid is Curve B.

Explanation of Solution

The titration curve for the two acids, titrated against $\text{NaOH}$ is shown in Figure $1$ .

Figure $1$

Here,

• Curve A represents acid having initial $\text{pH}3$ .
• Curve B represents acid having initial $\text{pH}1$ .

The acid having $\text{pH}1$ is a stronger acid since it has lower $\text{pH}$ than acid having $\text{pH}3$ .

Conclusion

The curve that corresponds to a strong acid is Curve B, due to relatively lower $\text{pH}$ .

Interpretation Introduction

To determine: The $\text{pH}$ at the equivalence point of each titration curve.

Answer to Problem 1E

Solution: The $\text{pH}$ at the equivalence point of titration Curve A is $8$ and that of titration Curve B is $7$ .

Explanation of Solution

The titration curve for the two acids, titrated against $\text{NaOH}$ is shown in Figure $1$ .

Figure $1$

Here,

• Curve A represents acid having initial $\text{pH}3$ .
• Curve B represents acid having initial $\text{pH}1$ .

The $\text{pH}$ at the equivalence point is the midpoint of the vertical part of the curve.

The value at the centre of the vertical part is determined by dividing the sum of the $\text{pH}$ corresponding to the top and the bottom of the vertical part by $2$ .

The $\text{pH}$ corresponding to the top of the vertical part of Curve A is approximately $10$ .

The $\text{pH}$ corresponding to the bottom of the vertical part of Curve A is approximately $6$ .

The $\text{pH}$ corresponding to the top of the vertical part of Curve B is approximately $10$ .

The $\text{pH}$ corresponding to the bottom of the vertical part of Curve B is approximately $4$ .

Therefore, the $\text{pH}$ corresponding to the equivalence point of Curve A is calculated as,

$\begin{array}{c}\text{pH}\text{at}\text{equivalence}\text{point}=\frac{10+6}{2}\\ =\frac{16}{2}\\ =8\end{array}$

The $\text{pH}$ corresponding to the equivalence point of Curve B is calculated as,

$\begin{array}{c}\text{pH}\text{at}\text{equivalence}\text{point}=\frac{10+4}{2}\\ =\frac{14}{2}\\ =7\end{array}$

Therefore, the $\text{pH}$ at the equivalence point of Curve A and Curve B is $8$ and $7$ respectively.

Conclusion

Curve A has a $\text{pH}$

$8$ at the equivalence point and Curve B has a $\text{pH}$

$7$ at the equivalence point.

Interpretation Introduction

To identify: The curve that corresponds to the more concentrated acid solution.

Answer to Problem 1E

Solution: The Curve B corresponds to the more concentrated acid solution.

Explanation of Solution

Given Equal volume of two acids is titrated using $40\text{mL}$ of $0.10\text{M}\text{NaOH}$ .

The two acids are monoprotic.

The titration curve for the two acids, titrated against $0.10\text{M}\text{NaOH}$ is shown in Figure $1$ .

Figure $1$

Here,

• Curve A represents acid having initial $\text{pH}3$ .
• Curve B represents acid having initial $\text{pH}1$ .
• The equivalence volume is the volume of the base required to obtain the equivalence point. This can be determined by finding the value of the volume on the $x-\text{axis}$ corresponding to the vertical part of the curves.

From Figure $1$ , the equivalence volume for Curve A is $30\text{mL}$ and that for Curve B is $40\text{mL}$ .

The number of moles of $\text{NaOH}$ corresponding to the equivalence volume for Curve A is calculated by the formula,

$\text{Number}\text{of}\text{moles}=\text{Molar}\text{concentration}\times \text{Volume}\text{of}\text{the}\text{solution}\text{in}\text{litres}$

Substitute the values of molar concentration and volume of the solution of $\text{NaOH}$ in the above formula.

$\begin{array}{c}\text{Number}\text{of}\text{moles}=\text{0}\text{.1}\text{M}\times \frac{30}{1000}\text{L}\\ =\text{3}\times {\text{10}}^{-3}\text{mol}\end{array}$

The number of moles of $\text{NaOH}$ corresponding to the equivalence volume for Curve B is calculated by the formula,

$\text{Number}\text{of}\text{moles}=\text{Molar}\text{concentration}\times \text{Volume}\text{of}\text{the}\text{solution}\text{in}\text{litres}$

Substitute the values of molar concentration and volume of the solution of $\text{NaOH}$ in the above formula.

$\begin{array}{c}\text{Number}\text{of}\text{moles}=\text{0}\text{.1}\text{M}\times \frac{40}{1000}\text{L}\\ =\text{4}\times {\text{10}}^{-3}\text{mol}\end{array}$

Since the acids are monoprotic, one mole of $\text{NaOH}$ reacts with one mole of the acid.

Higher amount of $\text{NaOH}$ is required to obtain the equivalence point for acid corresponding to Curve B, therefore the concentration of the acid corresponding to Curve B is more.

Conclusion

Curve B represents the acid that is relatively more concentrated than acid corresponding to Curve A.

Interpretation Introduction

To determine: The value of $\text{p}{K}_{\text{a}}$ of the weak acid.

Answer to Problem 1E

Solution: The value of $\text{p}{K}_{\text{a}}$ of the weak acid is $4.5$ .

Explanation of Solution

The titration curve for the two acids, titrated against $0.10\text{M}\text{NaOH}$ is shown in Figure $1$ .

Figure $1$

The acid corresponding to Curve A is weaker, since the initial $\text{pH}$ is lower than the acid corresponding to Curve B.

For a weak acid titrated against a strong base, the value of $\text{p}{K}_{\text{a}}$ is equal to $\text{pH}$ at the volume half of the equivalence volume.

The equivalence volume of the weak acid is $30\text{mL}$ .

The $\text{pH}$ at $15\text{mL}$

$\left(30\text{mL}/2\right)$ is approximately $4.5$ . Therefore, the value of $\text{p}{K}_{\text{a}}$ is $4.5$ .

Conclusion

The value of $\text{p}{K}_{\text{a}}$ for the acid corresponding to the curve that represents a weak acid is $4.5$ .