Weak Titrate-Strong Titrant Curves: Videos & Practice Problems

When titrating a weak acid or base with a strong titrant, a buffer region forms where the pH changes gradually. This region indicates the presence of a buffer system that resists changes in pH. The half-equivalence point occurs within this buffer region, where the concentration of the weak acid equals its conjugate base, creating an ideal buffer situation. At the equivalence point, the pH change is steepest; for a weak acid with a strong base, the pH will be greater than 7, while for a weak base with a strong acid, it will be less than 7. Beyond the equivalence point, excess strong titrant is present, leading to a further gradual change in pH until it plateaus. The strong component in the reaction ultimately determines the pH at the equivalence point, with strong acids driving it below 7 and strong bases above 7.

Weak Titrate-Strong Titrant Curve

In a titration involving a weak titrate and a strong titrant, a significant feature is the presence of a buffer region. This buffer region is characterized by a pH that is relatively resistant to change, which occurs after the initial addition of the titrant. Initially, the pH of the solution rises quickly as the strong titrant is added to the weak titrate. However, as more titrant is introduced, the pH increase begins to level off, indicating the formation of a buffer system.

The buffer is established when the concentrations of the weak acid (the titrate) and its conjugate base are approximately equal. This point is known as the half equivalence point, which occurs at the midpoint of the buffer region. At this stage, the solution contains equal amounts of the weak acid and its conjugate base, creating an ideal buffer. Mathematically, this can be represented by the Henderson-Hasselbalch equation:

$$ pH = pK_a + \log\left(\frac{[A^-]}{[HA]}\right) $$

Here, \( pK_a \) is the negative logarithm of the acid dissociation constant, and \([A^-]\) and \([HA]\) represent the concentrations of the conjugate base and the weak acid, respectively.

As titration continues beyond the half equivalence point, the pH begins to rise sharply again, indicating that the buffer capacity has been exceeded. The equivalence point, which is the point at which the amount of titrant added is stoichiometrically equivalent to the amount of titrate present, is marked by the steepest incline on the titration curve. For a typical titration curve involving a weak acid and a strong base, the equivalence point is reached after approximately 50 mL of titrant has been added, while the half equivalence point occurs at around 25 mL.

After surpassing the equivalence point, the solution contains an excess of the strong titrant, leading to a rapid increase in pH. Understanding these key features—buffer region, half equivalence point, and equivalence point—is essential for interpreting titration curves involving weak titrates and strong titrants.

Acid-Base Titration Formulas Example

In the titration of 55 mL of 0.120 M hydrocyanic acid (HCN) with 0.160 M lithium hydroxide (LiOH), the process involves determining the volume of the titrant needed to reach the half equivalence point. The titrant in this case is lithium hydroxide, which reacts with the hydrocyanic acid.

To find the volume of the titrant required to reach the equivalence point, we can use the formula:

m_acid × V_acid = m_base × V_base

Here, m_acid is the molarity of the acid, V_acid is the volume of the acid, m_base is the molarity of the base, and V_base is the volume of the base. Plugging in the values:

0.120 M × 55 mL = 0.160 M × V_base

To find V_base, rearranging the equation gives:

V_base = (0.120 M × 55 mL) / 0.160 M

Calculating this yields:

V_base = 41.25 mL

Next, to find the volume needed to reach the half equivalence point, we recognize that this point occurs when the amount of weak acid and its conjugate base are equal. At the half equivalence point, the pH equals the pK_a of the weak acid, simplifying the Henderson-Hasselbalch equation to:

pH = pK_a

Since the half equivalence point is defined as half the volume required to reach the equivalence point, we simply divide the volume of the base at the equivalence point by 2:

V_half = 41.25 mL / 2 = 20.625 mL

Thus, the volume of lithium hydroxide needed to reach the half equivalence point in this titration is 20.625 mL.

Consider the titration of 30.0 mL of 0.100 M HC₂H₃O₂ with 0.100 M NaNH₂. Which volume of NaNH₂ would take place within the buffer region? 
a) 30.0 mL                    b) 50.0 mL                    c) 10.0 mL                     d) 100.0 mL                   e) 1.5 L

• A. 30.0 mL
• B. 50.0 mL
• C. 10.0 mL
• D. 100.0 mL
• E. 1.5 L

Answer: (C)

Weak Acid-Strong Base Titration Curve

Titration curves are essential for understanding the behavior of acids and bases during a titration process. In the case of a weak acid being titrated with a strong base, the initial pH is less than 7, indicating the presence of the weak acid. As a strong base is gradually added, the pH begins to rise slowly due to the formation of a buffer region. This buffer region is characterized by a gradual increase in pH, as the weak acid partially neutralizes the strong base, allowing for a more stable pH change.

As the titration progresses, the pH will experience a significant jump at the equivalence point, where all the weak acid has been neutralized. In this scenario, the strong base dominates, resulting in a pH greater than 7 at the equivalence point, typically around 8. This is a crucial aspect to remember: in a weak acid-strong base titration, the equivalence point pH is elevated due to the presence of excess strong base.

After reaching the equivalence point, the addition of more strong base leads to a continued increase in pH, although this increase will eventually plateau. The reason for this plateau is that while the pH can rise with the addition of more base, it cannot increase indefinitely. The key takeaway is that in a weak acid-strong base titration, the strong base's influence results in a final pH that is above 7, highlighting the dominance of the strong species in the reaction.

Weak Base-Strong Acid Titration Curve

In the context of acid-base titration, when a weak base is titrated with a strong acid, the initial pH is above 7, indicating a basic solution. As strong acid is added, the pH decreases gradually. Initially, there is a rapid drop in pH due to the strong acid neutralizing the weak base. However, as the titration progresses, a buffer region is established, which resists further significant changes in pH. This buffer effect causes the rate of pH decrease to slow down, even though the pH continues to drop.

At the equivalence point of this titration, the pH is influenced by the nature of the species involved. Since a strong acid is present, the pH at the equivalence point will be less than 7, typically around pH 5. This is because the strong acid dominates the solution, leading to an acidic environment. After reaching the equivalence point, if more strong acid is added, the pH will continue to decrease and eventually plateau, reflecting the excess strong acid in the solution.

In summary, the key takeaway is that in titrations involving a weak base and a strong acid, the pH at the equivalence point will always be less than 7 due to the strong acid's influence, contrasting with titrations involving a strong base and a weak acid, where the pH at the equivalence point is above 7.

Weak Titrate-Strong Titrant Curve Example

In the context of titration, particularly at the half equivalence point, the concentration of a weak monoprotic acid is equal to the concentration of its conjugate base. For a weak acid, this relationship allows us to determine the acid dissociation constant, \( K_a \), using the pH of the solution. In this scenario, we are titrating 100 mL of a 0.200 M weak monoprotic acid with 50 mL of 0.200 M sodium hydroxide, reaching the half equivalence point where the pH is measured at 4.18.

At the half equivalence point, the pH is equal to the \( pK_a \) of the weak acid, which can be expressed mathematically as:

\( pK_a = -\log(K_a) \)

To isolate \( K_a \), we can rearrange the equation. By taking the negative of the pH, we have:

\( -pH = \log(K_a) \)

Next, we apply the inverse logarithm to both sides, leading to:

\( K_a = 10^{-pH} \)

Substituting the given pH value of 4.18 into the equation, we calculate:

\( K_a = 10^{-4.18} \)

This results in:

\( K_a \approx 6.61 \times 10^{-5} \)

Thus, the acid dissociation constant \( K_a \) for the weak monoprotic acid in this titration scenario is approximately \( 6.61 \times 10^{-5} \).

In titration of NH₃ and HCl, what is the predominant species beyond the equivalence point?
a) NH₃                                      b) HCl                                       c) CH₃NH­₂                                d) Cl^–

• A. NH₃
• B. HCl
• C. CH₃NH₂
• D. Cl^–

Answer: (B)

Here’s what students ask on this topic:

Which point on the titration curve is the point where the pH equals the pKa for BH⁺?

The point on a titration curve where the pH equals the pKa for BH⁺ (a conjugate acid of a weak base B) is known as the half-equivalence point or the midpoint of the buffering region. This is the stage in the titration where exactly half of the BH⁺ has been deprotonated to form B. At this point, the concentrations of the weak base (B) and its conjugate acid (BH⁺) are equal. Since the Henderson-Hasselbalch equation states that

pH = pKa + log(^[B]/_[BH⁺_])

when [B] = [BH⁺], the log term becomes log(1), which is 0. Therefore, at the half-equivalence point, pH = pKa. This is a key concept in understanding buffer systems and acid-base titrations.

What species is/are present in the solution at point 2, given the following titration curve for a weak acid/strong base titration?

At point 2 of a titration curve for a weak acid with a strong base, you are likely observing the part of the curve where the weak acid has started to react with the strong base but has not yet reached the equivalence point. At this stage, the species present in the solution are primarily the unreacted weak acid (HA) and its conjugate base (A^-), which is formed as the acid donates protons (H⁺) to the hydroxide ions (OH^-) from the strong base.

The chemical reaction occurring is:

HA + OH^- → A^- + H₂O

This means that in the solution, you have a mixture of the original weak acid and the conjugate base that it forms upon reacting with the base. This combination of HA and A^- can establish a buffer system, which resists changes in pH. The exact ratio of HA to A^- depends on how much base has been added at this point and can be calculated using the Henderson-Hasselbalch equation if the pKa of the acid and the pH of the solution are known.

A weak unknown monoprotic acid is titrated with a strong base. The titration curve is shown below. What is the Ka for the unknown acid?

To determine the Ka (acid dissociation constant) for a weak monoprotic acid from a titration curve with a strong base, you need to identify the half-equivalence point on the curve. At the half-equivalence point, the amount of acid is equal to the amount of its conjugate base, and the pH at this point is equal to the pKa of the acid.

1. Locate the half-equivalence point on the titration curve. This is the point where exactly half of the acid has been neutralized by the base. It is also the point where the curve begins to rise the most steeply.
2. Read the pH value at the half-equivalence point directly from the curve.
3. Convert the pKa to Ka using the formula 10^-pKa.

For example, if the pH at the half-equivalence point is 4.75, then the pKa is 4.75, and the Ka is 10