Diprotic Buffers : Videos & Practice Problems

Diprotic buffer systems involve acids with two acidic hydrogens, leading to two distinct acid dissociation constants (Ka1 and Ka2). The Henderson-Hasselbalch equation adapts for these systems, allowing calculations based on the forms present: pH = pKa1 + log([intermediate]/[acid]) or pH = pKa2 + log([base]/[intermediate]). Understanding which form to use is crucial for accurate pH determination. This knowledge is essential for mastering acid-base reactions and buffer capacity in various chemical contexts.

Diprotic Buffers

In the study of buffer systems, we can extend our understanding from monoprotic buffers to diprotic buffers, which are characterized by having two acidic hydrogens. This distinction is crucial as it leads to the presence of two dissociation constants, denoted as pK_a1 and pK_a2, corresponding to the two acidic protons that can be released.

To refresh our understanding, a monoprotic buffer consists of a weak acid and its conjugate base, where the acid can donate one hydrogen ion (H⁺). The strength of this acid is measured by its acid dissociation constant, K_a; a higher K_a indicates a stronger acid that is more likely to release H⁺. For example, hypochlorous acid (HClO) serves as a monoprotic acid, and upon losing an H⁺, it forms its conjugate base, which is neutral due to the replacement of the hydrogen with a group 1 metal ion.

The Henderson-Hasselbalch equation, which is pivotal in calculating the pH of buffer solutions, is expressed as:

pH = pK_a + log([A^-]/[HA])

In this equation, [A^-] represents the concentration of the conjugate base, while [HA] is the concentration of the weak acid. For monoprotic systems, only one K_a value is utilized.

When dealing with diprotic buffer systems, the challenge arises in determining whether to use pK_a1 or pK_a2 in our calculations. This choice depends on the specific pH range we are targeting and the relative concentrations of the species involved. Understanding how to navigate these two dissociation constants is essential for accurately managing the pH in diprotic systems.

Diprotic Buffers

Diprotic buffers involve acids that can donate two protons (H⁺ ions), leading to the presence of two dissociation constants, K_a1 and K_a2. The generic diprotic acid can be represented as H₂A, where it is fully protonated with two acidic hydrogens. Upon removal of the first hydrogen, we obtain the intermediate form, HSO₃^-, associated with K_a1. The removal of the second hydrogen results in the base form, A^2-, linked to K_a2. This distinction is crucial for calculations involving the Henderson-Hasselbalch equation, which varies depending on the forms being analyzed.

When using the Henderson-Hasselbalch equation, if the acid form and the intermediate form are involved, the equation is expressed as:

pH = pK_a1 + log([Intermediate] / [Acid])

Conversely, if the intermediate form and the base form are considered, the equation becomes:

pH = pK_a2 + log([Base] / [Intermediate])

For example, with sulfurous acid (H₂SO₃), removing the first acidic hydrogen yields HSO₃^- (the intermediate form), and removing the second gives the sulfite ion (SO₃^2-, the base form). The pH can be calculated using the appropriate form of the Henderson-Hasselbalch equation, leading to a specific pH value based on the concentrations of the involved species.

In practical applications, when calculating moles from volume and molarity, the formula moles = liters × molarity is utilized. For instance, converting milliliters to liters and applying the molarity allows for the determination of moles of each component in the buffer system. This is essential for accurately applying the Henderson-Hasselbalch equation.

As we explore diprotic buffer systems, it is vital to identify the correct forms and corresponding pK values to ensure accurate pH calculations. This understanding will pave the way for further discussions on polyprotic acids, which can donate more than two protons and involve even more complex buffering scenarios.

Monoprotic & Diprotic Buffer Calculations 1

To determine the pH of a solution containing 2.5 M potassium dihydrogen phosphite and 2.75 M phosphorous acid (H₃PO₃), it is essential to understand the acid's properties. Although H₃PO₃ appears to be a triprotic acid due to its three hydrogen atoms, it is actually a diprotic acid because only two of these hydrogens are acidic. The structure of phosphorous acid allows for only two acidic protons to dissociate.

In this scenario, we are working with the fully protonated form of the acid and its intermediate form, which has lost one hydrogen and is represented by potassium dihydrogen phosphite. This situation requires the use of the first dissociation constant, K_a1, for calculations. The relationship between pH, pK_a1, and the concentrations of the acid and its intermediate form can be expressed using the Henderson-Hasselbalch equation:

pH = pK_a1 + log(_{[Intermediate Form]}/_{[Acid Form]})

Given that K_a1 is 3.0 × 10⁻², we first calculate pK_a1 as:

pK_a1 = -log(3.0 × 10⁻²) ≈ 1.52

Substituting the concentrations into the equation, we have:

pH = 1.52 + log(2.5/2.75)

Calculating the logarithm gives:

log(2.5/2.75) ≈ -0.05

Thus, the pH can be calculated as:

pH ≈ 1.52 - 0.05 = 1.47

Therefore, the pH of the solution is approximately 1.48. When solving similar problems, it is crucial to identify the forms of the acid and its conjugate base to determine which dissociation constant (K_a1 or K_a2) to use in the calculations.

Monoprotic & Diprotic Buffer Calculations 1

Sulfuric acid, represented as H₂SO₄, plays a significant role in the production of commercial fertilizers. When analyzing buffer solutions, the Henderson-Hasselbalch equation is essential for determining the pH of a solution based on the concentrations of the conjugate base and the weak acid. The equation is expressed as:

pH = pK_a + log([A^-]/[HA])

In this context, the question focuses on finding the concentration ratio of the conjugate base to the weak acid for a buffer with a pH of 1.15. Since sulfuric acid is a diprotic acid, it has two dissociation constants (K_a1 and K_a2), which correspond to the two stages of hydrogen ion removal. The first dissociation leads to the formation of the bisulfate ion (HSO₄^-), while the second dissociation results in the sulfate ion (SO₄^2-).

To determine which pK_a to use, we calculate the pK_a values from the dissociation constants. The first pK_a (pK_a1) is found to be 1.86, and the second pK_a (pK_a2) is 7.17. Given that the pH of 1.15 is less than pK_a1, we conclude that the predominant species in the buffer is the weak acid form (H₂SO₄).

Using the Henderson-Hasselbalch equation, we substitute the known values:

1.15 = 1.86 + log([HSO₄^-]/[H₂SO₄])

Rearranging the equation gives:

log([HSO₄^-]/[H₂SO₄]) = 1.15 - 1.86 = -0.71

To find the ratio of the conjugate base to the weak acid, we take the inverse log:

[HSO₄^-]/[H₂SO₄] = 10^-0.71 ≈ 0.195

This ratio indicates that for every 1 part of the weak acid (H₂SO₄), there are approximately 0.195 parts of the conjugate base (HSO₄^-). Thus, the buffer solution predominantly contains the weak acid form, confirming that the concentration of the weak acid is greater than that of the conjugate base.

In summary, understanding the relationship between pH, pK_a, and the concentrations of the species involved is crucial when working with buffers, especially in the context of polyprotic acids like sulfuric acid. This knowledge allows for accurate calculations of concentration ratios and the behavior of acids in solution.

Calculate the pH of a solution made by mixing 8.627 g of sodium butanoate in enough 0.452 M butanoic acid, HC₄H₇O₂, to make 250.0 mL of solution. K_a = 1.5 x 10^-5. 

• A. 4.82
• B. 4.98
• C. 5.85
• D. 4.66
• E. 4.06

Answer: (D)

Here’s what students ask on this topic:

What is a diprotic buffer system?

A diprotic buffer system involves an acid that has two acidic hydrogens, meaning it can donate two protons (H⁺). This results in two distinct acid dissociation constants, Ka₁ and Ka₂. The system can be described using the Henderson-Hasselbalch equation, which adapts to the different forms present: pH = pKa₁ + log([intermediate]/[acid]) or pH = pKa₂ + log([base]/[intermediate]). Understanding which form to use is crucial for accurate pH determination in various chemical contexts.

How do you calculate the pH of a diprotic buffer system?

To calculate the pH of a diprotic buffer system, you need to identify the forms present: the fully protonated acid (H₂A), the intermediate form (HA^-), and the fully deprotonated base (A^2-). Use the Henderson-Hasselbalch equation: for the acid and intermediate forms, pH = pKa₁ + log([intermediate]/[acid]); for the intermediate and base forms, pH = pKa₂ + log([base]/[intermediate]). Ensure you use the correct pKa value and concentrations for accurate pH determination.

What are the key differences between monoprotic and diprotic buffer systems?

The key difference between monoprotic and diprotic buffer systems is the number of acidic hydrogens. Monoprotic acids have one acidic hydrogen and one dissociation constant (Ka), while diprotic acids have two acidic hydrogens and two dissociation constants (Ka₁ and Ka₂). This results in different forms and equations for pH calculations. Monoprotic systems use pH = pKa + log([base]/[acid]), whereas diprotic systems use either pH = pKa₁ + log([intermediate]/[acid]) or pH = pKa₂ + log([base]/[intermediate]).

Why is it important to choose the correct pKa value in diprotic buffer calculations?

Choosing the correct pKa value in diprotic buffer calculations is crucial because it ensures accurate pH determination. Diprotic acids have two dissociation constants, Ka₁ and Ka₂, corresponding to the removal of the first and second acidic hydrogens, respectively. Using the wrong pKa value can lead to incorrect pH calculations, affecting the buffer's effectiveness. For the acid and intermediate forms, use pKa₁; for the intermediate and base forms, use pKa₂.

How does the Henderson-Hasselbalch equation adapt for diprotic buffer systems?

The Henderson-Hasselbalch equation adapts for diprotic buffer systems by incorporating the two dissociation constants (Ka₁ and Ka₂). For the acid (H₂A) and intermediate (HA^-) forms, the equation is pH = pKa₁ + log([intermediate]/[acid]). For the intermediate (HA^-) and base (A^2-) forms, the equation is pH = pKa₂ + log([base]/[intermediate]). This adaptation allows for accurate pH calculations based on the specific forms present in the buffer system.