Question

Aspartic acid acts as a triprotic acid with successive dissociation constants of \(8.0 \times 10^{-3}, 1.4 \times 10^{-4}\), and \(1.5 \times 10^{-10}\). Depending upon \(\mathrm{pH}\), aspartic acid can exist in four different forms in water solution. Draw these forms and calculate the pH range over which each form is the principal species.

Short answer

Answer: The four forms of aspartic acid and their respective pH ranges are: 1. \(\mathrm{H_3A}\): pH < 2.10 2. \(\mathrm{H_2A^{-}}\): 2.10 < pH < 3.85 3. \(\mathrm{HA^{2-}}\): 3.85 < pH < 9.82 4. \(\mathrm{A^{3-}}\): pH > 9.82

Step-by-step solution

Identify the dissociation processes

We need to identify each step in the dissociation process. Aspartic acid is a triprotic acid, so it can lose up to three protons. The dissociation steps are: 1. \(\mathrm{H_3A}\longrightarrow\mathrm{H^+}+\mathrm{H_2A^-}\) 2. \(\mathrm{H_2A^-}\longrightarrow\mathrm{H^+}+\mathrm{HA^{2-}}\) 3. \(\mathrm{HA^{2-}}\longrightarrow\mathrm{H^+}+\mathrm{A^{3-}}\)

Draw each form of aspartic acid

We will draw the four forms of aspartic acid according to the dissociation processes: 1. \(\mathrm{H_3A}\): Aspartic acid with all three protons attached. 2. \(\mathrm{H_2A^-}\): Aspartic acid after losing one proton. 3. \(\mathrm{HA^{2-}}\): Aspartic acid after losing two protons. 4. \(\mathrm{A^{3-}}\): Aspartic acid after losing all three protons.

Calculate the pH range for each form

We will now calculate the pH range for each form using their dissociation constants: 1. pH range for \(\mathrm{H_3A}\): To find the pH range for \(\mathrm{H_3A}\), consider the equilibrium between it and the first dissociation step \(\mathrm{H_2A^-}\). We find the pKa for this step using the formula: \(pK_{a1}=-\log K_{a1}=-\log(8.0\times10^{-3}) = 2.10\) The pH range of the first form can be approximated as pH < pK₁ or pH < 2.10. 2. pH range for \(\mathrm{H_2A^-}\): The pH range for this form is determined by considering the equilibria between it and both \(\mathrm{H_3A}\) and \(\mathrm{HA^{2-}}\). The pKa for the second dissociation step is: \(pK_{a2}=-\log K_{a2}=-\log(1.4\times10^{-4 })= 3.85\) Thus, the pH range for the second form can be approximated as: pK₁ < pH < pK₂ or 2.10 < pH < 3.85. 3. pH range for \(\mathrm{HA^{2-}}\): The pH range for this form is determined by considering the equilibria between it and both \(\mathrm{H_2A^-}\) and \(\mathrm{A^{3-}}\). The pKa for the third dissociation step is: \(pK_{a3}=-\log K_{a3}=-\log(1.5\times10^{-10})= 9.82\) Thus, the pH range for the third form can be approximated as: pK₂ < pH < pK₃ or 3.85 < pH < 9.82. 4. pH range for \(\mathrm{A^{3-}}\): To find the pH range for \(\mathrm{A^{3-}}\), consider the equilibrium between it and the third dissociation step \(\mathrm{HA^{2-}}\). The pH range of the fourth form can be approximated as pH > pK₃ or pH > 9.82. #Conclusion# The four forms of aspartic acid can be found depending on the pH range. Form 1. \(\mathrm{H_3A}\): pH < 2.10 2. \(\mathrm{H_2A^-}\): 2.10 < pH < 3.85 3. \(\mathrm{HA^{2-}}\): 3.85 < pH < 9.82 4. \(\mathrm{A^{3-}}\): pH > 9.82

Key concepts

Dissociation Constants

In acid-base chemistry, dissociation constants are crucial for understanding how acids dissociate in a solution. For triprotic acids like aspartic acid, there are three dissociation steps, each represented by a dissociation constant, denoted as \( K_{a1} \), \( K_{a2} \), and \( K_{a3} \). These constants indicate the strength of an acid; a smaller value means a weaker acid.

For aspartic acid, the constants are \( 8.0 \times 10^{-3} \), \( 1.4 \times 10^{-4} \), and \( 1.5 \times 10^{-10} \) respectively. These values reflect the stepwise loss of protons and help in calculating the pH range where each form of the acid predominates. Understanding these dissociation steps is fundamental to predicting and calculating the behavior of triprotic acids in solution.

pH Range Calculations

Calculating pH ranges is vital in predicting the dominant species of a triprotic acid in solution. Each dissociation step provides a specific \( pK_a \), which helps define the pH range where each form of aspartic acid dominates. The equation \( pK_a = -\log K_a \) allows for these calculations.

For aspartic acid, the forms are as follows:

• The initial form \( \mathrm{H_3A} \) predominates at pH < 2.10.
• \( \mathrm{H_2A^-} \) is the principal species between pH 2.10 and 3.85.
• \( \mathrm{HA^{2-}} \) dominates from pH 3.85 to 9.82.
• Beyond pH 9.82, \( \mathrm{A^{3-}} \) is the primary form.

By using \( pK_a \) values, we can easily determine how a substance behaves in varying pH levels, which is crucial for practical applications like enzyme activity in biochemistry.

Chemical Equilibria

Chemical equilibria explain the balance between the different forms of an acid in solution. For a triprotic acid like aspartic acid, each dissociation event can be seen as a dynamic equilibrium between two forms of the acid.

Equilibria are essential because they describe how concentrations of reactants and products remain constant over time. For instance, the equilibrium between \( \mathrm{H_3A} \) and \( \mathrm{H_2A^-} \) is established at a certain pH, and it is dictated by the first dissociation constant \( K_{a1} \). Understanding these equilibrium states is fundamental in predicting how a compound like aspartic acid will behave under varying conditions in solution, influencing factors like buffer capacity.

Acid-Base Chemistry

Acid-base chemistry revolves around the behavior of acids and bases, particularly regarding proton transfer. In this domain, triprotic acids like aspartic acid are interesting because they can donate three protons, leading to multiple forms in solution. Each form represents a different protonation state, affecting the compound's properties such as solubility and reactivity.

Understanding acid-base interactions helps in grasping how pH and \( pK_a \) values dictate the species present in a solution. This understanding is applied in fields like biochemistry, environmental science, and medicine to manipulate reactions, stabilize compounds, or create effective buffers. Grasping the fundamentals of acid-base reactions and equilibrium is key to mastering this branch of chemistry.