Citric acid, which is present in citrus fruits, is a triprotic acid (Table 16.3). (a) Calculate the pH of a 0.040 M solution of citric acid. (b) Did you have to make any approximations or assumptions in completing your calculations? (c) Is the concentration of citrate ion 1C6H5O7 3-2 equal to, less than, or greater than the H+ ion concentration?

Verified step by step guidance

1. insert step 1: Identify the chemical nature of citric acid as a triprotic acid, which means it can donate three protons (H+). The dissociation can be represented as: C6H8O7 ⇌ H+ + C6H7O7- ⇌ 2H+ + C6H6O7^2- ⇌ 3H+ + C6H5O7^3-.
2. insert step 2: Write the expression for the first dissociation constant (Ka1) of citric acid, which is the most significant in determining the pH of the solution: Ka1 = [H+][C6H7O7-]/[C6H8O7].
3. insert step 3: Assume that the initial concentration of citric acid is 0.040 M and that the concentration of H+ ions produced is x. Set up the equilibrium expression using Ka1 and solve for x, which represents the [H+] concentration.
4. insert step 4: Calculate the pH of the solution using the formula pH = -log[H+].
5. insert step 5: Discuss any assumptions made, such as neglecting the second and third dissociation steps due to their much smaller Ka values, and compare the concentration of citrate ion (C6H5O7^3-) to the H+ ion concentration, noting that it is less than the H+ concentration due to the stepwise dissociation process.

Key Concepts

Triprotic Acids

Triprotic acids, like citric acid, can donate three protons (H+) per molecule in solution. This characteristic affects their dissociation constants (Ka1, Ka2, Ka3), which determine the extent of ionization at different pH levels. Understanding the stepwise dissociation is crucial for calculating pH and concentrations of ions in solution.

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, calculated using the formula pH = -log[H+]. For weak acids, such as citric acid, the pH can be determined using the acid dissociation constants and the initial concentration of the acid. This often involves approximations, especially when the acid is not fully dissociated.

Equilibrium Concentrations

In a solution of a weak acid, the concentrations of the acid, its conjugate base, and hydrogen ions reach an equilibrium. For citric acid, the concentration of the citrate ion (C6H5O7^3-) will depend on the degree of dissociation and the pH. Understanding the relationship between these concentrations is essential for answering questions about their relative amounts.