Question

Calculate the pH of a 0.03 M NaO2CCO2H solution. pK1 = 1.250 and pK2 = 4.266.

THE ANSWER IS NOT 2.89 IT IS 2.76

Please show your work. Thanks!

Answer 1

Answer 2

To calculate the pH of a solution, we need to determine the concentration of H+ ions in the solution. In this case, we have a weak acid, NaO2CCO2H (also known as acetic acid), with known pKa values. Acetic acid has two ionizable hydrogen atoms.

The dissociation reactions for acetic acid are as follows:

1. CH3COOH ⇌ CH3COO- + H+

2. CH3COO- ⇌ CH3COO- + H+

Given that the concentration of acetic acid is 0.03 M, we can assume that the initial concentration of CH3COOH is equal to the given concentration. Since acetic acid is a weak acid, we can use the Henderson-Hasselbalch equation to calculate the pH:

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

For the first dissociation:

pH1 = pK1 + log([CH3COO-]/[CH3COOH])

For the second dissociation:

pH2 = pK2 + log([CH3COO-]/[CH3COO-])

To calculate the final pH, we need to consider the concentrations of both dissociated and undissociated forms of the acid.

1. Calculate the concentration of CH3COO-: [CH3COO-] = [H+] (since one molecule of acid dissociates to one H+ ion and one CH3COO- ion)

2. Calculate the concentration of CH3COOH: [CH3COOH] = initial concentration - [CH3COO-]

3. Calculate the pH using the Henderson-Hasselbalch equation for the first dissociation: pH1 = pK1 + log([CH3COO-]/[CH3COOH])

4. Calculate the pH using the Henderson-Hasselbalch equation for the second dissociation: pH2 = pK2 + log([CH3COO-]/[CH3COO-])

5. Take the average of pH1 and pH2 to get the final pH of the solution.

Let's calculate the pH using the given pKa values:

pK1 = 1.250 pK2 = 4.266 Concentration of acetic acid (CH3COOH) = 0.03 M

1. Calculate the concentration of CH3COO-: [CH3COO-] = [H+] (since one molecule of acid dissociates to one H+ ion and one CH3COO- ion)

2. Calculate the concentration of CH3COOH: [CH3COOH] = 0.03 M - [CH3COO-]

3. Calculate the pH1 using the Henderson-Hasselbalch equation for the first dissociation: pH1 = 1.250 + log([CH3COO-]/[CH3COOH])

4. Calculate the pH2 using the Henderson-Hasselbalch equation for the second dissociation: pH2 = 4.266 + log([CH3COO-]/[CH3COO-])

5. Take the average of pH1 and pH2 to get the final pH of the solution.

Please note that the concentration of CH3COO- depends on the extent of dissociation, which is determined by the equilibrium constant and the initial concentration of the acid.