Determine the equilibrium constant for a 0.10M phenol (HC6H5O) solution that has a pH of 5.43 at 25 degrees C. What is the degree of ionization of this weak acid? Why is the pH value important for this problem?
Let phenol = HP
pH = -log(H^+). You know pH, solve for H^+
.....................HP.........H^+ + P^-
K = (H^+)(P^-)/(HP)
From the pH you get H^+ and P^- and HP. Substitute into the K expression and solve for K.
Post your work if you get stuck.
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To determine the equilibrium constant for a weak acid, such as phenol (HC6H5O), we need to consider the disassociation of the acid in water. The equilibrium constant, denoted as Ka, can be expressed as the ratio of products to reactants at equilibrium.
1. Start by writing the balanced chemical equation for the disassociation of phenol, a weak acid, in water:
HC6H5O (aq) ↔ H+ (aq) + C6H5O- (aq)
2. The equilibrium constant expression, Ka, can be written as:
Ka = [H+][C6H5O-] / [HC6H5O]
3. The pH value is crucial in determining the concentration of H+ ions in the solution. The concentration of H+ ions can be calculated using the formula:
[H+] = 10^(-pH)
4. In this case, the pH is given as 5.43, so the concentration of H+ ions would be:
[H+] = 10^(-5.43)
5. Since phenol is a weak acid, it does not completely dissociate, and the degree of ionization, denoted as α, represents the proportion of the acid that disassociates. For a weak acid, we can approximate that [H+] ≈ α[HC6H5O].
6. To determine α, we can substitute the concentration of H+ ions and the concentration of phenol into the equation:
[H+] ≈ α[HC6H5O]
10^(-5.43) ≈ α(0.10M)
7. Solving for α:
α ≈ (10^(-5.43))/(0.10M)
8. The equilibrium constant, Ka, can be determined by substituting the value of [H+], [C6H5O-] (which is equal to [H+]), and [HC6H5O] into the expression:
Ka = [H+][C6H5O-] / [HC6H5O]
= (10^(-5.43))(10^(-5.43)) / 0.10M
9. Simplifying the expression further:
Ka ≈ (10^(-5.43 + (-5.43)))/(0.10M)
≈ 10^(-10.86)/(0.10M)
The equilibrium constant, Ka, can be calculated using the above equation. The degree of ionization, α, represents the proportion of the weak acid that has dissociated in solution. The pH value is important because it provides the concentration of H+ ions, which is essential for the calculation of both α and Ka.