Use activity coefficients to find the concentration of hydrogen ions in a solution of 75.0 mM butanoic acid and 0.01 M NaCl. The ionization constant of butanoic acid is Ka = 1.52 × 10-5. Take the size of C3H7COO– to be 500 pm.
What is the concentration of H+?
What is the pH of this solution? (Include activity coefficients in your calculation.)
What is the fraction of dissociation of butanoic acid in this solution?
874.2 pm
pH=4.21
Can you please show work?
To find the concentration of H+ ions in a solution of butanoic acid and NaCl, we can use the principles of activity coefficients and the ionization constant (Ka) of butanoic acid. Here's how to do it:
1. Calculate the activity coefficients of butanoic acid and NaCl:
- For butanoic acid (C3H7COOH), the activity coefficient (γ1) can be estimated using the Debye-Hückel equation:
γ1 = (1 + A × √(I)) / (1 + B × √(I))
Where A and B are constants dependent on the solvent and temperature, and I is the ionic strength of the solution. For dilute solutions, I can be approximated as:
I = 0.5 × ((C1 × z1^2) + (C2 × z2^2)) + (C3 × z1 × z2)
Where C1 and C2 are the molar concentrations of the species (in mol/L), z1 and z2 are their respective charges, and C3 is a constant dependent on the solvent. In this case, C1 is the molar concentration of butanoic acid and C2 is the molar concentration of NaCl.
- For NaCl, the activity coefficient (γ2) is approximately 1, as strong electrolytes like NaCl exhibit close to ideal behavior.
2. Calculate the equilibrium concentration of butanoic acid (C3H7COOH) after considering its dissociation using the ionization constant (Ka):
- The ionization of butanoic acid can be represented as: C3H7COOH ⇌ C3H7COO- + H+
- After reaching equilibrium, if x is the concentration of butanoic acid that dissociates, the equilibrium concentrations can be expressed as:
[C3H7COOH]equilibrium = [C3H7COOH]initial - x
[C3H7COO-]equilibrium = x
[H+]equilibrium = x
- Using the expression for Ka, we can set up the equilibrium constant expression:
Ka = [C3H7COO-]equilibrium × [H+]equilibrium / [C3H7COOH]equilibrium
Substitute the equilibrium concentrations and the value of Ka to solve for x.
3. Calculate the concentration of H+ ions and the pH:
- The concentration of H+ ions can be calculated as [H+] = [H+]equilibrium × γ3, where γ3 is the activity coefficient of H+.
- The pH can be calculated using the equation: pH = -log10[H+].
4. Calculate the fraction of dissociation of butanoic acid:
- The fraction of dissociation (α) is calculated by dividing the concentration of dissociated butanoic acid ([C3H7COO-]) by the initial concentration of butanoic acid ([C3H7COOH]): α = [C3H7COO-]equilibrium / [C3H7COOH]initial
By following these steps, we can determine the concentration of H+ ions, the pH of the solution (taking into account the activity coefficients), and the fraction of dissociation of butanoic acid.