Use activity coefficients to find the concentration of hydrogen ions in a solution of 70.0 mM butanoic acid and 0.1 M NaCl. The ionization constant of butanoic acid is Ka = 1.52 × 10-5. Take the size of C3H7COO– to be 500 pm.
My biggest problem is knowing where to start. So I calculate the ionic strength then the activity coefficients. Then do I just "plug and chug"
Thank you!
To find the concentration of hydrogen ions (H+) in a solution of butanoic acid and NaCl, we need to consider the activity coefficients. Activity coefficients take into account the deviations from ideal behavior in a solution and are used to correct the concentrations of ions in the solution.
Here's how you can use activity coefficients to find the concentration of H+ ions:
Step 1: Calculate the activity coefficients.
- The activity coefficient, γ±, for an ion depends on the ion's size and charge.
- In this case, we need the activity coefficient for H+ ions and for C3H7COO- ions (butanoate ions).
Step 2: Calculate the effective concentrations.
- The effective concentration, C*, is the product of the activity coefficient and the actual concentration of the species.
- For H+ ions: C* (H+) = γ±(H+) * [H+]
- For C3H7COO- ions: C* (C3H7COO-) = γ±(C3H7COO-) * [C3H7COO-]
Step 3: Use the ionization constant.
- The ionization constant, Ka, describes the equilibrium between a weak acid and its conjugate base in solution. In this case, Ka = [H+] * [C3H7COO-] / [butanoic acid]
Step 4: Solve for [H+].
- Rearrange the equation from step 3 to solve for [H+].
- [H+] = (Ka * [butanoic acid]) / [C3H7COO-]
Now, let's calculate the concentration of H+ ions using the given values:
Step 1: Calculate the activity coefficients.
- The activity coefficient for H+ ions can be approximated as 1 since it's a small, highly charged ion.
- The activity coefficient for C3H7COO- ions can be calculated using the Debye-Hückel equation, which considers the size and charge of the ion.
Step 2: Calculate the effective concentrations.
- C* (H+) = (1) * [H+]
- C* (C3H7COO-) = γ±(C3H7COO-) * [C3H7COO-]
Step 3: Use the ionization constant.
- Ka = (C* (H+)) * (C* (C3H7COO-)) / [butanoic acid]
Step 4: Solve for [H+].
- Rearrange the equation to solve for [H+]:
- [H+] = (Ka * [butanoic acid]) / (C* (C3H7COO-))
By following these steps and substituting the given values for the concentration of butanoic acid and the ionization constant (Ka), you can determine the concentration of H+ ions in the solution.