Final answer:
To find the pH of a 0.250 M solution of NaC₂H3O₂, we need to determine the concentration of the conjugate acid, CH3CO₂H. We can use the relationship between the Ka and Kb values to find the concentration of CH3CO₂H and then calculate the pH using the formula pH = -log[H₃O⁺].
Step-by-step explanation:
To find the pH of a 0.250 M solution of NaC₂H3O₂, we need to determine the concentration of CH3CO₂H, which is the conjugate acid of C₂H3O₂. The Ka value of HC₂H₃O₂ is given as 1.80×10⁵. Since C₂H3O₂ is the conjugate base of HC₂H₃O₂, we can use the relationship between Ka and Kb to find the concentration of CH3CO₂H. After finding the concentration, we can calculate the pH using the formula pH = -log[H₃O⁺].
First, we need to find Kb for C₂H3O₂. Using the relationship between Ka and Kb, we can calculate Kb = Kw/ Ka = 1.0 x 10⁻¹⁴ /1.80 x 10⁵. Solving for Kb, we get Kb = 5.56 x 10⁻¹⁰.
Next, we can use the Kb value to find the concentration of CH3CO₂H. Kb = [CH3CO₂][OH⁻]/[CH3CO₂H]. Since NaC₂H3O₂ is a strong electrolyte, it will completely dissociate and NaOH will contribute OH⁻ ions. Therefore, the concentration of OH⁻ is equal to the concentration of NaOH, which is 0.250 M. We can then rearrange the equation to solve for [CH3CO₂H].
Finally, we can calculate the pH using the [H₃O⁺] concentration we found. pH = -log[H₃O⁺].