Final answer:
To find the pH of a solution with 0.15 M acetic acid and 0.25 M sodium acetate, apply the Henderson-Hasselbalch equation using the provided concentrations and the calculated pKa from the acetic acid's Ka value.
Step-by-step explanation:
To calculate the pH of a solution containing 0.15 M acetic acid and 0.25 M sodium acetate, we apply the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
First, calculate the pKa from the given Ka value:
pKa = -log(Ka) = -log(1.8 x 10-5)
Prior calculations suggest that for an acetic acid concentration of 0.100 M, the pH is 2.87. However, in our case, the initial concentrations are different, and we must use them in the Henderson-Hasselbalch equation.
Using the provided concentrations:
pH = pKa + log([0.25]/[0.15])
pH can be calculated directly without needing a detailed ICE table, since we have both the acid and its conjugate base present, which simplifies the calculation. In this case, we don't solve for x (the [H+]) because we already have the information we need to use the Henderson-Hasselbalch equation directly.
Once you calculate the pKa and substitute in the values for [A-] (sodium acetate) and [HA] (acetic acid), the pH can be found using a calculator. This pH calculation method is most appropriate for buffer solutions like the one described in the question.