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So, we are given a mixture of acetic acid and sodium acetate with different concentrations. We want to know the pH of this mixture, which will require us to consider the equilibrium between acetic acid (HA) and acetate ion (A-) in solution.
The pKa of acetic acid tells us how easily it donates a proton in solution, with a higher pKa indicating a weaker acid. In this case, the pKa is 4.76, which means that acetic acid is a fairly weak acid.
To calculate the pH of the mixture, we can use the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
where [A-] and [HA] are the concentrations of acetate ion and acetic acid, respectively.
Using the given concentrations of 0.20M acetic acid and 0.30M sodium acetate, we can calculate their respective molar ratios:
[A-]/[HA] = (0.30/1)/(0.20/1) = 1.5
Substituting this into the Henderson-Hasselbalch equation, we get:
pH = 4.76 + log(1.5) = 4.96
Therefore, the pH of the mixture is approximately 4.96.