Calculate the pH of a buffer solution prepared by mixing 0.2 moles of acetic acid (CH₃COOH) and 0.2 moles of sodium acetate (CH₃COONa) in enough water to make a total volume of 1 liter. The pKa of acetic acid is 5.42.Select one:a.5.4b.5.8c.6.3d.4.5
Question
Calculate the pH of a buffer solution prepared by mixing 0.2 moles of acetic acid (CH₃COOH) and 0.2 moles of sodium acetate (CH₃COONa) in enough water to make a total volume of 1 liter. The pKa of acetic acid is 5.42.Select one:a.5.4b.5.8c.6.3d.4.5
Solution
To calculate the pH of a buffer solution, we can use the Henderson-Hasselbalch equation, which is:
pH = pKa + log([A-]/[HA])
where:
- [A-] is the concentration of the base (acetate ion from sodium acetate in this case)
- [HA] is the concentration of the acid (acetic acid in this case)
Given that we have equal moles (0.2 moles) of acetic acid and sodium acetate, the concentrations of these in the solution are also equal because the total volume is the same (1 liter). Therefore, the ratio [A-]/[HA] is 1.
So, the Henderson-Hasselbalch equation simplifies to:
pH = pKa + log(1)
Since the log(1) is 0, the equation further simplifies to:
pH = pKa
The pKa of acetic acid is given as 5.42. Therefore, the pH of the solution is also 5.42.
So, the correct answer is a. 5.4.
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