Which of the following buffers will have the lowest pH?

a solution containing 0.20 M HC2H3O2 and 0.20 M NaC2H3O2
a solution containing 0.25 M HC2H3O2 and 0.15 M NaC2H3O2
a solution containing 0.15 M HC2H3O2 and 0.25 M NaC2H3O2
they all have the same pH

Answer:
No, they have different pH values.

The equation needed is the Henderson - Hasselbach equation;

pH = pKa + log (base/acid). For acetic acid, the pKa = 4.74

So for the first one, pH = 4.74 + log (0.20/0.20), pH = 4.74, since (0.20/0.20) = 1 and the log (1) = 0.

Second one: pH = 4.74 + log (0.15/0.25), (0.15/0.25) < 1, so log of this number is going to be negative, so pH < 4.74

pH = 4.74 + log(0.6) ==> 4.74 - 0.22 = 4.52

Last one: pH = 4.74 + log(0.25/0.15), (0.25/0.15) > 1, so this log value is going to be positive.

pH = 4.74 + log(1.67) ==> 4.74 + 0.22 = 4.96

therefore, second equation is going to have the lowest pH.

An easy way to do this is by looking at the ratio, if you have more acid than base in a buffer, the pH will be lower than then pKa, if the opposite is true, the pH > pKa and if they are both the same, pH = pKa, as demonstrated mathematically in the examples.

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