Understanding Buffers: pKa, pH & Solutions

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An buffer solution consists of a mixture of a weak acid and its salt (conjugate base and a cation)
or a mixture of a weak base and its salt (conjugate acid and an anion).

When you titrate (for example) a weak acid with a strong base, then at the half equivalence point, there are equal amounts of the acid and its conjugate base, right?

i think i understand that... I am confused where the pKa and the pH parts come in...

Why, when making a buffer solution, do we want to pick an acid whose pKa is close to the pH at which we want to buffer the solution?
 
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Buffers are generally figured to be most efficient at a pH within 1 unit from their pKa.

At the half-equivalence point, what is the pH? How does that compare to the pKa?
 
For a buffer to be efficient it needs to be able to absorb both H+ and OH- - that means it has to contain both weak acid and its conjugate base. If they are in a "reasonable" (comparable) quantities ratio of their concentrations is close to 1. If you put ratio of 1 into Henderson-Hasselbalch equation, what pH of the buffer solution will you get?