Understanding Buffers: pKa, pH & Solutions

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A buffer solution is created by mixing a weak acid with its salt (conjugate base and cation) or a weak base with its salt (conjugate acid and anion). During titration of a weak acid with a strong base, the half-equivalence point is where equal amounts of the acid and its conjugate base exist. At this point, the pH equals the pKa of the weak acid. It is crucial to select an acid with a pKa close to the desired pH for effective buffering, as buffers work best within one pH unit of their pKa. For a buffer to function efficiently, it must contain both the weak acid and its conjugate base in comparable concentrations, ideally with a ratio close to 1. When this ratio is applied in the Henderson-Hasselbalch equation, the resulting pH of the buffer solution will equal the pKa.
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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?
 
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