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Can I make a buffer using two different acids/bases? For example, adding 1 mole of acetic acid and 1 mole of ammonia?
The only information I can ever find is that I can make a buffer using only an acid (or base) and its conjugate base (or conjugate acid). So, carbonic acid and carbonate, $\ce{H2CO3}$ and $\ce{HCO3-}$.
Why do I need a conjugate acid-base pair and not two random weak acid-base pairs to make a buffer?
Yes, having multiple weak acids and/or bases having different pKa values would give buffering capacity in more than one pH range, or over a greater pK range.
There is a term "universal buffer" which refers to a buffer having multiple pKas spaced thoughout the pH ~2-12 range to give some buffering capacity over the enter pH range.
As explained in A Neutral Buffered Standard for Hydrogen Ion Work and Accurate Titrations Which Can be Prepared in One Minute J. Am. Chem. Soc., 1932, 54, pp 1911–1912, ammonium aceate has the property that if it is added to pure water it produces a buffered solution of pH 7.00, accurate to a hundreth of a pH unit.
In theory you can, but it depends on the way you prepare the buffer.
A buffer solution is prepared by mixing a weak acid (or base) with a strong salt of that acid
For example you can prepare the following buffer in two ways:
$\ce{HOAc + NaOAc}$
1: Mixing directly a solution of the salt with the acid
2: Adding (let's say dropwise) a solution of $\ce{NaOH}$ to the acid. In this case $\ce{NaOAc}$ will be formed in situ.
Prepare a buffer by mixing $\ce{HOAc}$ with $\ce{NaCl}$ for example
On the other hand you can mix two different buffers to get a new one with a different pH range like in the case of universal buffers.
