What are the "Universal" buffer mixtures?

Answer 1

Universal buffer mixtures are mixtures of buffers.

No, that's not a jesting response.

A weak acid and its conjugate base, or vice versa, are combined to form a buffer.

It has its best buffering capacity in the range of #"p"K_a±1#.
If you combine substances with #"p"K_a# values differing by only 2 #"pH"# units or less, you can prepare a wide range of buffers.
Citric acid is a useful component of a buffer mixture because it has three #"p"K_a# values (3.13, 4.76, and 6.40), and these are separated by less than two #"pH"# units.
If you add another acid such as #"H"_2"PO"_4^- //"HPO"_4^-# (#"p"K_a = 7.2#), you can extend the range by another two #"pH"# units.
By adjusting the relative amounts of #"Na"_2"HPO"_4# and citric acid, you can prepare a buffer solution for any #"pH"# between #"pH"=3# and #"pH"=8#.

We refer to the mixture as a universal buffer.

If you add more acids like diethylbarbituric acid (#"p"K_a = 7.98#) and boric acid (#"p"K_a = 9.27#) and adjust the #"pH"# by adding #"NaOH"#, you can prepare a buffer for any #"pH"# in the range from #"pH"=2# to #"pH" = 12#.
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Answer 2

"Universal" buffer mixtures are solutions containing a mixture of weak acids and their conjugate bases (or weak bases and their conjugate acids) that can maintain a relatively constant pH over a wide range of acidic or basic conditions. Common examples include the acetic acid/sodium acetate buffer and the phosphate buffer system.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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