Confusion about buffers

[deleted647690]

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This is an extremely basic question, but what exactly is meant by "one half equivalent"?
A question asks, "which of the following results in a buffer with a pH of 5.0, given that HA has a pKa of 4.7?"
A. HA with one half equivalent of A-
B. A- wiht one equivalent of HA
C. HA with one third equivalent of OH-
D. A- with one third equivalent of H3O+


I know that the ratio of 1/2 is considered a "one third equivalence" because there is 1 part base to 2 parts acid, making 3 parts total, so that it is considered "HA with one third equivalence of OH-"

One equivalent would be a 1 to 1 ratio of acid to base..

So what is a half equivalent??

 

[theonlytycrane]

For choice A, I interpret that as twice as much A- as HA.

One equivalent of A- and HA means they are 1:1.

One half equivalent of HA to A- means they are 1:2.

 

[sazerac]

This is an extremely basic question, but what exactly is meant by "one half equivalent"?
A question asks, "which of the following results in a buffer with a pH of 5.0, given that HA has a pKa of 4.7?"
A. HA with one half equivalent of A-
B. A- wiht one equivalent of HA
C. HA with one third equivalent of OH-
D. A- with one third equivalent of H3O+


I know that the ratio of 1/2 is considered a "one third equivalence" because there is 1 part base to 2 parts acid, making 3 parts total, so that it is considered "HA with one third equivalence of OH-"

One equivalent would be a 1 to 1 ratio of acid to base..

So what is a half equivalent??

When I was teaching, I found the best explanation of "equivalent" to be "one mole of crap per volume", where "crap" is understood given the context of the question.

If this was a question about ionic charge, then one mole of Mg2+ per liter would be two equivalents, because magnesium ions have two positive charges.

Since this question is about acid base equilibria, one equivalent is equal to one mole of HA, A-, OH-, or H3O+ per liter. The first answer above describes a situation with say one mole of HA and 0.5 mole A- in solution. Or 6 moles of HA with 3 moles of A- in solution. Whatever. You get the idea.

 

[aldol16]

One thing to note about equivalents is that it's commonly used in chemistry because it's easier to use if your reaction mixture is easily scaled up or down. 1 equiv. of A to B means that the mole ratio of A to B is exactly one. So if I have a reaction like H2 + 1/2 O2, then it would be correct to say that this reaction requires 0.5 equiv. of O2 relative to H2. You'll notice that there always must be a reference because equiv. is a relative measure. You're measuring the equivalents relative to something else. In a reaction, that reference is usually substrate. So you say, "I added 2 equiv. of reagent" with the assumption of a set amount of substrate. In acid-base chemistry, it's usually relative to the acid or base being titrated. So if you say you added 1 equiv. of base to 2 moles of HCl, then you added 2 moles of -OH.