Which solution has the lowest pH?

Method 1 :

In a solution containing a weak acid and its salt, the higher the proportion the acid, the lower the pH is.
As the solution in A) contains the highest proportion of acetic acid, it has the lowest pH.

The answer: A) a buffer made with 0.10 M acetic acid and 0.01 M sodium acetate


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Method 2 :

pH = pKa + log([CH₃COO⁻]/[CH₃COOH])
In A) pH = pKa + log(0.01/0.10) = pKa - 1
In B) pH = pKa + log(0.10/0.10) = pKa
In C) pH = pKa + log(0.10/0.01) = pKa + 1
In D) pH = pKa + log(0.01/0.01) = pKa

The answer: A) a buffer made with 0.10 M acetic acid and 0.01 M sodium acetate

pH of a buffer solution....

We can use the Henderson-Hasselbalch equation to approximate the pH of a buffer solution. For that you need to know the pKa of the acid.

Ka of acetic acid is 1.8x10^-5
pKa = -log(Ka) = -log(1.8x10^-5) = 4.74

pH = pKa + log([base] / [acid])
note: [ ] means "concentration in moles per liter"

Solutions (B) and (D) will have the same pH, although the one with the greater concentrations will have a greater buffering capacity.

The log of a number less than 1 is negative, which will decrease the pH value below that of the pKa. Therefore, the case where [base]/[acid] is less than 1 will have the lowest pH. Therefore, it will be the one where the [base] is less than the [acid]. That will be choice (A).

I think the answer is A but idk

Tiff, I've read all the answers you've been given and I really don't think they'll help you understand what's happening. There's two things you must understand about buffers. They're made by combining a weak acid or base with a salt of the acid or base which completely ionizes. In this case you have acetic acid which ionizes very little (that is, it doesn't separate to give you many hydrogen ions), and the sodium salt of the acid, which completely ionizes and gives you tons of acetate ions. What happens is that all those extra acetate ions are attracted to the few hydrogen ions produced by the weak acetic acid. Remember. the more hydrogen ions you have, the lower the pH, (or the higher the acidity). Okay, so if your concentration of acetic acid is really high compared to the concentration of acetate ions from the sodium salt, then there won't be many extra acetate ions around (from the salt) to grab hydrogen ions and take them out of solution. This equals more H+ ions and a lower pH. I know it's a little confusing to remember the lower the pH, the higher the acid concentration. Pisgahchemist talks of this, but just knowing equations like the Henderson/ Hasselbalch equation doesn't explain what's happening. He's right, (he usually is) about the answer being "a" because the acid concentration is 10 times higher than the acetate salt concentration, so there won't be many of those acetate guys to join with the H+ ions, which means they'll be more free H+ ions. I hope this helps. Using algorithms like the Henderson/Hasselbalch equation solves problems but it does nothing in helping you understand what's happening.

When I tried to teach this stuff to a bunch of nursing students, I used an analogy where I compared unionized acid as a couple dancing together. If they separated, you'd have a boy and a girl without a partner. Then I said if there were more girls than boys (like if you bring in 10 times more acetate ions), wouldn't my chances of getting a girl to dance with me be greater? Of course the girls always loudly answered NO!! ....my students really hated me.