Rank the following in order of acidity of the most acidic hydrogens?

Well, the correct answer is the one you chose first (or had the answer to). :-)

Good question - you're dealing with:

1) methyl acetoacetate
2) dimethyl propanedioate
3) acetylacetone
4) 2-propanone

COMPARING (4) WITH (3)

Now, the most acidic hydrogen would be the central hydrogen in the dicarbonyl compounds because it is closest to both carbonyl oxygens, which are electron-withdrawing groups.

So, you know it's not 2-propanone (4) that's the most acidic; it only has its 'end' hydrogens; each one's #"pKa"# is around #\mathbf(color(blue)(20))#, which is fairly high, and it is only a monocarbonyl compound.

Acetylacetone (3) has a #"pKa"# of around #\mathbf(color(blue)(9))#, so that's a good possibility right now.

From there, you would have to consider what makes it even more (or less) acidic: an acetyl group (#"H"_3"C"("C"="O")-#) or an acetoxy group (#"H"_3"C"-"O"-("C"="O")-#).

So, consider how the increasing ester character instead of ketone character changes things. This means comparing (1) with (3) and (2) with (1).

COMPARING (1) WITH (3)

A methoxy group (#"CH"_3"O"-#) is electron-donating, so I'd expect an acetoxy group's carbonyl oxygen to withdraw more electron density from the methoxy oxygen than from the central hydrogen.

Because the hydrogen is made electropositive to a lesser extent, that should decrease the acidity by a little bit, relative to acetylacetone (3).

The actual #"pKa"# of methyl acetoacetate (1) is around #\mathbf(color(blue)(11))# (that of ethyl acetoacetate, instead of methyl acetoacetate, is #10.68#). That means it is less acidic indeed than (3).

COMPARING (2) WITH (1)

Since dimethyl propanedioate (2) has one more acetoxy group than methyl acetoacetate, I would predict based on comparing (1) with (3) that (2) is less acidic than (1).

Actually, the #"pKa"# of (2) is about #\mathbf(color(blue)(11.80))# according to SciFinder:

So indeed, (2) is less acidic than (1).

CONCLUSIONS

We've noted the following #"pKa"#s:

• (1): #~~11#
• (2): #~~11.80#
• (3): #~~9#
• (4): #~~20#

That means the acidities of the compounds above are ordered from most acidic to least acidic as follows:

#color(blue)((3) > (1) > (2) > (4))#

which correlates with the trend that:

• More carbonyl groups around a #"C"-"H"# makes that hydrogen significantly more acidic. Therefore, it makes sense that (4) is the least acidic.
• Replacing a ketone group with an ester group slightly decreases the acidity. (2) has one ester group more than (1), and (1) one more than (3).