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I got the answer from $K_a$ value that acetic acid is more acidic, but I have also read that inductive effect decreases as the length of alkyl group increases so acetic acid having a methyl group should have greater +I effect than ethyl group in propanoic acid.

And this comparitive large +I effect of methyl group in acetic acid should make it less acidic (as polarity of $\ce{O-H}$ bond decreases) than propanoic acid with ethyl group with less +I effect.

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    $\begingroup$ You need to consider inductive effects and resonance effects (especially hyperconjugative effects) on both the reactants and the products. The difference in effects on the reactants is likely small, but the effects will be more important on the charged products. $\endgroup$ – ron Feb 3 '16 at 17:32
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My best guess is you are interpreting the statement "inductive effect decreases as the length of alkyl group increases" somewhat out of context.

So, let's compare formic acid to acetic acid. Formic acid has hydrogen bonded to the carbonyl, while acetic acid has a methyl group. The methyl group is inductively donating, and as a result acetic acid is less acidic than formic acid. $p_{Ka}$ difference of $1$ full unit.

So now, let us compare methyl acetic acid (a precise, but incorrect, alternate name for propanoic acid) to acetic acid. Methyl acetic acid has an inductive donating group at the $\ce{CH2}$ carbon. As such, we expect some donation, and a lower acidity for methyl acetic acid as compared to acetic acid. True, the donating group is one group removed from the acidic site, which means the effect of the methyl group on methyl acetic acid's acidity is diminished as compared to an electron donating group directly attached to the carbonyl, so the acidity reduction will be smaller. $p_{Ka}$ difference, $0.12$ units.

After you have this concept in your head, purge the abomination of nomenclature that is methyl acetic acid from your memory.

Ron has some views on hyperconjugation that may also be useful in this context, but strictly speaking, I don't find them necessary.

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Besides purely electronic effects, one should take into account also the solvation phenomena. Since propanoic acid possesses larger alkyl chain, compared to the acetic acid, lower solvation of the anion is expected, which in turn leads to lower stabilization of this anion (by hydrogen bonds in case of water solution). Lower stabilization has its reflection in shifting of dissociation reaction equilibrium and eventually makes larger pKa value for propanoic acid.

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  • $\begingroup$ Welcome to chemistry.SE! If you had any questions about the policies of our community, please ‎visit the help center. $\endgroup$ – M.A.R. Mar 5 '16 at 16:40
  • $\begingroup$ The Merck index lists both acetic acid and propionic acid as 'miscible' with water. There is likely no effect on solubility in this case. This argument may be relevant for larger alykl chains. $\endgroup$ – Lighthart Mar 5 '16 at 17:31

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