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$\ce{(CH_3)_2O^+ H}$ has $\rm pK_a \; -3.8$ while $\ce{H_3O^+}$ has $\rm pK_a \; 1.74\;.$ So, the former is stronger acid than latter hydronium ion.

But why is it so?

Is it due to the $\rm +I$-effect of $\ce{-(CH_3)}$? But it would rather decrease the attraction of $\ce O$ on the electron pair of $\ce H$ and that would make it indifferent to release $\ce {H^+}$ isn't it?

What is actually going that makes $\ce{(CH_3)_2O^+ H}$ stronger acid than $\ce{H_3O^+}$ ?

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A powerful but often overlooked factor in determining a substance's acidity and basicity is the effect of the solvent (or lack thereof) in which it is dissolved.

You are not wrong; in the gas phase, $\ce{H_3O^{+}}$ is indeed a stronger acid than $\ce{(CH_3)_2OH^{+}}$, by a factor of about $5\times 10^{18}$. This can be seen by comparing the proton affinities of the conjugated bases, dimethyl ether ($\mathrm{804\ kJ\ mol^{-1}}$) and water ($\mathrm{697\ kJ\ mol^{-1}}$), respectively.

In other words, a mole of gaseous dimethyl ether reacting with a mole of gaseous protons releases $\mathrm{804\ kJ}$, while a mole of gaseous water releases only $\mathrm{697\ kJ}$. This means that in the gas phase, water is a weaker base than dimethyl ether, which implies that protonated water is a stronger acid than protonated dimethyl ether.

Why does the tendency invert in aqueous solution? Water can form hydrogen bonds, a very strong type of molecular interaction. $\ce{H_3O^{+}}$ has three protons available for hydrogen bond donation, whereas $\ce{(CH_3)_2OH^{+}}$ only has one. This means that the solvating water stabilises $\ce{H_3O^{+}}$ more than $\ce{(CH_3)_2OH^{+}}$. Higher stability means reduced acidity, and the difference happens to be enough that the relative order of acidity in water is the opposite of that in the gas phase.

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  • $\begingroup$ So, it has no relation with inductive effect? $\endgroup$
    – user5764
    Feb 18, 2016 at 13:06
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    $\begingroup$ The inductive effect suggests that hydronium should be a stronger acid than dimethyloxonium, which indeed is observed in the gas phase. However, the solvent effect overpowers the inductive effect for determining the acidity in aqueous solutions. $\endgroup$
    – Nicolau Saker Neto
    Feb 18, 2016 at 13:10
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    $\begingroup$ Here (1, 2), are some older answers of mine which touch on the importance of solvation for acidity and basicity. $\endgroup$
    – Nicolau Saker Neto
    Feb 18, 2016 at 13:10
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    $\begingroup$ In this case, yes. If you were to analyze the same substances in another solvent (e.g. DMSO, toluene, etc), induction could still prevail. $\endgroup$
    – Nicolau Saker Neto
    Feb 18, 2016 at 13:16
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    $\begingroup$ @NicolauSakerNeto would like to make a short comment to supplement your excellent answer, which the OP might find interesting (since the importance of solvents with regard to determination of acidity was mentioned). The upper limit to the strength of any acid is fixed by the solvent. In essence in a aqueous media, nothing is more acidic than the hydronium ion (final proton acceptor); thus, a weaker proton acceptor solvent is needed to discriminate between very strong acids. read more here: en.wikipedia.org/wiki/Leveling_effect $\endgroup$
    – getafix
    Mar 18, 2016 at 14:03

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