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Which has stronger hydrogen bonding, $\ce{CH3OH}$ or $\ce{CH3NH2}$

I think it comes down to which has more dominance; number of hydrogens, number of lone pairs, or electronegativity.

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    $\begingroup$ Alcohols form stronger H-bonds compared to amines. $\endgroup$ – Zenix May 15 at 4:00
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The boiling point of non-ionic compounds are highly depend on their H-bonding abilities. For example, boiling point of water (molar mass: $\pu{18.02 g/mol}$) is $\pu{100 ^\circ C}$ at $\pu{1 atm}$ while that of ethanol (molar mass: $\pu{46.07 g/mol}$) is $\pu{78.4 ^\circ C}$ at $\pu{1 atm}$, even though ethanol is heavier and have more other intermolecular attractions, excluding H-bonding, such as van der Waals interactions than water. This difference in boiling points displays clear dominamce of H-bonding (HB) on boiling point over other forces on these non-ionic compounds.

Therefore, since molar masses of methanol and methylamine is very close ($\pu{32.04 g/mol}$ for $\ce{CH3OH}$ versus $\pu{31.05 g/mol}$ for $\ce{CH3NH2}$), comparition of their boiling point would be excellent indicator of the comparison of their H-bonding strength: Boiling point of $\ce{CH3OH}$ is $\pu{64.7 ^\circ C}$ at $\pu{1 atm}$ while that of $\ce{CH3NH2}$ is $\pu{-6 ^\circ C}$ at $\pu{1 atm}$. Therefore, it is safe one to say that $\ce{CH3OH}$ has stronger H-bonding capabilities than that of $\ce{CH3NH2}$ even though $\ce{CH3NH2}$ has extra $\ce{H}$ compared to only one in $\ce{CH3OH}$. The best comparison measures of these two types of hydrogen bonding (HB) are the $\Delta H_\mathrm{HB}$ values in Wikipedia (Hydrogen Bonding):

  • $\Delta H_\mathrm{HB} = \pu{21 kJ/mol}$, listed for $\ce{O−H···:O}$ in water-water.
  • $\Delta H_\mathrm{HB} = \pu{13 kJ/mol}$, listed for $\ce{N−H···:N}$ in ammonia-ammonia.
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Mathew Mahindaratne has provided analysis based on experimental values of the boiling points of the two compounds. I would like to offer a different view using bonding analysis.

Before I begin tackling the question, we shall first clarify the concept of the hydrogen bond. While the popular view of the hydrogen bond is as a particularly strong type of "dipole-dipole" interaction (more of a charge-dominated interaction), the more chemically accurate view manifests itself as a type of "fractional chemical bond" (more of a covalent interaction) between the two participating molecules (Weinhold & Klein, 2014). In fact, in their paper, authors define the hydrogen bond as:

a fractional chemical bond due to partial intermolecular $\ce {A-H...:B <-> A:^{-}...H-B^{+}}$ resonance delocalisation (partial 3-centre 4-electron sharing between Lewis bases), arising commonly from quantum mechanical $n_\ce{B} \rightarrow \sigma^{*}_\ce{A-H}$ donor-acceptor interaction.

Based on the above definition for the hydrogen bond, we can easily explain why $\ce {O-H...:O}$ would be a stronger hydrogen bond than $\ce {N-H...:N}$. To adopt this type of resonance, there is a need for heterolytic cleavage of the single bond. As the more polar of the two, the $\ce {O-H}$ bond undergoes heterolytic cleavage more easily and hence, the hydrogen bond formed between the alcohols would be certainly stronger than that formed between the amines.

To explore this further, we can look at the whole range of hydrogen bond enthalpies provided on the Wikipedia page:

\begin{array}{|c|c|c|c|} \hline \text{Hydrogen bond} & \text{Enthalpy, } \pu{kJ/mol}\\ \hline \ce{F-H...F} & 161.5\\ \hline \ce{O-H...N} & 29\\ \hline \ce{O-H...O} & 21\\ \hline \ce{N-H...N} & 13\\ \hline \ce{N-H...O} & 8\\ \hline \end{array}

Notice that as the polarity of the $\ce {X-H}$ bond increases, the hydrogen bond strength increases. Comparing between $\ce {O-H...O}$ and $\ce {O-H...N}$, we also observe that as the the availability of the lone pair on the hydrogen bond acceptor increases, the strength of the $\ce {H}$ bond also increases. In terms of molecular orbitals, we can say that the $\ce {\sigma^ {*}_\ce{O-H}}$ is lower in energy and more energetically accessible to the lone pair orbital of the acceptor, compared to $\ce {\sigma^ {*}_\ce{N-H}}$ while the $\ce {n_N}$ nonbonding lone pair orbital is higher in energy and is able to better access the $\sigma^{*}$ orbital of the hydrogen bond donor, compared to $n_\ce{O}$.

Reference:

Frank Weinhold, Roger A. Klein, "What is a hydrogen bond? Resonance covalency in the supramolecular domain," Chem. Educ. Res. Prac. 2014, 15, 276-285 (DOI: 10.1039/C4RP00030G).

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