The dipole moment plays a key role in deciding the boiling points of organic liquids. The dipole moment of N,N-dimethylethanamide is 3.7D while that of butanoic acid is 1.65D.
Introductory Remarks
This is a tricky question. Yes, your intuition is correct. Compounds capable of hydrogen-bonding often show higher boiling points (BPs) than those that are not. However, BP depends on several other factors, including molecular weight ($M$), dipole moment ($\mu$), symmetry, effects of functional group, and, perhaps most importantly, molecular structure.
Preliminary Observations
Before I get into the analysis, since, Wikipedia is not a reputable source, let us first verify the BPs of the N,N-dimethylethanamide (more commonly known as dimehtylacetamide, DMA, and DMAc) and butanoic acid and also check for another important factor that plays a key role in the determination of boiling points. I obtained the following data from PubChem.
Remarks on Data
Thus, despite N,N-dimethylacetamide not showing hydrogen-bonding and having a lower $M$ than butanoic acid, it has a higher BP. The value quoted on Wikipedia seems to be the lower end of the range.
The next step was to check for $\mu$, which, according to Reference 1, is 3.7D and 1.65D for N,N-dimethylacetamide and butanoic acid, respectively.
At this point, I could tell you that the deciding factor for this BP anomaly is the large difference in the dipole moments. But, who am I to decide the deciding factors. Although, $\mu$ is probably going to be major factor in determining the BPs, for accuracy, we must consider other factors such as molecular structure as well. The problem is, even the most accurate methods show up to $10\%$ error, and our difference in BPs ($\approx \pu{1.5 ^\circ C}$) is about $0.9\%$ of the values. Thus, our best efforts might just not be fruitful.
QSPR Approach
Quantity-structure property relation (QSPR$^\text{2}$) is a broad field which aims to predict a physical/chemical quantity (property) by looking at the structure of the molecule. There are numerous, specific and generalized, QSPR methods, but I am going to create a simple model here. I will consider a series of amides and carboxylic acids/esters. Our response variable, which I am trying to predict, will be BP, where, if a range is provided, I have used the lower value. Our predictor variables, which we use for predicting the response variable, will be the following:
- Molecular weight ($M$)
- Dipole moment ($\mu$)
- N-substitution ($N_s$)
- O-substitution ($O_s$)
Variables 3 and 4 account for hydrogen bonding. I constructed a multilinear regression model. I have used Reference 1 for all the data; where data is missing, I have used PubChem.
Data
Visualization
The model I have used is:
$$
\begin{align}
\text{BP} =& + 2.03M + 108.63\mu-49.48N_s-90.84O_s \\
&-0.15M*\mu -9.01\mu^2 -141.16 \tag{1}
\end{align}
$$
$$
r^2 = 0.97
$$
$$
\text{BP}_\text{predicted}\text{(N,N-dimethylethanamide)} = \pu{166.97 ^\circ C}\\
\text{BP}_\text{predicted}\text{(butanoic acid)} = \pu{170.61 ^\circ C}
$$
Inferences
$r^2 = 0.97$ is not bad at all, especially for such a simple model. From Equation (1), we see that boiling points are dependent on all factors that we considered contribute to the BP of the compound. The coefficients for $\mu$, $N_s$, and $O_s$ are large because the values are smaller compared to values of $M$, for which the coefficient is small. However, this doesn't imply that any one factor is more decisive than the other, all factors must be considered for an accurate prediction. However, the following can be inferred from these results.
- BP increases with $M$ and $\mu$.
- BP decreases with $N_s$ and $O_s$.
Reason for the first inference is that intermolecular interactions increase with increasing $M$ and $\mu$ (the latter commonly known as dipole-dipole interactions).
Reason for the second inference is that hydrogen bonding decreases with increasing substitution on the $\ce{N}$ of amides and $\ce{O}$ of carboxylic acids; accordingly, BP decreases.
References
- Haynes, W. M. (2017), CRC Handbook of Chemistry and Physics, 97$^\text{th}$ edition.
- Roy, K, Kar, S., Das R. N. (2015). A Primer on QSAR/QSPR Modeling: Fundamental Concepts.
