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According to Wikipedia, N,N-dimethylethanamide has a boiling point of $\pu{165.1 °C},$ while butanoic acid has a boiling point of $\pu{163.75 °C}.$

From what I learned, butanoic acid should have a higher boiling point than N,N-dimethylethanamide since it can undergo hydrogen bonding and form dimer structures, while N,N-dimethylethanamide, as a tertiary amide, cannot undergo hydrogen bonding. Butanoic acid even has a higher molecular mass than N,N-dimethylethanamide which also means it has greater dispersion forces.

All these factors indicate that butanoic acid should have a (much) higher boiling point than N,N-dimethylethanamide. Can someone explain the discrepancy in my reasoning and other (maybe more advanced or niche) factors that I have missed that can explain these boiling points?

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    $\begingroup$ It's just that you can't expect some "hydrogen bond beats dipole" rule to be an oracle. If you need a reason here, then I think the temperature gets high enough to seriously hamper the hydrogen bonding. $\endgroup$
    – Mithoron
    May 26, 2023 at 1:06
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    $\begingroup$ @Mithoron Sorry, I don't really get the" temperature gets high enough to seriously hamper the hydrogen bonding" part. Wouldn't this apply to all intermolecular bonds since, as temperature increases, the molecules have more kinetic energy and start spreading out, reducing the attraction of all intermolecular bonds? $\endgroup$ May 26, 2023 at 3:51
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    $\begingroup$ I knew it was a next thing to explain, but all in all, it rather needs rather long answer than comments and I don't feel like making it. pubs.acs.org/doi/10.1021/jp3062465; sciencedirect.com/science/article/abs/pii/S0378381214004105 $\endgroup$
    – Mithoron
    May 26, 2023 at 15:59
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    $\begingroup$ The bp’s are so close that a comparison is improbable. It is the equivalent of asking, “Do you walk to school or carry your lunch?”. $\endgroup$
    – user55119
    May 28, 2023 at 16:46
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    $\begingroup$ I dont think we can justify the rules of which substance out of 2 has the highest boiling temperature especially when the substances are so much different from each other... $\endgroup$
    – Volpina
    May 30, 2023 at 9:06

1 Answer 1

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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.

Property N,N-Dimethylacetamide Butanoic acid
Normal BP 165 to 166.1 °C 163.5 °C
Molecular weight $\pu{87.12 u}$ $\pu{88.11 u}$

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:

  1. Molecular weight ($M$)
  2. Dipole moment ($\mu$)
  3. N-substitution ($N_s$)
  4. 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

prediction of boiling points of substituted amides and carboxylic acids using multilinear regression

Visualization

predicted and actual boiling points of amides and carboxylic acids using multilinear regression

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.

  1. BP increases with $M$ and $\mu$.
  2. 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

  1. Haynes, W. M. (2017), CRC Handbook of Chemistry and Physics, 97$^\text{th}$ edition.
  2. Roy, K, Kar, S., Das R. N. (2015). A Primer on QSAR/QSPR Modeling: Fundamental Concepts.
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    $\begingroup$ Interesting modelling, but a couple of comments: (1) $r^2 = 0.97$ for 7 features and a training set of 15 is not really very impressive. It would be more interesting to see how the model generalises to data points outside the training set. (2) You need to scale your features to have the same range before you can draw any conclusions about which one is more important. $\endgroup$ May 29, 2023 at 11:39
  • $\begingroup$ @orthocresol that is true. Proper analysis would constitute a structure like those of research articles on machine learning, just pointing the OP to the right directions here. Afterall, it is just a simple model that I came up with, and it may not agree with other models out there. However, I will take your advice and modify the answer to include better features and a more comprehensive dataset with a test set as well. By the way, I thought I have only used four features. Do second order terms count as features? $\endgroup$
    – ananta
    May 29, 2023 at 11:46
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    $\begingroup$ PubChem isn't particularly reliable either - both are as good as their sources and these sources should be used instead. $\endgroup$
    – Mithoron
    May 29, 2023 at 15:22
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    $\begingroup$ Didn't you see PubChem cites sources much like Wikipedia? You can check them, at least in theory. $\endgroup$
    – Mithoron
    May 29, 2023 at 22:07
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    $\begingroup$ I think people do call them features, see e.g. scikit-learn.org/stable/modules/generated/… — although I should've been more accurate and said that your model has 7 parameters. The point is that these terms make your model more flexible. If you had 15 parameters you could fit the data perfectly. You have 7, it's easy to fit the data well. The model is fine, it's the data that is too small. Anyway, the scaling is a bigger issue. $N_s$ and $O_s$ are smaller numbers, so their coefficients will be larger. You can't draw conclusions from that. $\endgroup$ May 30, 2023 at 1:12

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