The series of isodesmic reactions shown below has been...

The series of isodesmic reactions shown below has been calculated at the MP2/aug-cc-PVDZ level. The results are in good agreement with experimental gas phase proton affinity data. Data are also available for the $\mathrm{p} K_{a}$ of mono-, di-, and tri-cyanomethane. These data suggest substantially less cumulative drop-off as compared to an acetyl substituent. The first acetyl group causes a substantially larger increase in acidity, whereas the second acetyl has a smaller effect.$\begin{array}{ccccccc} & & & & & 0 & 0 \\ & \mathrm{CH}_{4} & \mathrm{CH}_{3} \mathrm{CN} & \mathrm{CH}_{2}(\mathrm{CN})_{2} & \mathrm{CH}(\mathrm{CN})_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{2} \mathrm{CCH}_{3} \\ \mathrm{pK} & 49.6 & 29.4 & 11.7 & -5.1 & 19.3 & 8.9\end{array}$ $\beta$-Cyano substituents also have a quite strong acidifying effect. A value of $29 \pm 6 \mathrm{kcal} / \mathrm{mol}$ has been estimated, as compared to $42 \mathrm{kcal} / \mathrm{mol}$ for $\alpha$-cyano. Structural computations find a shortening of the $\mathrm{C}(\alpha)$ - $\mathrm{CN}$ bond in $\alpha$-cyanoethyl anion but a lengthening of the $C(\beta)-C N$ bond in the $\beta$-cyanoethyl anion. What structural features of the CN might contribute to its anion stabilizing capacity, as compared with other EWG substituents such as acetyl.

The series of isodesmic reactions shown below has been calculated at the MP2/aug-cc-PVDZ level. The results are in good agreement with experimental gas phase proton affinity data.
Data are also available for the $\mathrm{p} K_{a}$ of mono-, di-, and tri-cyanomethane. These data suggest substantially less cumulative drop-off as compared to an acetyl substituent. The first acetyl group causes a substantially larger increase in acidity, whereas the second acetyl has a smaller effect.$\begin{array}{ccccccc} & & & & & 0 & 0 \\ & \mathrm{CH}_{4} & \mathrm{CH}_{3} \mathrm{CN} & \mathrm{CH}_{2}(\mathrm{CN})_{2} & \mathrm{CH}(\mathrm{CN})_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{3} & \mathrm{CH}_{3} \mathrm{CCH}_{2} \mathrm{CCH}_{3} \\ \mathrm{pK} & 49.6 & 29.4 & 11.7 & -5.1 & 19.3 & 8.9\end{array}$ $\beta$-Cyano substituents also have a quite strong acidifying effect. A value of $29 \pm 6 \mathrm{kcal} / \mathrm{mol}$ has been estimated, as compared to $42 \mathrm{kcal} / \mathrm{mol}$ for $\alpha$-cyano. Structural computations find a shortening of the $\mathrm{C}(\alpha)$ - $\mathrm{CN}$ bond in $\alpha$-cyanoethyl anion but a lengthening of the $C(\beta)-C N$ bond in the $\beta$-cyanoethyl anion. What structural features of the CN might contribute to its anion stabilizing capacity, as compared with other EWG substituents such as acetyl.

Key Concepts

Isodesmic Reactions

Isodesmic reactions are a type of theoretical reaction where the number and types of bonds broken are the same as those formed. This allows chemists to cancel out many of the systematic errors and focus on the effects of substituents or other structural details, making them particularly useful for dissecting subtle contributions to molecular stability and reaction energetics.

Proton Affinity and pKa

Proton affinity is a measure of how readily a molecule will accept a proton, while pKa quantitatively describes the acidity by indicating the equilibrium tendency of a compound to donate a proton. Both properties provide insights into the electronic characteristics of molecules and the influence of substituents on acid-base behavior, allowing for comparisons of reactivity across different chemical systems.

Electron-Withdrawing Groups (EWGs)

Electron-withdrawing groups are substituents that pull electron density away from the core of a molecule through inductive or resonance effects. This withdrawal of electron density can stabilize negative charges on adjacent atoms or groups, thereby influencing the overall acidity and reactivity of the molecule. Their ability to stabilize an anion is crucial in understanding trends in acid strength and the structure-activity relationship in organic compounds.

Substituent Effects on Acidity

Substituent effects on acidity refer to how different groups attached to a molecule can either enhance or reduce its acidic character. This occurs primarily through the induction of electron density redistribution via inductive and resonance interactions, leading to cumulative or diminishing impacts on a molecule's tendency to donate a proton. Analyzing these effects is important for predicting reactivity and designing molecules with tailored acid-base properties.

Computational Methods (MP2/aug-cc-PVDZ)

MP2/aug-cc-PVDZ is a computational method that combines Møller–Plesset perturbation theory with an augmented correlation-consistent double-zeta basis set. This method accurately accounts for electron correlation and is widely used in computational chemistry to predict molecular geometries, energies, and other properties. It provides essential theoretical validation for experimental results, helping to decipher the influence of substituents and structural features on molecular behavior.

Structural Features Influencing Anion Stability

Structural features such as bond lengths, bond polarities, and the spatial arrangement of atoms can significantly impact the stabilization of anions. Changes in these parameters can alter the extent of charge delocalization through resonance and the effectiveness of inductive stabilization. Understanding these structural aspects is key to rationalizing the differing capacities of substituents to stabilize negative charges in various chemical contexts.

Transcript

00:01 Chapter 14, question 122.

00:04 So i'm not going to read the entire question, but let's go one by one.

00:09 They give us a reaction over here.

00:12 Ch4 plus cl2, and this reaction is very slow in the absence of light.

00:19 With light, however, chlorine with the presence of light, you get two chlorine radicals.

00:27 So they don't show this as radicals over here, but what we normally see is chlorine fits an electron.

00:37 This single electron means that's a radical and this highly active.

00:43 So once the chlorine atoms are generated, they can catalyze the reaction of ch4 and cl2, according to the proposed mechanism.

00:51 They're given two reactions, reactions three and four.

00:55 And ch4 is becoming a ch3 radical with the chlorine catching up one of the hydrogens.

01:05 And ch3 radical is catching one of the chlorines and yielding a chlorine radical.

01:13 So what happens is this, this chlorine radical then again goes into the reaction with ch4 and chlorine then again goes.

01:22 So this is a typical catalyst where you see one of the molecules or atoms in this case, in the reactants and in the end of the products, so that can react again.

01:37 The enthalpy chains and activation energies for these two reactions are tabulated as follows.

01:43 By using the bond enthalpy for cl2 in table 8 .4, though i believe they want to say table 8 .3, because 8 .4 does not have anything with chlorine.

01:55 Determine the longest wavelength of light that is energetic enough to cause reaction to to occur.

02:02 So for this reaction two to occur, we need this light.

02:07 And what we need to do is if you can recall the formula, energy equals to h, c or lambda.

02:21 They're asking us the wavelength, lambda over here.

02:25 So let's remember what they were.

02:28 Energy is going to be in jules and h is planx constant.

02:40 That is 6 .626 times 10 to the power of negative 224 joules.

02:55 Second, c is going to be three times 10 to the power of 8 meters per seconds.

03:11 And we need to find the lambda using these two values.

03:16 And we also need the energy.

03:18 So let's look at the energy for chlorine.

03:23 It should be over here.

03:25 242.

03:26 This is kilojoules per moles.

03:28 So i'm going to adjust this.

03:30 As if you want jules.

03:35 So i'm going to multiply this by a thousand.

03:42 And if you solve for lambda, what you're going to get is units of meters, but you want to convert that to nanometers with a conversion factor of 10 to the power of negative 9.

04:00 So if you solve this equation, this equation over here, you're going to find lambda to be 494 nanometers.

04:15 So that was a.

04:20 And at b, using the data tabulated here, sketch a quantitative energy profile for the catalyzed reaction representing 3 and 4.

04:33 So we can do that, but let's make it a little bit more detailed by using the chapter the c2 by using bone energy bond etatopils estimate where the reactants should be placed on your diagram so let's just draw everything that is possible to be able to solve b and c together okay there's a graph and this is energy versus the reaction coordinate so if i want to look at the energy for ch4, i want to look at the entelope for ch.

05:24 This is 413.

05:28 So if i multiply this number, let's solve it over here.

05:35 413 times 4.

05:41 What we're going to get is 1 ,652.

05:51 So this is going to be energy of ch4.

05:57 Now, what else do we need? we don't have the energy for chlorine because there's no bond.

06:05 Over here, we have a ch3.

06:07 So for ch3, 413, multiply by 3.

06:16 And then we're going to add cl2, which is 242.

06:26 This is going to be equal to 100239.

06:33 These are in kilojoules per moles.

06:46 So now we can draw these two of them easily.

06:50 And let's write this was again for ch3 plus cl2.

07:01 So this first one is at a higher energy.

07:06 So let's start it from here.

07:09 And over here you can see the overall enthalpy is going to be a positive value so this is going to be endothermic and energy of activation is 17 so let's say i start from here go up 17 come down to a positive value so what we start with is going to be 100 1 ,652 plus 17 1669 this value plus 4 1 ,600 56.

07:55 Now this other value starts from lower and it goes up for 4 and comes down 109.

08:09 So it starts with thousand to a hundred thirty nine goes up to thousand to a hundred forty three and comes down to 1 ,130...

Please give Ace some feedback