Question

For the given compound Choose the correct option(s). (A) If \(\mathrm{R}_{1}=\mathrm{CH}_{3}, \mathrm{R}_{2}=\mathrm{H}, \mathrm{R}_{3}=\mathrm{CH}_{3}\), then \(K_{\mathrm{eq}}>1\) (B) If \(\mathrm{R}_{1}=\mathrm{CH}_{2}-\mathrm{CH}_{3}, \mathrm{R}_{2}=\mathrm{H}, \mathrm{R}_{3}=\mathrm{CH}_{3}\), then \(K_{\mathrm{eq}}<1\) (C) If \(R_{1}=\mathrm{Cl}, \mathrm{R}_{2}=\mathrm{Br}, \mathrm{R}_{3}=\mathrm{H}\), then \(K_{\mathrm{eq}}<1\) (D) If \(\mathrm{R}_{1}=\mathrm{CH}_{3}, \mathrm{R}_{2}=\mathrm{CH}_{3}, \mathrm{R}_{3}=-\mathrm{CH}_{2}-\mathrm{CH}_{3}\), then \(K_{\text {eq }}<1\)

Short answer

The short answer is: The correct options are (A) and (C).

Step-by-step solution

Analyze the effects of substituents

When analyzing the effects of substituents, we can look at their inductive effect, which could either be electron-donating or electron-withdrawing. Electron-donating groups (EDG) tend to stabilize the molecule and increase Keq, while electron-withdrawing groups (EWG) cause destabilization and decrease Keq. Now let's examine each option and consider the effects of the substituents.

Option (A)

In this case, R1 = CH3 (an electron-donating group), R2 = H (neutral), and R3 = CH3 (an electron-donating group). The presence of two electron-donating groups favors the formation of products, so we can expect that Keq > 1. Therefore, Option (A) is correct.

Option (B)

In this case, R1 = CH2-CH3 (an electron-donating group), R2 = H (neutral), and R3 = CH3 (an electron-donating group). Just like in option (A), the presence of two electron-donating groups favors the formation of products. Thus, in this case, Keq should be greater than 1, not less as stated. So, Option (B) is incorrect.

Option (C)

In this case, R1 = Cl (an electron-withdrawing group), R2 = Br (an electron-withdrawing group), and R3 = H (neutral). The presence of two electron-withdrawing groups favors the formation of reactants. So, we can expect that Keq < 1. Therefore, Option (C) is correct.

Option (D)

In this case, R1 = CH3 (an electron-donating group), R2 = CH3 (an electron-donating group), and R3 = -CH2-CH3 (an electron-donating group). Here, we have three electron-donating groups, which favor the formation of products. Thus, in this case, Keq should be greater than 1, not less as stated. So, Option (D) is incorrect. In conclusion, the correct options are (A) and (C).

Key concepts

Equilibrium Constant (Keq)

The equilibrium constant, abbreviated as \( K_{\mathrm{eq}} \), is a fundamental concept in chemistry that describes the ratio of the concentrations of products to reactants at equilibrium. When a reaction reaches equilibrium, it means that the rate of the forward reaction is equal to the rate of the backward reaction. However, this does not necessarily imply that the amounts of reactants and products are the same. Instead, \( K_{\mathrm{eq}} \) provides a measure of the position of equilibrium.
If \( K_{\mathrm{eq}} > 1 \), the reaction tends to favor the formation of products, suggesting that at equilibrium, the concentration of products is greater than that of reactants. Conversely, if \( K_{\mathrm{eq}} < 1 \), the reactants are favored, and their concentration is higher at equilibrium. The value of \( K_{\mathrm{eq}} \) can be influenced by factors such as temperature and the nature of substituents in the molecules involved.
The concept of \( K_{\mathrm{eq}} \) is also crucial in predicting the direction of a chemical reaction. If a system is not at equilibrium, comparing the reaction quotient \( Q \) with \( K_{\mathrm{eq}} \) can indicate which way the reaction will proceed to achieve equilibrium. This makes \( K_{\mathrm{eq}} \) not just a static snapshot of a reaction's status, but a dynamic tool to understand chemical processes.

Electron-Donating Groups (EDG)

Electron-donating groups (EDG) are groups of atoms that release electrons towards other parts of a molecule through both inductive and resonance effects. By releasing electrons, these groups help to stabilize positive charges within molecules, often making the compounds more reactive towards specific reactions where electron density is crucial.
EDGs generally include alkyl groups, such as methyl (\(\mathrm{CH}_3\)) or ethyl (\(\mathrm{CH}_2\)-\(\mathrm{CH}_3\)), because they push electron density towards other atoms due to their less electronegative nature. This can stabilize a cation or positively charged center in a reaction, shifting the equilibrium towards more product formation, thereby increasing \( K_{\mathrm{eq}} \).

• Examples of EDGs: Alkyl groups, methoxy (\(\mathrm{OCH}_3\)), and amino groups (\(\mathrm{NH}_2\)).
• Impact: Stabilizes molecules, increases product formation.

Understanding the influence of EDGs is particularly important when predicting the behavior of chemical reactions and designing compounds for specific purposes, such as in pharmaceuticals or catalysis.

Electron-Withdrawing Groups (EWG)

In contrast to EDG, electron-withdrawing groups (EWG) pull electrons away from other parts of a molecule. This often results in the destabilization of positive charges and reduces the overall electron density, making the molecule less reactive and frequently more stable than molecules with many electron-donating groups would be.
Common EWGs include halogens like chlorine (\(\mathrm{Cl}\)) and bromine (\(\mathrm{Br}\)), as they are more electronegative and attract electrons towards themselves, effectively lowering the electron density on adjacent atoms. This effect usually results in a preference for the reactants rather than the products, thereby decreasing \( K_{\mathrm{eq}} \).
By decreasing the electron density, EWGs play a critical role in stabilizing carbanions and anions. Their presence is often leveraged in organic chemistry to control the direction and outcome of chemical reactions.

• Examples of EWGs: Nitro (\(\mathrm{NO}_2\)), carbonyl groups (\(\mathrm{C}=\mathrm{O}\)), and halogens.
• Impact: Favors reactant formation, decreases product formation.

Knowledge of EWGs is invaluable for chemists when predicting reaction mechanisms and in the design of synthetic pathways.