Chapter 15, Problem 15.60AP

Interpretation Introduction

(a)

Interpretation:

The dissociation constants for the complexes of $N-\text{methylquinolinium}$ and $4-\text{methylquinoline}$ with molecule $A$ in water are to be calculated.

Concept introduction:

The dissociation constant is the constant which tells the extent of dissociation of a particular species into its ions and is equal to the ratio of the product of dissociated ions to that of the undissociated molecule.

Answer to Problem 15.60AP

The dissociation constant for the complex of $N-\text{methylquinolinium}$ ion with a molecule $A$ in water is $\text{8}{\text{.59×10}}^{-\text{6}}$.

The dissociation constant for the complex of $4-\text{methylquinoline}$ with molecule $A$ in water is $\text{9}\text{.70}\times {\text{10}}^{-5}$.

Explanation of Solution

Free energy $\left(\text{Δ}G\right)$ is a thermodynamic state function which is used to calculate the maximum amount of work done by a thermodynamic system. The relation between free energy and the dissociation constant $\left(K\right)$ is given below.

$\Delta G°=-RT\ln K$ …(1)

Where,

• $R$ is the gas constant and it has a value of $8.314\text{J}{\text{mol}}^{-1}\text{K}$.

• $T$ is temperature and its value at standard conditions is taken as $298\text{ K}$.

• $K$ is the dissociation constant.

• $\Delta G°$ is standard free energy.

The standard free energy of the complex of $N-\text{methylquinolinium}$ ion with the molecule $A$ in water is $\text{28}\text{.9}\text{kJ}{\text{mol}}^{-\text{1}}$.

The structure of the complex of $N-\text{methylquinolinium}$ ion with a molecule $A$ in water is shown below.

Figure 1

Rearrange equation (1) and substitute the value of $\Delta G°$, $R$,$T$ as shown below.

$\begin{array}{rll}\Delta G°& =& -RT\ln K\\ \ln K& =& -\frac{\Delta G°}{RT}\\ & =& -\frac{28.9\times {10}^3}{8.314\times 298}\end{array}$

This equation can be simplified as shown below.

$\begin{array}{rll}K& =& -11.664\\ & =& e^{-11.664}\\ & =& \text{8}{\text{.59×10}}^{-\text{6}}\end{array}$

Therefore, the value of the dissociation constant for the complex is $\text{8}{\text{.59×10}}^{-\text{6}}$.

The standard free energy of the complex of $4-\text{methylquinoline}$ with molecule $A$ in water is $\text{22}\text{.2}\text{kJ}{\text{mol}}^{-\text{1}}$.

The structure of the complex of $4-\text{methylquinoline}$ with molecule $A$ in water is shown below.

Figure 2

Rearrange equation (1) and substitute the value of $\Delta G°$, $R$,$T$ as shown below.

$\begin{array}{rll}\Delta G°& =& -RT\ln K\\ \ln K& =& -\frac{\Delta G°}{RT}\\ & =& -\frac{22.9\times {10}^3}{8.314\times 298}\\ & =& -9.24\end{array}$

This equation can be simplified as shown below.

$\begin{array}{rll}K& =& e^{-9.24}\\ K& =& 9.70\times {10}^{-5}\end{array}$

Therefore, the value of the dissociation constant for the complex is $\text{9}\text{.70}\times {\text{10}}^{-5}$.

Conclusion

The dissociation constant for the complex of $N-\text{methylquinolinium}$ ion with the molecule $A$ in water is $\text{8}{\text{.59×10}}^{-\text{6}}$.

The dissociation constant for the complex of $4-\text{methylquinoline}$ with molecule $A$ in water is $\text{9}\text{.70}\times {\text{10}}^{-5}$.

Interpretation Introduction

(b)

Interpretation:

The reason corresponding to the strong binding of $N-\text{methylquinolinium}$ ion to $A$ is to be stated.

Concept introduction:

Interactions present between the aromatic ring and the cation are known as cation-pi interactions. This interaction is a noncovalent type of interaction which is present between a monopole (cation) and a quadrupole ($\text{π}$- system).

Answer to Problem 15.60AP

The reason corresponding to the stronger binding of $N-\text{methylquinolinium}$ ion to $A$ is the presence of cation-pi interactions.

Explanation of Solution

In organic chemistry, aromaticity is a property of cycloalkene molecules which leads to enhancement in the stability of the molecules. The system is said to be aromatic if it follows certain rules as given below.

• It follows Huckel’s $\text{4n+2}$ rule
• The system is conjugated.
• The ring is planar.

N-methylquinolinium ion is an aromatic system so cation-pi interactions are present in the ion. This interaction increases the affinity of the molecule towards $A$ for the formation of the complex. Whereas, no such interactions are seen in the neutral molecule $4-\text{methylquinoline}$.

Conclusion

The reason corresponding to the stronger binding of ion to $A$ is the presence of cation-pi interactions.

Interpretation Introduction

(c)

Interpretation:

The reason for the smaller value of the dissociation constant of complex of N-methylquinolinium with molecule $B$ than molecule $A$ is to be stated.

Concept introduction:

The dissociation constant $K$ is the constant which tells the extent of dissociation of a particular species into its ions.and is equal to the ratio of the product of dissociated ions to that of the undissociated molecule.

Answer to Problem 15.60AP

Due to the presence of ion-ion interactions the affinity of $N-\text{methylquinolinium}$ ion with $B$ increases and thus, the value of dissociation complex has a smaller value.

Explanation of Solution

Free energy $\left(\text{Δ}G\right)$ is a thermodynamic state function which is used to calculate the maximum amount of work done by a thermodynamic system. The relation between free energy and the dissociation constant $\left(K\right)$ is given below.

$\Delta G^o=-RT\ln K$ …(1)

Where,

• $R$ is the gas constant and it has a value of $8.314\text{J}{\text{mol}}^{-1}\text{K}$.

• $T$ is temperature and it has a value of $298\text{ K}$.

• $K$ is the dissociation constant.

• $\Delta G$ is standard free energy.

The standard free energy of the complex of $N-\text{methylquinolinium}$ ion with the molecule B is $35.2\text{kJ}{\text{mol}}^{\text{-1}}$.

Substitute the value of $\Delta G^o$, $R$, $T$ in equation 1.

The dissociation constant of the complex is calculated below.

$\begin{array}{rll}\Delta G°& =& -RT\ln K\\ \ln K& =& -\frac{\Delta G°}{RT}\\ & =& -\frac{35.2\times {10}^3}{8.314\times 298}\\ & =& -14.2\end{array}$

This equation can be simplified as shown below.

$\begin{array}{rll}K& =& e^{-14.2}\\ K& =& 6.76{\text{×10}}^{-7}\end{array}$

The value of dissociation complex of $N-\text{methylquinolinium}$ ion with the molecule $B$ is found to be less than that of the value of the $N-\text{methylquinolinium}$ ion with the molecule $A$ due to the presence of ion-ion interactions which increases the stability of the complex formed between molecule $B$ and $N-\text{methylquinolinium}$ ion and thereby, decreasing the value of the dissociation constant.

Conclusion

The ion-ion interaction present in complex formed by the molecule $B$ and $N-\text{methylquinolinium}$ ion is the reason behind the smaller value of dissociation complex.