Chapter 13, Problem 13.35P

(a)

Interpretation Introduction

Interpretation:

Whether ${\text{I}}^{-}$ or ${\text{Br}}^{-}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{I}}^{-}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

Both bromine and iodine are present in the same group of the periodic table. But iodine lies below bromine so it will have a large size and volume than that of bromine. So ${\text{I}}^{-}$ will have a lower ratio of charge to volume than that of ${\text{Br}}^{-}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(b)

Interpretation Introduction

Interpretation:

Whether ${\text{Sc}}^{3+}$ or ${\text{Ca}}^{2+}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{Ca}}^{2+}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The charge on ${\text{Ca}}^{2+}$ is less than that of ${\text{Sc}}^{3+}$. So ${\text{Ca}}^{2+}$ will have a lower ratio of charge to volume than that of ${\text{Sc}}^{3+}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(c)

Interpretation Introduction

Interpretation:

Whether ${\text{K}}^{+}$ or ${\text{Br}}^{-}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{Br}}^{-}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The anions are larger than cations so the ionic volume of ${\text{Br}}^{-}$ is more than that of ${\text{K}}^{+}$ and therefore ${\text{Br}}^{-}$ will have a lower ratio of charge to volume than that of ${\text{K}}^{+}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(d)

Interpretation Introduction

Interpretation:

Whether ${\text{Cl}}^{-}$ or ${\text{S}}^{2-}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{Cl}}^{-}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

${\text{Cl}}^{-}$ has a smaller ionic charge as compared to ${\text{S}}^{2-}$. So ${\text{Cl}}^{-}$ will have a lower ratio of charge to volume than that of ${\text{S}}^{2-}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(e)

Interpretation Introduction

Interpretation:

Whether ${\text{Sc}}^{3+}$ or ${\text{Al}}^{3+}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{Sc}}^{3+}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The size of scandium is larger than that of aluminium so ${\text{Sc}}^{3+}$ will have the larger volume as compared to that of ${\text{Al}}^{3+}$. So ${\text{Sc}}^{3+}$ will have a lower ratio of charge to volume than that of ${\text{Al}}^{3+}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(f)

Interpretation Introduction

Interpretation:

Whether ${\text{ClO}}_4^{-}$ or ${\text{SO}}_4^{2-}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{ClO}}_4^{-}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The charge on ${\text{ClO}}_4^{-}$ is less than that of ${\text{SO}}_4^{2-}$. So ${\text{ClO}}_4^{-}$ will have a lower ratio of charge to volume than that of ${\text{SO}}_4^{2-}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(g)

Interpretation Introduction

Interpretation:

Whether ${\text{Fe}}^{2+}$ or ${\text{Fe}}^{3+}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{Fe}}^{2+}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The ionic charge of ${\text{Fe}}^{2+}$ is less than that of ${\text{Fe}}^{3+}$. So the ratio of ionic charge to the volume of ${\text{Fe}}^{2+}$ will be lower than that of ${\text{Fe}}^{3+}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.

(h)

Interpretation Introduction

Interpretation:

Whether ${\text{K}}^{+}$ or ${\text{Ca}}^{2+}$ has smaller $\Delta H_{\text{hydration}}$ is to be determined.

Concept introduction:

The charge density is defined as the ratio of ionic charge and volume. It is directly proportional to the ionic charge and inversely proportional to the ionic volume. Volume is directly related to the ionic size. Smaller ion will have the charge spread over a small space so charge density will be more and vice-versa.

The enthalpy change of hydration is the enthalpy change when one mole of the ionic species is dissolved in water to give a solution of infinite dilution. It is represented by $\Delta H_{\text{hydration}}$. It is always negative.

$\Delta H_{\text{hydration}}$ is directly related to the charge density on an ion. Higher the charge density, more will be $\Delta H_{\text{hydration}}$ and vice-versa.

Answer to Problem 13.35P

${\text{K}}^{+}$ will have a smaller $\Delta H_{\text{hydration}}$.

Explanation of Solution

The ionic charge of ${\text{K}}^{+}$ is smaller than that of ${\text{Ca}}^{2+}$. So ${\text{K}}^{+}$ will have a lower ratio of charge to volume than that of ${\text{Ca}}^{2+}$ and therefore it has smaller $\Delta H_{\text{hydration}}$.

Conclusion

The species with a lower  ratio of ionic charge to volume has smaller $\Delta H_{\text{hydration}}$.