Chapter 13, Problem 13.34P

(a)

Interpretation Introduction

Interpretation:

Whether ${\text{Na}}^{+}$ or ${\text{Cs}}^{+}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{Na}}^{+}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

Both sodium and cesium are present in the same period of the periodic table. But sodium lies above cesium so its ionic volume is less than that of cesium and therefore ${\text{Na}}^{+}$ will have higher charge density than that of ${\text{Cs}}^{+}$. So $\Delta H_{\text{hydration}}$ of ${\text{Na}}^{+}$ is more than that of ${\text{Cs}}^{+}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(b)

Interpretation Introduction

Interpretation:

Whether ${\text{Sr}}^{2+}$ or ${\text{Rb}}^{+}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{Sr}}^{2+}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

Both rubidium and strontium are present in the same period of the periodic table. But strontium lies to the right of rubidium so its size and therefore volume are small. Also, the charge on ${\text{Sr}}^{2+}$ is more than that of ${\text{Rb}}^{+}$. So the charge density of ${\text{Sr}}^{2+}$ is more than that of ${\text{Rb}}^{+}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{Sr}}^{2+}$ is more than that of ${\text{Rb}}^{+}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(c)

Interpretation Introduction

Interpretation:

Whether ${\text{Na}}^{+}$ or ${\text{Cl}}^{-}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{Na}}^{+}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

Both sodium and chlorine are present in the same period of the periodic table. But cations are smaller than anions so the charge density of ${\text{Na}}^{+}$ is greater than that of ${\text{Cl}}^{-}$ and $\Delta H_{\text{hydration}}$ of ${\text{Na}}^{+}$ is greater than that of ${\text{Cl}}^{-}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(d)

Interpretation Introduction

Interpretation:

Whether ${\text{O}}^{2-}$ or ${\text{F}}^{-}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{O}}^{2-}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

${\text{O}}^{2-}$ has a greater ionic charge as compared to ${\text{F}}^{-}$. But both the ions have similar ionic volume. So ${\text{O}}^{2-}$ will have a higher charge density than that of ${\text{F}}^{-}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{O}}^{2-}$ is greater than that of ${\text{F}}^{-}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(e)

Interpretation Introduction

Interpretation:

Whether ${\text{OH}}^{-}$ or ${\text{SH}}^{-}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{OH}}^{-}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

Oxygen and sulfur are present in the same group of the periodic table. But oxygen lies above sulfur so its size and therefore volume is smaller than that of sulfur. So the charge density of ${\text{OH}}^{-}$ is larger than that of ${\text{SH}}^{-}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{OH}}^{-}$ is greater than that of ${\text{SH}}^{-}$

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(f)

Interpretation Introduction

Interpretation:

Whether ${\text{Mg}}^{2+}$ or ${\text{Ba}}^{2+}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{Mg}}^{2+}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

Magnesium and barium are present in the same group of the periodic table. But magnesium lies above barium so its size, as well as volume, is smaller than that of barium. So the charge density of ${\text{Mg}}^{2+}$ is greater than that of ${\text{Ba}}^{2+}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{Mg}}^{2+}$ is greater than that of ${\text{Ba}}^{2+}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(g)

Interpretation Introduction

Interpretation:

Whether ${\text{Mg}}^{2+}$ or ${\text{Na}}^{+}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{Mg}}^{2+}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

The ionic charge of ${\text{Mg}}^{2+}$ is greater than that of ${\text{Na}}^{+}$. Also, the volume of ${\text{Mg}}^{2+}$ is also smaller than that of ${\text{Na}}^{+}$. So the charge density of ${\text{Mg}}^{2+}$ is greater than that of ${\text{Na}}^{+}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{Mg}}^{2+}$ is greater than that of ${\text{Na}}^{+}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.

(h)

Interpretation Introduction

Interpretation:

Whether ${\text{CO}}_3^{2-}$ or ${\text{NO}}_3^{-}$ has greater $\Delta H_{\text{hydration}}$ 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 13.34P

${\text{CO}}_3^{2-}$ will have a greater $\Delta H_{\text{hydration}}$.

Explanation of Solution

The ionic charge of ${\text{CO}}_3^{2-}$ is greater than that of ${\text{NO}}_3^{-}$. Also, the volume of ${\text{CO}}_3^{2-}$ is also smaller than that of ${\text{NO}}_3^{-}$. So the charge density of ${\text{CO}}_3^{2-}$ is greater than that of ${\text{NO}}_3^{-}$ and therefore $\Delta H_{\text{hydration}}$ of ${\text{CO}}_3^{2-}$ is greater than that of ${\text{NO}}_3^{-}$.

Conclusion

$\Delta H_{\text{hydration}}$ depends on the charge density of the ions.