Chapter 6, Problem 6.26E

(a)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is valid for the sublimation ice in your freezer.

Explanation of Solution

Sublimation is a process in which the substance in a solid state is directly converted into a vapor state without going through the liquid state. The sublimation of ice consists of a gas phase and is at a normal pressure. Therefore, the Clausius-Clapeyron equation is valid.

Conclusion

Yes, the Clausius-Clapeyron equation is applicable to the given phase transition.

(b)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is valid for the condensation of steam into water.

Explanation of Solution

Condensation is defined as the phase change from the gaseous phase to the liquid phase. The condensation of steam involves a gas phase and at extreme pressure, it is not specified. Therefore, the Clausius-Clapeyron equation is valid.

Conclusion

Yes, the Clausius-Clapeyron equation is applicable to the given phase transition.

(c)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is not valid for the freezing of cyclohexane at $6.{\text{5 }}^{\text{ο}}\text{C}$.

Explanation of Solution

Freezing of cyclohexane at $6.{\text{5 }}^{\text{ο}}\text{C}$ is solid-liquid equilibrium. It does not involve gas phase. Therefore, the absence of gas phase causes the assumption of ideal gas behaviour to fail. Hence, the Clausius-Clapeyron equation is not valid.

Conclusion

No, the Clausius-Clapeyron equation is not valid to the given phase transition.

(d)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is not valid for the conversion of ice V to ice VI.

Explanation of Solution

The conversion of ice V to ice VI takes place at a pressure greater than $600\text{0 bar}$. Therefore, the assumption of ideal gas behaviour fails. Hence, the Clausius-Clapeyron equation is not valid.

Conclusion

No, the Clausius-Clapeyron equation is not valid to the given phase transition.

(e)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is not valid for the conversion of diatomic oxygen, ${\text{O}}_{\text{2}}\left(\text{g}\right)$, to triatomic ozone, ${\text{O}}_3\left(\text{g}\right)$.

Explanation of Solution

The conversion of diatomic oxygen, ${\text{O}}_{\text{2}}\left(\text{g}\right)$, to triatomic ozone, ${\text{O}}_3\left(\text{g}\right)$ consists of only gaseous phases. Due to the absence of a condensed liquid or solid phase, the Clausius-Clapeyron equation is not valid.

Conclusion

No, the Clausius-Clapeyron equation is not valid to the given phase transition.

(f)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is not valid for the formation of diamonds under pressure.

Explanation of Solution

The formation of diamonds takes place under a high pressure that does not involve the gas phase. Therefore, the assumption of ideal gas behaviour fails. Hence, the Clausius-Clapeyron equation is not valid.

Conclusion

No, the Clausius-Clapeyron equation is not valid to the given phase transition.

(g)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is not valid for the formation of metallic solid hydrogen, ${\text{H}}_{\text{2}}$, from liquid hydrogen.

Explanation of Solution

The formation of metallic solid hydrogen, ${\text{H}}_{\text{2}}$, from liquid hydrogen takes place under megabars of pressure. Therefore, the assumption of ideal gas behaviour fails. Hence, the Clausius-Clapeyron equation is not valid.

Conclusion

No, the Clausius-Clapeyron equation is not valid to the given phase transition.

(h)

Interpretation Introduction

Interpretation:

If the Clausius-Clapeyron equation is strictly applicable to the given phase transitions is to be predicted.

Concept introduction:

The clausius-clapeyron equation states the relation between vapor pressure and the absolute temperature. It is derived by using some assumptions like the ideal gas behaviour and the change in volume of phases is equal to the volume of gas phase.

Some another assumptions include non-varying enthalpy and entropy of transition values. At high pressure, near the critical point and over range of large temperature, these assumptions get failed.

Answer to Problem 6.26E

The Clausius-Clapeyron equation is valid for the evaporation of mercury liquid, $\text{Hg}\left(l\right)$, from a broken thermometer.

Explanation of Solution

The evaporation of mercury liquid, $\text{Hg}\left(l\right)$, from a broken thermometer consists of a gas phase and is at a normal pressure conditions. Therefore, the Clausius-Clapeyron equation is valid.

Conclusion

Yes, the Clausius-Clapeyron equation is applicable to the given phase transition.