# 8.5: Chapter 8 Problems


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(a) Find the standard boiling point of benzene.

(b) Use the Clausius–Clapeyron equation to evaluate the molar enthalpy of vaporization of benzene at $$298.15\K$$.

8.7
At a pressure of one atmosphere, water and steam are in equilibrium at $$99.97\units{\(\degC$$}\) (the normal boiling point of water). At this pressure and temperature, the water density is $$0.958\units{g cm\(^{-3}$$}\), the steam density is $$5.98\timesten{-4}\units{g cm\(^{-3}$$}\), and the molar enthalpy of vaporization is $$40.66\units{kJ mol\(^{-1}$$}\).

(a) Use the Clapeyron equation to calculate the slope $$\difp/\dif T$$ of the liquid–gas coexistence curve at this point.

(b) Repeat the calculation using the Clausius–Clapeyron equation.

(c) Use your results to estimate the standard boiling point of water. (Note: The experimental value is $$99.61\units{\(\degC$$}\).)

8.8
At the standard pressure of $$1\br$$, liquid and gaseous H$$_2$$O coexist in equilibrium at $$372.76\K$$, the standard boiling point of water.

(a) Do you expect the standard molar enthalpy of vaporization to have the same value as the molar enthalpy of vaporization at this temperature? Explain.

(b) The molar enthalpy of vaporization at $$372.76\K$$ has the value $$\Delsub{vap}H=40.67\units{kJ mol\(^{-1}$$}\). Estimate the value of $$\Delsub{vap}H\st$$ at this temperature with the help of Table 7.5 and the following data for the second virial coefficient of gaseous H$$_2$$O at $$372.76\K$$: $B=-4.60\timesten{-4}\units{m$$^3$$ mol$$^{-1}$$} \qquad \dif B/\dif T=3.4\timesten{-6}\units{m$$^3$$ K$$^{-1}$$ mol$$^{-1}$$}$

(c) Would you expect the values of $$\Delsub{fus}H$$ and $$\Delsub{fus}H\st$$ to be equal at the standard freezing point of water? Explain.

8.9
The standard boiling point of H$$_2$$O is $$99.61\units{\(\degC$$}\). The molar enthalpy of vaporization at this temperature is $$\Delsub{vap}H=40.67\units{kJ mol\(^{-1}$$}\). The molar heat capacity of the liquid at temperatures close to this value is given by \begin{equation*} \Cpm=a+b(t-c) \end{equation*} where $$t$$ is the Celsius temperature and the constants have the values $a=75.94\units{J K$$^{-1}$$ mol$$^{-1}$$} \qquad b = 0.022\units{J K$$^{-2}$$ mol$$^{-1}$$} \qquad c = 99.61\units{$$\degC$$}$ Suppose $$100.00\mol$$ of liquid H$$_2$$O is placed in a container maintained at a constant pressure of $$1\br$$, and is carefully heated to a temperature $$5.00\units{\(\degC$$}\) above the standard boiling point, resulting in an unstable phase of superheated water. If the container is enclosed with an adiabatic boundary and the system subsequently changes spontaneously to an equilibrium state, what amount of water will vaporize? (Hint: The temperature will drop to the standard boiling point, and the enthalpy change will be zero.)

8.5: Chapter 8 Problems is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Howard DeVoe via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.