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Chapter 12: Problem 39

Cyclohexanol has a vapor pressure of \(10.0 \mathrm{mmHg}\) at \(56.0^{\circ} \mathrm{C}\) and \(100.0 \mathrm{mmHg}\) at \(103.7^{\circ} \mathrm{C} .\) Calculate its enthalpy of vaporization, \(\Delta H_{\mathrm{vap}}\)

Short Answer

Expert verified
\(\Delta H_{\mathrm{vap}} \approx 41\,454 \, J/mol\).

Step by step solution

01

Converting Temperatures to Kelvin

Firstly, temperatures need to be converted from degrees Celsius to Kelvin. This can be done by adding 273.15 to the Celsius temperature. Therefore, \(T1 = 56.0 + 273.15 = 329.15K\) and \(T2 = 103.7 + 273.15 = 376.85K\).
02

Rearranging the Clausius-Clapeyron Equation

We rearrange the Clausius-Clapeyron equation to isolate \(\Delta H_{\mathrm{vap}}\): \(\Delta H_{\mathrm{vap}} = -R\left(\frac{1}{T2} - \frac{1}{T1}\right) / \ln\left(\frac{P2}{P1}\right)\). We express the pressures in the same units as the constant R (which is in atmospheres), so we have \(P1 = 10.0\,mmHg/760 = 0.01316 \, atmospheres\) and \(P2 = 100.0\,mmHg/760 = 0.1316 \, atmospheres\).
03

Substitution and Calculation

Substitute the values into the rearranged equation: \(\Delta H_{\mathrm{vap}} = - 8.314 \, J/(K \cdot mol) \cdot [(1/376.85 - 1/329.15) / \ln (0.1316/0.01316)]\). After performing the operations, you will find \(\Delta H_{\mathrm{vap}} \approx 41\,454 \, J/mol\).

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Most popular questions from this chapter

Trace the phase changes that occur as a sample of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}),\) originally at \(1.00 \mathrm{mmHg}\) and \(-0.10^{\circ} \mathrm{C},\) is compressed at constant temperature until the pressure reaches 100 atm.

Determine the lattice energy of \(\mathrm{KF}(\mathrm{s})\) from the following data: \(\Delta \mathrm{H}_{\mathrm{f}}[\mathrm{KF}(\mathrm{s})]=-567.3 \mathrm{kJ} \mathrm{mol}^{-1} ;\) enthalpy of sub- limation of \(\mathrm{K}(\mathrm{s}), 89.24 \mathrm{kJ} \mathrm{mol}^{-1} ;\) enthalpy of dissociation of \(\mathrm{F}_{2}(\mathrm{g}), 159 \mathrm{kJ} \mathrm{mol}^{-1} \mathrm{F}_{2} ; I_{1}\) for \(\mathrm{K}(\mathrm{g}), 418.9 \mathrm{kJmol}^{-1}\) EA for \(\mathrm{F}(\mathrm{g}),-328 \mathrm{kJ} \mathrm{mol}^{-1}\)

Explain why vaporization occurs only at the surface of a liquid until the boiling point temperature is reached. That is, why does vapor not form throughout the liquid at all temperatures?

Argon, copper, sodium chloride, and carbon dioxide all crystallize in the fcc structure. How can this be when their physical properties are so different?

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