Suppose the vapor pressure of a substance is measured at two different temperatures. (a)

Chapter 18, Problem 11.84

(choose chapter or problem)

Suppose the vapor pressure of a substance is measured at two different temperatures. (a) By using the Clausius–Clapeyron equation (Equation 11.1) derive the following relationship between the vapor pressures, \(P_{1}\) and \(P_{2}\), and the absolute temperatures at which they were measured, \(T_{1}\) and \(T_{2}\) :

\(\ln \frac{P_{1}}{P_{2}}=-\frac{\Delta H_{\text {vap }}}{R}\left(\frac{1}{T_{1}}-\frac{1}{T_{2}}\right)\)

(b) Gasoline is a mixture of hydrocarbons, a major component of which is octane, \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}\).Octane has a vapor pressure of 13.95 torr at  \(25^{\circ} \mathrm{C}\) and a vapor pressure of 144.78 torr at \(75^{\circ} \mathrm{C}\). Use these data and the equation in part (a) to calculate the heat of vaporization of octane.(c) By using the equation in part (a) and the data given in part (b), calculate the normal boiling point of octane. Compare your answer to the one you obtained from Exercise 11.80. (d) Calculate the vapor pressure of octane at \(-30^{\circ} \mathrm{C}\).

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