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Chapter 12: Problem 81

The vapor pressure of liquid \(X\) is lower than that of liquid \(Y\) at \(20^{\circ} \mathrm{C}\), but higher at \(60^{\circ} \mathrm{C}\). What can you deduce about the relative magnitude of the molar heats of vaporization of \(X\) and \(Y ?\)

Short Answer

Expert verified
The molar heat of vaporization of \(X\) is smaller than that of \(Y\).

Step by step solution

01

Understanding the Vapor Pressure and Molar Heat of Vaporization

The vapor pressure of a liquid increases with increasing temperature. The rate at which it increases depends on the molar heat of vaporization of the liquid: the larger the molar heat, the slower vapor pressure rises with an increase in temperature.
02

Relating Vapor Pressure and Molar Heat of Vaporization

If at \(20^{\circ} \mathrm{C}\) \(X\) has a lower vapor pressure than \(Y\), and at \(60^{\circ} \mathrm{C}\) \(X\) has a higher vapor pressure, this indicates that the vapor pressure of \(X\) increases more rapidly with temperature than does the vapor pressure of \(Y\).
03

Deduction

From the above information, it can be deduced that the molar heat of vaporization of \(X\) is lower than \(Y\), because a lower molar heat of vaporization results in a faster increase in vapor pressure with temperature.

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