The heat of vaporization of water at the normal boiling point, 373.2 K, is 40.66 kJ/mol. The molar heat capacity of liquid water is 75.37 J K-1 mol-1 and that of gaseous water is 36.4 J K-1 mol-1. Assume that these values are independent of temperature. What is the heat of vaporization of water at 300.2 K?

Explanation:

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In this case, according to the Kirchhoff's law for the enthalpy change, it is possible to compute the heat of vaporization at 300.2 K by considering the following thermodynamic route:

Whereas the first term stands for the effect of taking the liquid from 298.15 K to 373.15 K, the second term stands for the standard enthalpy of vaporization and the last term that of the vapor from the boiling point to 300.2 K; thus we plug in to obtain:

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there are two significant figures.