Chapter 6, Problem 6.13E

Assume that the ${\Delta }_{\text{vap}}H$ of an evaporating liquid comes from the liquid itself, which then changes temperature according to equation ${\Delta }_{\text{vap}}H=-q=mc\Delta T$.

(a) Explain the presence of the negative sign in this equation.

(b) If $\text{1}\text{.00 g}$ of ${\text{H}}_{\text{2}}\text{O}$ evaporates at $\text{25}\text{.0°C}$ in an adiabatic container initially containing $\text{100}\text{.0 g}$ of ${\text{H}}_{\text{2}}\text{O}$, what is the final temperature of the water? Use $c=4.18\text{J}/\text{g}\text{°C}$ and ${\Delta }_{\text{vap}}H=43.99\text{kJ}/\text{mol}$ at $\text{25}\text{.0°C}$. The vapour pressure of ${\text{H}}_{\text{2}}\text{O}$ at $\text{25}\text{.0°C}$ is $\text{23}\text{.77 torr}$; assume it remains constant throughout the temperature change of liquid.