Use vapor pressure.

A student leaving campus for spring break wants to make sure the air in his dorm room has a high water vapor pressure so that his plants are comfortable. The dorm room measures $3\mathrm{.}18m4\mathrm{.}36m3\mathrm{.}99m$ and the student places a pan containing $0\mathrm{.}792L$ of water in the room. Assume that the room is airtight, that there is no water vapor in the air when he closes the door, and that the temperature remains a constant $23C.$ The vapor pressure of water at $23C$ is $21\mathrm{.}1mmHg.$

$($a$)$ Calculate the pressure that the water vapor would exert if all of the liquid water evaporated.

$mmHg$

$($b$)$ Will all of the water in the pan evaporate?