A bucket full of water is paced in a room at 15°C with initial relative humidity 40%. The volume of the room is 50 cm³.

(a) How much water will evaporate?

(b) If the room temperature is increased by 5°C, how much more water will evaporate? The saturation vapor pressure of water at 15°C and 20°C are 1.6 kPa and 2.4 kPa respectively.

Given

Temperature =15

Relative humidity=40%

Volume =50cm³

Molar mass of H₂O M=2+16=18g.

We know ideal gas equation

PV=nRT

Where V= volume of gas

R=gas constant =8.3JK^-1mol^-1

T=temperature

n=number of moles of gas

P=pressure of gas.

The saturation vapor pressure (SVP)of water at 15°C=1.6kPa=1.610³Pa.

P=0.41.610³Pa

Evaporation will occur if the atmosphere is not saturated.

Net pressure change= SVP-P

P’ =1.6103-0.41.610³=0.9610³Pa

Number of moles n=

Applying equation of ideal gas.

The amount of water that will evaporate=361g

(b)

SVP at 20=2.4kPa

SVP at 15=1.6kPa

Net pressure changes in increasing the temperature,

Net pressure changes P’’=2.4-1.6=0.8kPa=0.8Pa.

Applying equation of ideal gas.

So, if the room temperature is increased by 5°C, the amount of water will evaporate is 296g.