Q. 625.0( 1 Vote )

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.

Answer :

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.


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