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.

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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