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A greenhouse contains256m3of air at a temperature of26°C, and a humidifier in it vaporizes 4.20 L of water.

(a) What is the pressure of water vapor in the greenhouse, assuming that none escapes and that the air was originally completely dry (d ofH2O= 1.00 g/mL)?

(b) What total volume of liquid water would have to be vaporized to saturate the air (i.e., achieve100% relative humidity)? (See Table 5.4, p. 221.)

Short Answer

Expert verified
  1. The pressure of water vapour in the greenhouse is 0.22atm.
  2. Total volume of liquid water that would have to be vaporized to saturate the air is 1.6×10-7.

Step by step solution

01

Subpart (a) The pressure of water vapor in the greenhouse.

Given,

The temperature =26oC=299k.

Volumeofthewater=4.2L1L=1000mLVolumeofthewater=4.20L×1000mL1L

Density of H2O=1.00g/mL

As,

NumberofMoles=MassMolarMass

And,

Density=MassVolume

²Ñ²¹²õ²õ=³Õ´Ç±ô³Ü³¾±ð×¶Ù±ð²Ô²õ¾±³Ù²â

Therefore,

±·³Ü³¾²ú±ð°ù o´Ú â¶Ä‰M´Ç±ô±ð²õ=4.20³¢Ã—1000mL1L×1.00²µ/³¾³¢18g/mole

As,

Gas Constant, R=0.0821Latm/k/mole

Then, the pressure at temperature =26oC=299k.

PV=nRT

Therefore,

P=n×R×TP=4.20×1000mL1L×1.00g/mL18.02g/mL256m3×1000L1m3×(0.0821Latm/mol/k)×(299k)P=233.07×24.55P=0.022atm

02

Subpart (b) The total volume of liquid water would have to be vaporized to saturate the air. 

The Absolute Humidity as the saturated air with water vapour.

AbsoluteHumidity=Pressure³Ò²¹²õ C´Ç²õ²Ô³Ù²¹²Ô³Ù o´Ú W²¹³Ù±ð°ùװձ𳾱è±ð°ù²¹³Ù³Ü°ù±ðAbsoluteHumidity=0.022atm461.5×299°ì´¡²ú²õ´Ç±ô³Ü³Ù±ð±á³Ü³¾¾±»å¾±³Ù²â=1.6×10-7

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