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A physics lecture room has a volume of 237 m3. (a) For a gas pressure of...

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A physics lecture room has a volume of 237 m3. (a) For a gaspressure of 1.00 atm and a temperature of 26.0 oC, use the idealgas law to estimate the number of air molecules in the room. Assumeall the air is N2. (b) Calculate the particle density â that is,the number of N2 molecules per cubic centimeter. (c) Calculate themass of the air in the room.

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3.8 Ratings (673 Votes)

a) Moles of air molecules= PV/RT

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =1.00*237*10³/0.0821*299

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =9.655*10³ mol

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Molecules of air=9.655*10³*6.022*10²³=5.814*10²⁷ molecule

b) Molecule density= Molecules/ volume in cm³

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =5.814*10²⁷/237*10⁶

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =2.453*10¹⁹ molecule/cm³

c) Mass of air= moles of air*mol wt of N₂

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =9.655*10³*28

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =270.340 kg

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