Question

A 1.00 L sample of dry air at 25 degree C and 786 mm Hg contains 0.925 g N_2 plus other gases including oxygen, argon, and carbon dioxide. A. What is the partial pressure (in mm Hg) of N_2 in the air sample? B. What is the mole fraction and mole percent of N_2 in the mixture? (Daltons law of partial pressures) Calculate the rms speed of O_2 molecules in a tank at 21 degree C and 15.7 atm.

Answer 1

using ideal gas equation ....we have

PV =nRT

n =PV/RT

n = (786/760) X 1.00 / 0.0821 X 298

= 0.04227

and given that moles of N2 present = 0.925/ 28

= 0.0330

hence excess moles ar ethe mole of other gases present ..that is ..0.04227 - 0.0330

= 0.00923 moles

or moles fraction of N2 = moles of N2 / total moles

= 0.0330/ 0.04227

= 0.7806

or acc to daltons partial pressure law

pN2 = XN2 X Ptotal

= 0.7806 X 786

= 613.62 mm of Hg

2)

rms =( 3RT/M)^0.5

R = 8.314 ; T = 273+ 21 = 294 k

M = 0.032 kg

hence we have

(3X 8.314 X 294 / 0.032)^0.5

= 478.7 m/s