1. Ten grams of N 2 is mixed with 5g of O 2 and held at 25 o C and 0.75 bar. a)

Question

1. Ten grams of N2 is mixed with 5g of O2 and held at 25 oC and 0.75 bar. a) What are the partial pressures of N2 and O2? b) What is the volume of the ideal mixture?

2. Calculate the mean free path and the root mean square speed of 1 mol of air molecules at standar temperature and pressure ( 1 atm and 0 oC) Assume diameter of molecule is 3.0 x 10-10 m.

3. Determine the specific volume (in m3/kg) for carbon dioxide at 0oC and 625 kPa using (a) the Ideal Gas Law (b) the van der Waal Equation of State.

Explanation / Answer

1)

a) 10 g N2 is 10/28 = 0.357 moles

5/32 = 0.156 moles

mole fraction N2 = 0.357/(0.357+0.156) =0.696

mole fraction of O2 is 0.156/(0.357+0.156) = 0.304

Dalton’s Law of Partial Pressures can be used to calculate the partial pressure of any gas in a mixture if we know the total pressure and the number of moles of each gas

P1/Ptot = n1/ntot

Partial pressure of nitrogen = mole fraction of nitrogen x total pressure

= 0.696 x 0.75 bar = 0.522 bar

Partial pressure of oxygen = mole fraction of oxygen x total pressure

= 0.304 x 0.75 bar = 0.228 bar

b) PV = nRT

0.75 bar x V = (0.357+0.156) mol x 8.314 x 10-2 Lbar K1mol1 x 298K

V = 16.94 L

2) Mean free path in an ideal gas is given by
l = kT/(2d²p)
(k Boltzmann constant, T absolute temperature, d particle diameter,p pressure)

I = 1.38×10²³J/K (0 + 273)K / (2 (3×10¹m)² 101325) = 9.298 x 10-8 m

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