A mixture of H_2(g) and N_2(g) has a density of 0.216 g/L at 300 K. and 6.667 mi

Question

A mixture of H_2(g) and N_2(g) has a density of 0.216 g/L at 300 K. and 6.667 middot 10^4 Pa. What is the mole fraction composition of the mixture? Use M_H2 = 2.01588 g middot moil^-1 and M_N2 = 28.01348 g-mol^-1. Kinetic Theory of Gases Consider a vacuum apparatus consisting of a cubic chamber with length 0.2 m. Assume that the apparatus is filled with N_2(g). Estimate an upper limit for the pressure in the apparatus (in mbar) if molecules have on average more collisions with the wall than with each other at 300 K. Determine the ratio of the mean speeds of He and Hg atoms at 25 degree C. Consider a very thin metallic film. The conduction electrons in the film can be described as a gas confined to two dimensions. Calculate the distribution of speeds of this gas and the mean speed at temperature T. Using the kinetic theory of gases, show that the mean kinetic energy of a gas 3 molecule is given by (E_kln) = 3/2 kT, independent of molecular mass.

Explanation / Answer

(g)

suppose there are n1 moles of H2 and n2 moles of N2.

then total number of moles = n1 + n2

Applying Gas equation,

P V = n R T

(6.667 x 10^4) (V ) = n (8.314) (300)

n / V = 26.73 moles / m^3

in 1 m^3 -> 26.73 moles

in 1000 L -> 26.73 moles

in 1 L -> 0.02673 moles.

hence n1 + n2 = 0.02673

n1 = 0.02673 - n2 .....(i)

mass of gas in 1L = 0.216 g

2.01588n1 + 28.01348n2 = 0.216 .....(ii)

2.0158 ( 0.02673 - n2) + 28.01348 n2 = 0.216

n2 = 6.236 x 10^-3 moles

n1 = 0.0205

mole fraction of H2 = n1 / (n1 + n2) = 0,767

mole fraction of N2 = n2 / (n1 + n2) = 0.233

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