A V 10-3 m3 chamber of a gas bottle contains some argon gas (atomic weight 0.040

Question

A V 10-3 m3 chamber of a gas bottle contains some argon gas (atomic weight 0.040 kg/mole) at a pressure of 105 Pa and a temperature of 31° C. 1) What is the number density of atoms in this chamber? N/V atoms/m3 Submit Help 2) A valve to a new chamber in the bottle is opened, and the gas expands to 4 x 103 m3. (The gas does no work in this process because the gas molecules don't have anything moving to push on.) After a while, the parts of the gas re equilibrate, without exchanging heat with the outside. What is the new temperature, T? Submit Help Pa Submit Help

Explanation / Answer

Given,

Vi = 10^-3 m^3 ; P = 10^5 Pa; T = 31 deg C

1)we know that

PV = n R T =. n = PV/RT

n = (9.87 x 10^-6 x 10^5)(10^-3)/(0.0821 x 304) = 3.9 x 10^-5

N = 3.9 x 10^-5 x 6.023 x 10^23 = 2.35 x 10^19

N/V = 2.35 x 10^19/10^-3 = 2.35 x 10^22 atoms/m^3

Hence, N/V = 2.35 x 10^22 atoms/m^3

2)T = 31 deg C

remains same since there is no transfer of heat energy in the given system

3)We know that

P1V1 = P2V2

P2 = P1 (V1/V2)

P2 = 10^5 x (10^-3/4 x 10^-3) = 2.5 x 10^4 Pa

Hence, P2 = 2.5 x 10^4 Pa

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