Question

three 6-L flasks filled with pressure gauges and small valves each contain 2 g of gas at 268K. Flask A contains H2 flask B contains CH4 and flask C contains He. Rank the flask contents in terms of :

pressure

average molecular kinetic energy

diffusion rate after valve is opened

total kinetic energy of the molecules

density

collision frequency

(please do in form of A>B>C)

Answer 1

We have given-

• 6-L flasks filled with pressure gauges
• 2 g of gas at 268K.
• Flask A contains H2
• flask B contains CH4
• flask C contains He.

​​​​​​​Pressure :

We have a relation of gas as :PV = nRT

n(number of.moles) = given mass(2g)/molecular mass(M)

P= pressure

V= volume (6L)

R= universal gas constant

T= Temperature 268 K

P = (given mass/M) × RT/V

=> P= (2 × R × 268 )/6×M

Only P depends upon M all other factors are same so,

Pressure is inversely proportional to Molar mass.

• Molar mass

H2 (2 g/mol) < He (4 g/mol) < CH4 (16 g/mol)

=> pressure is CH4 > He> H2

so, B>C>A.

Average molecular kinetic energy:

Kinetic energy: (1/2)mv2

Ekinetic energy is directly proportional to molar mass.

so,

A>C>B

Diffusion rate after valve open:

as diffusion rate depends upon density.

diffusion rate inversely proportional to density and density = mass/volume .

so,

Diffusion rate is inversely proportional to Molar mass

OR using Graham's law:

Rate1/Rate2 = (mass2/mass1)0.5

So, trend is CH4 > He > H2

then , B> C> A

Total kinetic energy of molecules:

given same temperature .

all molecules have equal total kinetic energy which depends upon temperature

A=B=C

Density:

density = mass/volume

here mass is molar mass.

so, density is proportional to molar mass.

=> A>C>B

Collision frequency:

collision frequency is inversely proportional to molar mass as:

Z(collision frequency) (8kBT/πM)0.5

So, smaller the molar mass more the collision frequency:

=> B>C>A

*for anq query regarding this question feel free to contact in comments section.

​​​​​​​