Here is the complete question.
Be sure to answer all parts. Three 8−L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 276 K. Flask A contains He, flask B contains CH4, and flask C contains H2. Rank the flask contents in terms of: the following properties. (Use the notation >, <, or =, for example B=C>A.)
(a) pressure
(b) average molecular kinetic energy
(c) diffusion rate after the valve is opened
(d) total kinetic energy of the molecules
Answer:
Explanation:
Given that:
Three flask A,B, C:
contains a volume of 8-L
mass m = 4g &;
Temperature = 276 K
Flask A = He
Flask B = H₂
Flask C = CH₄
a) From the ideal gas equation:
PV = nRT
where;
n = number of moles = mass (m)/molar mass (mm)
Then:
PV = m/mm RT
If T ,m and V are constant for the three flasks ; then
P ∝ 1/mm
As such ; the smaller the molar mass the larger the pressure.
Now; since the molecular weight of CH₄ is greater than He and H₂ and also between He and H₂, He has an higher molecular weight .
Then the order of pressure in the flask is :
[tex]\mathbf{P_B >P_A>P_C}[/tex]
where :
[tex]P_A[/tex] = pressure in the flask A
[tex]P_B[/tex] = pressure in the flask B
[tex]P_C[/tex]= Pressure in the flask C
b)
average molecular kinetic energy
We all know that the average molecular kinetic energy varies directly proportional to the temperature.
Thus; the given temperature = 276 K
∴ The order of the average molecular kinetic energy is [tex]\mathbf{K.E_A =K.E_B =K.E_C}[/tex]
c)
The rate of diffusion of gas is inversely proportional to the square root of it density . Here the density is given in relation to their molar mass.
So;
rate of diffusion ∝ [tex]\dfrac{1}{\sqrt{mm} }[/tex]
where;
[tex]D_A[/tex] = rate of diffusion in flask A
[tex]D_B[/tex] = rate of diffusion in flask B
[tex]D_C[/tex] = rate of diffusion in flask C
Thus; the order of the rate of diffusion = [tex]D_B[/tex] > [tex]D_A[/tex] > [tex]D_C[/tex]
d) total kinetic energy of the molecules .
The kinetic energy deals with how the speed of particles of a substance determines how fast the substances will diffuse in a given set of condition.
The the order of the total kinetic energy depends on the molecular speed
Thus; the order of the total kinetic energy for the three flask is as follows:
[tex]\mathbf{ K.E_B>K.E_A>K.E_C}[/tex]
