Consider three identical flasks filled with different gases: Flask 1: CO at 750
ID: 1057791 • Letter: C
Question
Consider three identical flasks filled with different gases: Flask 1: CO at 750 tort and 0 degree C Flask 2: N_2 at 250 tort and 0 degree C Flask 3: H_2 at 500 tort and 0 degree C In which flask will the molecules have the greatest average kinetic energy? Flask: In which flask will the molecules have the greatest u_rms? Flask: In which flask will the molecules have the smallest u_rms? Flask: Which flask will have the largest number of molecules? Flask: Rank the flasks in term of increasing gas density Sketch the Boltzmann distributions for the root mean square velocity of CO_2 gas at 50 K, 298 K, and 500 K. Draw all three curves on the same set of axes for comparison and label with corresponding temperature (x-axis = # of moles, y-axis = u_rms). Sketch the Boltzmann distributions for the root mean square velocity of the first four noble gases at 298 K: He, Ne, Ar, and Kr. Draw all four curves on the same set of axes for comparison and label the noble gas (x-axis = # of atoms, y-axis = u_rms).Explanation / Answer
a. The average Kinetic energy of gas is given by the Kinetic Molecular theory of gases.
The kinetic molecular theory of gases postulates that gases are particles & have following properties:
1. Volume of individual particles is negligible
2. The particles are in constant motion
3. No force exercted by the gas particles
4. The average kinetic energy of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.
(KE)avg = 3/2 RT
R = Ideal gas constant = 8.314 J / K mole & T = temperature in Kelvin
In our case, all the three flask are kept at the same temperature i.e. 0C or 273k; hence all the flask will have same Average Kinetic Energy.
b. In the question Urms stands for "Root square mean velocity" which is = square root (3RT / Mw)
Mw = Molecular weight of gas
Mw (H2) = 2 g/mole ; Mw (N2) = 14 g/mole & Mw (CO) = 28 g/mole
Using these values & equation, you can easily calculate
Urms (H2) = 58.3488
Urms (CO) = 15.59
Urms (N2) = 22.05
Hence flask 3 will have greatest Urms.
c. Flask 1 will have the smallest Urms (CO) = 15.59
d. The number of molecules in the flask can be determined by finding the number of moles present of each gas in the flask.
Let assume the volume of flask to be 1 m3
1 torr = 133.3 Pascals
By ideal gas equation we have PV = n RT
n = PV / RT
Using these values & equation, you can easily calculate
n (H2) = 29.36 moles
n (N2) = 14.68 moles
n (CO) = 44.04 moles
One mole of any gas is equivalent to Avagadro's number of molecules. Hence Flask 1 will have the largest number of molecules.
e. Gas density is the ratio of mass of gas divided by volume. As we are assuming volume of gas in the flask as 1 m3; hence the gas density will have the density based on their molecular weight itself.
So Gas density of CO > Gas density of N2 > Gas density of H2
So flasks with increasing gas density are as flask 1 > flask 2 > flask 3