Answer to Question #182360 in General Chemistry for Daniela(me)

Question

13. Consider two containers of volume 1.0 L at 298 K, as shown below. One container holds 0.10 mol N2 and the other holds 0.10 mol H2. The average kinetic energy of the nitrogen molecules is 6.2 X 10 -21 J. Assume that the N2 and the H2 exhibit ideal behavior. 

a. 

Is the pressure in the container holding the H2 less than, greater than, or equal to the pressure in the container holding the N2. Justify your answer.

b. What is the average kinetic energy of the H2 molecules?

c. The molecules of which gas, N2 or H2, have the greater average speed? Justify your answer.

d. What change could be made that would decrease the average kinetic energy of the molecules in the container?

Answer 1

a) The pressure in the container holding the H₂(g) is equal to the pressure in the container holding the N₂(g) because there is an equal number of moles of both gases at the same temperature and volume (P = nK , where the constant K = RT/V )

b) The average kinetic energy of the H₂(g) molecules is 6.2 × 10^-21 J because both gases are at the same temperature.

c) H₂(g) molecules will have the greater average speed. Both gases have the same average kinetic energy, but H₂(g) has the 

smaller molar mass. Therefore, the H₂(g) molecules will have a greater average speed because, at a given temperature , the 

average (root-mean-square) speed of gas molecules is inversely proportional to the square root of the molar mass of the gas:

$u_{rms} = \sqrt{\frac{3RT}{M}}$

d) The average kinetic energy of a gas particle depends on the temperature of the gas sample. To decrease the average kinetic 

energy of the gas particles in a gas sample, the temperature of the N₂(g) would have to be lowered.