21. Kinetic Theory of Ideal Gases

A flask contains a mixture of neon (Ne), krypton (Kr), and radon (Rn) gases. Compare the average kinetic energies of the three types of atoms.

What is the total translational kinetic energy of the air in an empty room that has dimensions $8.00$ m$\times 12.00$ m$\times 4.00$ m if the air is treated as an ideal gas at $1.00$ atm?

Consider a container like that shown in the Figure, with $n_1$ moles of a monatomic gas on one side and $n_2$ moles of a diatomic gas on the other. The monatomic gas has initial temperature $T_{1i}$. The diatomic gas has initial temperature $T_{2i}$. Show that the equilibrium temperature is

$T_f=\frac{3n_1{T}_{1i}+5n_2{T}_{2i}}{3n_1+5n_2}$

At 100℃ the rms speed of nitrogen molecules is 576 m/s. Nitrogen at 100℃ and a pressure of 2.0 atm is held in a container with a 10 cm x 10 cm square wall. Estimate the rate of molecular collisions (collisions/s) on this wall.

5.0 x 10²³ nitrogen molecules collide with a 10 cm² wall each second. Assume that the molecules all travel with a speed of 400 m/s and strike the wall head-on. What is the pressure on the wall?

What is the total rotational kinetic energy of 1.0 mol of nitrogen gas at 300 K?

A nitrogen molecule consists of two nitrogen atoms separated by 0.11 nm, the bond length. Treat the molecule as a rotating dumbbell and find the rms angular velocity at this temperature of a nitrogen molecule around the z-axis, as shown in Figure 20.10.

The 2010 Nobel Prize in Physics was awarded for the discovery of graphene, a two-dimensional form of carbon in which the atoms form a two-dimensional crystal-lattice sheet only one atom thick. Predict the molar specific heat of graphene. Give your answer as a multiple of R.

Consider a container like that shown in Figure, with $n_1$ moles of a monatomic gas on one side and $n_2$ moles of a diatomic gas on the other. The monatomic gas has initial temperature $T_{1i}$. The diatomic gas has initial temperature $T_{2i}$. Show that the equilibrium thermal energies are

$\begin{aligned}E_{1f} &= \frac{3n_1}{3n_1 + 5n_2} (E_{1i} + E_{2i}) \\E_{2f} &= \frac{5n_2}{3n_1 + 5n_2} (E_{1i} + E_{2i})\end{aligned}$

Estimate the time needed for a glycine molecule (see Table 18–3) to diffuse a distance of 25μm in water at 20°C if its concentration varies over that distance from 1.00 mol/m³ to 0.50 mol/m³. Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u.

At about what pressure would the mean free path of air molecules be equal to the diameter of air molecules, ≈ 3 x 10⁻¹⁰ m? Assume T = 20° C.

(I) What speed would a 1.5-g paper clip have if it had the same kinetic energy as a molecule at 22°C?

What is the total translational kinetic energy of 1.0 mol of N₂ molecules at 25°C?

A 1.0-mol sample of helium gas has a temperature of 18°C. What is the total kinetic energy of all the gas atoms in the sample?

(I) Approximately how long would it take for the ammonia of Example 18–9 to be detected 1.0 m from the bottle after it is opened? What does this suggest about the relative importance of diffusion and convection for carrying odors?