Kinetic Molecular Theory AP Chemistry Mrs. Ward

Kinetic Molecular Theory of Gases (1) Gases consist of discrete molecules. The individual molecules are very small and are very far apart relative to their own sizes. (2) The gas molecules are in continuous, random, straight-line motion with varying velocities. (3) The collisions between gas molecules and with the walls of the container are elastic; the total energy is conserved during a collision; that is, there is no net energy gain or loss. (4) Between collisions, the molecules exert no attractive or repulsive forces on one another; instead, each molecule travels in a straight line with constant velocity. 5.7

The average kinetic energy of gaseous molecules is directly proportional to the absolute temperature of the sample. The average kinetic energy of molecules of different gases are equal at a given temperature.

Velocity of a Gas

E= ½ mv2 where E is the kinetic energy a body possesses, m is the body’s mass, and v is it’s velocity. Kinetic energies at the same temperature are the same regardless of the molecule. When temperature increases, kinetic energy increases and when temperature decreases, kinetic energy decreases. The lightest molecules have higher velocities than heavier molecules at the same temperature.

Maxwell-Boltzmann Distribution Shows the distribution of speeds for a certain gas at a certain temperature, such as nitrogen at 298 K. The speed at the top of the curve is called the most probable speed because the largest number of molecules have that speed.   

This shows how the Maxwell-Boltzmann Distribution is affected by temperature. At lower temperatures, the molecules have less energy. Therefore, the speeds of the molecules are lower and the distribution has a smaller range. As the temperature of the molecules increases, the distribution flattens out. Because the molecules have greater energy at higher temperature, the molecules are moving faster.   

This shows the dependence of the Maxwell-Boltzmann Distribution on molecule size. On average, heavier molecules move more slowly than lighter molecules. Therefore, heavier molecules will have a smaller speed distribution, while lighter molecules will have a speed distribution that is more spread out.   

All molecules have the same kinetic energy (mv2/2) at the same temperature, so the fraction of molecules with higher velocities will increase as m, and thus the molecular weight, decreases.

How do the average kinetic energies and the average speeds of each gas in a mixture compare??

How do the average kinetic energies and the average speeds of each gas in a mixture compare?? At the same temperature, the average KE of the gas molecules is the same. The lighter molecules, however, will have a greater speed. In order for the average KE of each gas to be equal, the lighter molecules travel faster (therefore there are more collisions), yet they hit the wall w/less force than heavy molecules.

Heavy molecules travel slower (not as many collisions) but hit the walls with more force. These 2 factors of speed and mass of gas balance each other out.

The root-mean-square speed (rms) of gas molecule urms = 3RT M 

Example: Calculate the root-mean-square (rms) of H2 molecules in m/s at 20oC. Recall that 1 J = 1 kg∙m2 s2 R= 8.314 J/mol∙k Therefore, R= 8.314 kg∙m2 mol∙K∙s2

Urms = 8.314 kg∙m2 (293 K) mol∙K∙s2 (2.02 g/mol) ( 1 kg/1000g) = 3.62 x 106 m2/s2 (take square root) = 1.90 x 103 m/s

Diffusion of Gases

GAS DIFFUSION vs EFFUSION Diffusion is the gradual mixing of molecules of different gases. Effusion is the movement of molecules through a small hole into an empty container.

GAS DIFFUSION AND EFFUSION Molecules effuse through holes in a rubber balloon, for example, at a rate (= moles/time) that is proportional to T inversely proportional to M. Therefore, He effuses more rapidly than O2 at same T. He

Graham’s Law of Diffusion (and effusion) rate is inversely proportional to its molar mass

If you place HCl at one end of a tube and NH4OH at the other end, a white cloud (precipitate) will start to appear as NH4Cl forms. Why does the cloud appear closer to the end where HCl was placed? NH4OH(aq)

NH4OH The ammonia travels much quicker than HCl since it is lighter, so the product starts appearing closer to the HCl.

If the rate for HCl(g) was 5. 9 cm/min and the rate of NH4OH(g) was 8 If the rate for HCl(g) was 5.9 cm/min and the rate of NH4OH(g) was 8.5 cm/min and the molar mass of HCl is 36.45 g/mol, solve for the molar mass of NH4OH. ANSWER: 17.56 g/mol

The molar mass of ammonium hydroxide is 35. 05 g/mol The molar mass of ammonium hydroxide is 35.05 g/mol. What could have happened in the experiment to explain this error?

NH4OH decomposes into NH3 and H2O NH4OH decomposes into NH3 and H2O. So the molar mass you calculated was due to the ammonia gas.