5 Steps to a 5 AP Chemistry

It is the speed of a gas particle having the average kinetic energy of the gas particles.

Mathematically it can be represented as:

where Ris the molar gas constant (we’ll talk more about it in the section dealing with the

ideal gas equation), T is the Kelvintemperature and Mis the molar mass of the gas. These

root mean square speeds are very high. Hydrogen gas, H 2 , at 20°C has a value of approxi-

mately 2,000 m/s.

Postulate 5 relates the average kinetic energy of the gas particles to the Kelvintemper-

ature. Mathematically we can represent the average kinetic energy per molecule as:

KEper molecule =1/2 mv^2

where m is the mass of the molecule and v is its velocity.

The average kinetic energy per mol of gas is represented by:

KEper mol =3/2 RT

where R again is the ideal gas constant and Tis the Kelvintemperature. This shows the

direct relationship between the average kinetic energy of the gas particles and the Kelvin

temperature.

Gas Law Relationships

The gas laws relate the physical properties of volume, pressure, temperature, and moles

(amount) to each other. First we will examine the individual gas law relationships. You will

need to know these relations for the AP exam, but the use of the individual equation is

not required. Then we will combine the relationships in to a single equation that you

will need to be able to apply. But first, we need to describe a few things concerning

pressure.

Pressure

When we use the word pressure, we may be referring to the pressure of a gas inside a con-

tainer or to atmospheric pressure, the pressure due to the weight of the atmosphere above

us. These two different types of pressure are measured in slightly different ways.

Atmospheric pressure is measured using a barometer(Figure 8.1).

An evacuated hollow tube sealed at one end is filled with mercury, and then the open

end is immersed in a pool of mercury. Gravity will tend to pull the liquid level inside the

tube down, while the weight of the atmospheric gases on the surface of the mercury pool

will tend to force the liquid up into the tube. These two opposing forces will quickly bal-

ance each other, and the column of mercury inside the tube will stabilize. The height of the

column of mercury above the surface of the mercury pool is called the atmospheric pres-

sure. At sea level the column averages 760 mm high. This pressure is also called 1 atmos-

phere (atm). Commonly, the unit torr is used for pressure, where 1 torr =1 mm Hg, so that

atmospheric pressure at sea level equals 760 torr. The SI unit of pressure is the pascal (Pa),

so that 1 atm =760 mm Hg =760 torr =101,325 Pa (101.325 kPa). In the United States

pounds per square inch (psi) is sometimes used, so that 1 atm =14.69 psi.

To measure the gas pressure inside a container, a manometer(Figure 8.2) is used.

As in the barometer, the pressure of the gas is balanced against a column of mercury.

u

kT

m

RT

rms M

==

33

104  Step 4. Review the Knowledge You Need to Score High