5 Steps to a 5 AP Chemistry 2019

Gases ❮ 105

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

particles. Mathematically it can be represented as:

==

M

u

kT

m

33 RT

rms

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

the ideal gas equation), T is the Kelvin temperature, and M is 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

approximately 2,000 m/s.

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

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

KE per 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:

KE per mol = 3/2 RT

where R again is the ideal gas constant and T is the Kelvin temperature. 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 relationships for the AP exam, but the use of the individual equation is

not required. Then we will combine the relationships into 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

container 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

pressure. At sea level, the column averages 760 mm high. This pressure is also called

1 atmosphere (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.