Chapter 11 Notes
In the previous chapter, you learned that the kinetic molecular theory described how the
particles of matter are in constant motion and temperature is related to the kinetic energy
of the particles. Other properties such as pressure, volume, and the number of moles of a
gas can also affect the particles of matter.
Pressure can be influenced by the number of collisions between gas particles and the side
of a container. This pressure depends on volume, temperature, and the number of
molecules present. PRESSURE is defined as the force per unit area on a surface. The SI
unit for force is a NEWTON, the force that will increase the speed of 1 kilogram of mass
by 1 meter per second.
The earth’s atmosphere is filled mostly nitrogen and oxygen. These molecules collide
with the surface of the earth and objects on the earth creating atmospheric pressure. A
BAROMETER is a device used to measure atmospheric pressure. This pressure can be
measured in several units. The SI unit for pressure is ATMOSPHERE, the average
pressure at sea level and 0 degrees Celsius. Other units of pressure include millimeters
of mercury, inches of mercury, torr, pounds per square inch, and Pascals.
1 atm = 760 mm Hg = 760 torr = 14.7 pounds per square inch = 1.013 x 105 Pa
STANDARD TEMPERATURE AND PRESSURE is a universal set of conditions that
are considered standard conditions. They are exactly 1 atm and 0 degrees Celsius. You
will see this abbreviated as STP.
John Dalton, who proposed the atomic theory, helped to define pressure. He stated that
each gas in a mixture such as the nitrogen and oxygen in the atmosphere exert pressure
independently. The pressure exerted by each gas in a mixture is called PARTIAL
PRESSURE and these partial pressures can be added together making up the total
pressure exerted by the mixture. This is known as Dalton’s law of partial pressures.
In order to understand the relationships between volume, pressure, temperature, and the
amount of a gas there is a set of mathematical formulas called GAS LAWS. This first is
BOYLE’S LAW.
Boyle’s law was discovered by Robert
Boyle. By doubling the pressure on a
sample of gas at constant temperature,
Robert Boyle found that the volume
decreased by ½. He also found that by
reducing the pressure by ½ allowed the
volume to double. BOYLE’S LAW
states that the volume of a fixed mass of
gas varies inversely with the pressure at
constant temperature. If inversely
proportional, the mathematical formula can be determined.
PV = k, constant
Since pressure and volume vary inversely, their product remains the same and the
relationship can be expressed as,
P1V1 = P2V2
CHARLES’ LAW is the second gas law. Jacques Charles discovered that volume and
temperature are related by observing what happens in hot air balloons. Charles noted that
for each degree Celsius of temperature increase the size of the balloon increased 1/273 of
the original size. Ultimately, this observation leads to the development of the Kelvin
scale for temperature. The Kelvin scale take arbitrary temperature scales such as Celsius
or Fahrenheit out of the picture. To convert Celsius scale to Kelvin, you simply add 273
to the Celsius temperature.
Celsius + 273 = Kelvin
Zero Kelvin is equal to -273 degrees Celsius. This
temperature is the lowest known temperature and is
called ABSOLUTE ZERO. At absolute zero the
motion of particles in matter are believed to stop
creating what some
believe to be the
fifth state of matter.
It is important to
convert temperature
to Kelvin when
using gas laws.
Charles’ law states that volume of a fixed mass of gas
at constant pressure varies directly with the Kelvin
temperature. Mathematically, Charles’ law can be
expressed as
Volume = k, constant x Kelvin temperature
or
Volume/Kelvin temperature = k, constant
As in Boyle’s law, the formula can be converted to a
formula we can use.
V1/T1 = V2/T2
The third gas law takes into account that pressure and temperature
are related. Joseph Gay-Lussac noted that with every degree of
Celsius temperature increase the pressure increase by 1/273 as
long as the volume was held constant. Gay-Lussac’s law states
that the pressure of a fixed mass of gas at constant volume varies
directly with Kelvin temperature. Mathematically, Gay-Lussac’s
law is expressed as follows.
Pressure = k, constant x Kelvin temperature
or
Pressure/Kelvin temperature = k, constant
Again, the formula can be converted to a formula we can use.
P1/T1 = P2/T2
In reality, gas can undergo changes to pressure, temperature, and
volume all at the same time. The COMBINED GAS LAW
expresses the relationship between pressure, volume, and
temperature of a fixed amount of gas. Mathematically the
combined gas law can be expressed as the following.
Pressure x Volume/Kelvin temperature = k, constant
or
P1V1/T1 = P2V2/T2
Finally, we must look at how all four variables (pressure, temperature, volume, and the
amount of gas) can influence how a gas behaves. Avogadro determined that there were
6.022 x 1023 molecules in one mole. Avogadro’s law states that equal volumes of gases
at the same temperature and pressure contain equal numbers of molecules. Therefore, the
volume occupied by the gases is also the same. MOLAR VOLUME of a gas is the
volume occupied by 1 mole of a gas at STP. It has
been found to be 22.4 liters. With this in mind,
we must use the IDEAL GAS LAW to illustrate
the mathematical relationship among pressure,
volume, temperature, and the number of moles of a
gas.
PV = n RT
In this formula, n is the number of moles and R is
the universal gas constant. At STP, a value for R
can be calculated.
R = (1 atm) (22.4 liters)/ (1 mol) (273 K) = 0.08206 atm-l/mol-K