Gases
5.1 Early experiments
Physician Jean Baptista Van Helmont identified substances in air as “gas”, the
Flemish word for chaos.
In 1643, Evangelista Torricelli identified that the air in the atmosphere exerts
pressure. He designed the first barometer using mercury and observed how a
column of 760mm Hg always remained in the tube as a result of atmospheric
pressure.
Otto von Guericke invented the first vacuum pump, used in a famous demonstration
to the king of Prussia in 1654.
As instruments for measuring pressure, manometer, commonly use mercury, the
units are usually mm mercury also known as Torr in honour of Torricelli. Another
unit commonly used is standard atmosphere, which is equivalent to 760 torr.
As pressure is defined as force per unit area, the SI unit is defined as N/m 2 called as
Pascal (Pa). 1 atm is equivalent to 105 Pascal.
5.2 The Gas Laws of Boyle, Charles, and Avogadro
Robert Boyle was the first to perform quantitative experiments relating to gasses.
He identified that there is a constant found every time the product of a volume of a
gas with its pressure is presented. This law was identified as Boyle’s Law PV=k
According to Boyle’s findings, there is an inverse relationship between the pressure
and volume. A gas that obeys Boyle’s law is called an ideal gas.
Jacques Charles found that the volume of a gas at constant pressure increases
linearly with the temperature of the gas. An interesting observation is that the
volume of all gasses extrapolates to 0 at -273ºC.
The volume of a gas is directly proportional to its temperature, which extrapolates to
0 at -273ºC. The relation is known as Charles Law. V=kT
Avogadro’s hypothesis indicates that volumes of gasses at equal pressure and
temperature contain same number of particles. V=an. This relationship is obeyed by
gasses at low pressure.
5.3 The ideal gas law
Combining the three relationships previously seen, we can obtain the ideal gas law:
PV=RTn.
R is the universal gas constant equal to 0.08206L atm K-1 mol-1
A gas that follows the properties of the ideal gas law is an ideal gas.
Real gasses relate to ideal gasses when they’re at high temperatures and low
pressure.
, 5.4 Gas stoichiometry
Molar volume of an ideal gas is at 1mol of the gas at 0ºC and 1atm. It is very close to
22.42L (Ideal gas volume).
The conditions mentioned above are Standard Temperature and Pressure (STP).
Number of moles of gas “n” are grams of gas/molar mass. Substituting this
relationship into the ideal gas law we have:
P = ((m/M) *R*T)/V
As we know that density is m/V, we may derive the following equation:
P = dRT/M; M = dRT/P
5.5 Dalton’s Law of Partial pressures
Dalton’s Law of Partial Pressure: “For a mixture of gasses in a container, the total
pressure exerted would be the sum of pressures that each gas would exert if it were
alone.” (P)
This reveals that the volume of an individual gas particle as well as the forces
between the particles are not important characteristics of an ideal gas.
The mole fraction (X) is the ratio of number of moles of a given component in a
mixture to the total number of moles in the mixture.
The mole fraction of a particular component of the mixture is directly related to its
partial pressure. P1 = X1 x PTotal
5.6 Kinetic Molecular Theory of Gasses
Kinetic molecular theory is a model that tries to explain the ideal gas behaviour.
Distribution of velocities of the particles in the Ideal Gas is illustrated by the
Maxwell-Boltzmann distribution law.
Average Kinetic Energy = 3/2 RT
Root mean square velocity = sqrt (3RT / M)
Average velocity = sqrt (8RT/πM)M)
5.1 Early experiments
Physician Jean Baptista Van Helmont identified substances in air as “gas”, the
Flemish word for chaos.
In 1643, Evangelista Torricelli identified that the air in the atmosphere exerts
pressure. He designed the first barometer using mercury and observed how a
column of 760mm Hg always remained in the tube as a result of atmospheric
pressure.
Otto von Guericke invented the first vacuum pump, used in a famous demonstration
to the king of Prussia in 1654.
As instruments for measuring pressure, manometer, commonly use mercury, the
units are usually mm mercury also known as Torr in honour of Torricelli. Another
unit commonly used is standard atmosphere, which is equivalent to 760 torr.
As pressure is defined as force per unit area, the SI unit is defined as N/m 2 called as
Pascal (Pa). 1 atm is equivalent to 105 Pascal.
5.2 The Gas Laws of Boyle, Charles, and Avogadro
Robert Boyle was the first to perform quantitative experiments relating to gasses.
He identified that there is a constant found every time the product of a volume of a
gas with its pressure is presented. This law was identified as Boyle’s Law PV=k
According to Boyle’s findings, there is an inverse relationship between the pressure
and volume. A gas that obeys Boyle’s law is called an ideal gas.
Jacques Charles found that the volume of a gas at constant pressure increases
linearly with the temperature of the gas. An interesting observation is that the
volume of all gasses extrapolates to 0 at -273ºC.
The volume of a gas is directly proportional to its temperature, which extrapolates to
0 at -273ºC. The relation is known as Charles Law. V=kT
Avogadro’s hypothesis indicates that volumes of gasses at equal pressure and
temperature contain same number of particles. V=an. This relationship is obeyed by
gasses at low pressure.
5.3 The ideal gas law
Combining the three relationships previously seen, we can obtain the ideal gas law:
PV=RTn.
R is the universal gas constant equal to 0.08206L atm K-1 mol-1
A gas that follows the properties of the ideal gas law is an ideal gas.
Real gasses relate to ideal gasses when they’re at high temperatures and low
pressure.
, 5.4 Gas stoichiometry
Molar volume of an ideal gas is at 1mol of the gas at 0ºC and 1atm. It is very close to
22.42L (Ideal gas volume).
The conditions mentioned above are Standard Temperature and Pressure (STP).
Number of moles of gas “n” are grams of gas/molar mass. Substituting this
relationship into the ideal gas law we have:
P = ((m/M) *R*T)/V
As we know that density is m/V, we may derive the following equation:
P = dRT/M; M = dRT/P
5.5 Dalton’s Law of Partial pressures
Dalton’s Law of Partial Pressure: “For a mixture of gasses in a container, the total
pressure exerted would be the sum of pressures that each gas would exert if it were
alone.” (P)
This reveals that the volume of an individual gas particle as well as the forces
between the particles are not important characteristics of an ideal gas.
The mole fraction (X) is the ratio of number of moles of a given component in a
mixture to the total number of moles in the mixture.
The mole fraction of a particular component of the mixture is directly related to its
partial pressure. P1 = X1 x PTotal
5.6 Kinetic Molecular Theory of Gasses
Kinetic molecular theory is a model that tries to explain the ideal gas behaviour.
Distribution of velocities of the particles in the Ideal Gas is illustrated by the
Maxwell-Boltzmann distribution law.
Average Kinetic Energy = 3/2 RT
Root mean square velocity = sqrt (3RT / M)
Average velocity = sqrt (8RT/πM)M)
