Properties of Gases - Comprehensive Notes

Gases have unique properties due to the large distance between gas particles compared to liquids and solids.
Liquids and solids have small intermolecular distances.
Gases share some behaviors with liquids but also possess unique properties.

Gases are considered fluids, meaning they can flow.
Gas particles can flow due to their relatively large separation, allowing them to move past each other easily.

Gases have much lower densities compared to liquids and solids.
A significant portion of a gas's volume is empty space due to the large distances between particles.
The greater density of liquids and solids is attributed to the smaller interparticle distances.
The low density of gases allows particles to travel relatively long distances before colliding.

Liquids are virtually incompressible.
Gases are highly compressible because the space occupied by the gas particles is small compared to the total volume.
Applying pressure to a gas reduces its volume by moving the particles closer together.

Solids have a definite shape and volume.
Liquids have a definite volume but take the shape of the lower part of their container.
Gases completely fill their container.
Gas particles are in constant, high-speed motion and do not attract each other as much as solid and liquid particles do; therefore, a gas expands to fill the entire available volume.

Earth's atmosphere (air) is a mixture of gases, mainly nitrogen and oxygen.
Gases have mass and therefore weight in a gravitational field.
Gas molecules are pulled toward Earth's surface, colliding with each other and the surface, causing air pressure.

Air density varies with altitude.
The atmosphere is denser closer to Earth's surface due to the compression of gases by the weight of the atmospheric gases above.

Pressure is defined as force divided by area.
Pressure is the amount of force exerted per unit area of surface.
The SI unit of force is the newton (N).
The SI unit of pressure is the pascal (Pa), which is one newton per square meter.

Atmospheric pressure is measured using a barometer.
Atmospheric pressure acts on the surface of the mercury in the barometer.
The mercury settles when the downward pressure from its weight equals the atmospheric pressure.

At sea level, the atmosphere supports an average mercury column height of $760.0$ mm, which is defined as $1.00$ atmosphere (atm).
One millimeter of mercury is also called a torr.
The SI unit for pressure is the kilopascal (kPa). Average air pressure is $101.3$ kPa.
$1.00 atm = 760.0 mmHg = 760.0 torr = 101.3 kPa$

Standard temperature and pressure (STP) is a standard condition for comparing gases.
STP is defined as $0$ °C and $1.00$ atm.
$1.00 atm = 760.0 mmHg = 760.0 torr = 101.3 kPa$

The Kinetic-Molecular Theory explains the properties of gases based on molecular behavior.
It states that gas particles are in constant, rapid, random motion and are far apart relative to their size.
This theory explains the fluidity and compressibility of gases.

Gas particles can easily move past one another or move closer together because they are farther apart than liquid or solid particles.
Gas particles collide with each other and the walls of their container.
The pressure exerted by a gas results from the collisions of its molecules against the container walls.

The kinetic-molecular theory considers collisions of gas particles to be perfectly elastic, meaning energy is completely transferred during collisions.
The total energy of the system remains constant.

The average kinetic energy of random motion is proportional to the absolute temperature in kelvins.
Heat increases the energy of random motion of a gas.
Not all molecules travel at the same speed; there is a range of speeds due to multiple collisions.
Increasing the temperature of a gas shifts the energy distribution toward greater average kinetic energy.

Gases are described by their measurable properties:
- P = pressure exerted by the gas (atm, mm Hg, torr, or kPa)
- V = total volume occupied by the gas (L, mL, or dm³)
- T = temperature in kelvins of the gas (always in K, °C + 273)
- n = number of moles (amount) of the gas

Boyle’s law states that at constant temperature, the volume of a fixed amount of gas varies inversely with pressure.
For a fixed amount of gas at a constant temperature, volume increases as pressure decreases, and vice versa.
$P1V1 = P2V2$
Pressure-volume graphs demonstrate this inverse relationship: as pressure increases, volume decreases.

Heating a gas makes it expand, and cooling makes it contract.
Charles’ law describes the direct relationship between temperature and volume.
In 1787, Jacques Charles discovered that a gas's volume is directly proportional to its temperature on the Kelvin scale if the pressure remains constant.
For a fixed amount of gas at a constant pressure, volume increases as temperature increases, and vice versa.
Gas particles move faster on average at higher temperatures, causing them to hit the container walls with more force.
These strong collisions cause the volume of a flexible container to increase.
Gas volume decreases when the gas is cooled because of the lower average kinetic energy of the gas particles.
If the absolute temperature is halved, the average kinetic energy is halved, and the volume is reduced to half if the pressure remains constant.
When graphed with the Kelvin scale, a direct proportion between volume and temperature is shown.
$V1/T1 = V2/T2$

Pressure is the result of collisions of particles with the container walls, and average kinetic energy is proportional to the absolute temperature.
If the absolute temperature of gas particles is doubled, their average kinetic energy is doubled.
For a fixed amount of gas in a container of fixed volume, doubling the temperature doubles the pressure.
Temperature and pressure have a directly proportional relationship.
Gay-Lussac’s Law states that the pressure of a gas at a constant volume is directly proportional to the absolute temperature.
$P1/T1 = P2/T2$

Boyle’s, Charles’, and Gay-Lussac’s Laws can be combined into a single expression called the Combined Gas Law.
$P1V1/T1 = P2V2/T2$

In 1811, Amadeo Avogadro proposed that equal volumes of all gases, under the same conditions, have the same number of particles.
Stanislao Cannizzaro later used Avogadro’s principle to determine the true formulas of several gaseous compounds.

Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (or atoms).
Cannizzaro used Avogadro’s law to deduce that the correct formula for water is $H_2O$ .
Gas volume is directly proportional to the number of moles of gas at the same temperature and pressure.

Volumes of gases change with changes in temperature and pressure.
Argon has an atomic mass of $39.95$ g/mol, and 22.4 L of argon at 0°C and 1 atm has a mass of $39.95$ g.
Therefore, 22.4 L is the volume of 1 mol of any gas at STP. This is called the molar volume.
The mass of 22.4 L of a gas at $0$ °C and a pressure of $1$ atm will be equal to the gas’s molecular mass.