Gases: Properties, Laws, and Molecular Interpretation

Chapter 6: Gases

Atmospheric Pressure Effects

Atmospheric pressure is the force exerted by the weight of air in Earth's atmosphere. It varies with altitude and weather conditions, influencing wind and pressure systems.

• High pressure regions are usually associated with clear weather, while low pressure regions are linked to unstable weather.

• Pressure decreases with increasing altitude because the number of gas particles in a given volume decreases.

• Key Point: Pressure decreases with increasing altitude.

• Example: At the top of a mountain, the air pressure is lower than at sea level.

Pressure: The Result of Molecular Collision

Gas pressure arises from the constant motion of gas molecules and their collisions with surfaces.

• Pressure depends on:

  • Number of gas particles in a given volume

  • Volume of the container

  • Average speed of the gas particles

• Formula:

$\text{Pressure} = \frac{\text{force}}{\text{area}} = \frac{F}{A}$

• Example: Pumping more air into a tire increases the number of gas particles, raising the pressure.

Gas Pressure and Particle Density

The pressure exerted by a gas is directly related to the number of gas particles in a given volume.

• Fewer gas particles result in lower pressure; more particles result in higher pressure.

• Low density of gas particles = low pressure; high density = high pressure.

• Example: A sealed jar with more air molecules has higher pressure than one with fewer molecules.

The Barometer

A barometer is a device used to measure atmospheric pressure. The classic mercury barometer consists of an evacuated glass tube inverted in a dish of mercury.

• Atmospheric pressure pushes mercury up the tube; the height of the mercury column indicates the pressure.

• Standard atmospheric pressure supports a mercury column 760 mm high (1 atm).

• Example: At sea level, the barometric pressure is typically 760 mm Hg.

The Manometer

A manometer measures the pressure of a gas in a container. It compares the gas pressure to atmospheric pressure using a column of liquid (often mercury).

• If the gas pressure is greater than atmospheric pressure, the liquid level is lower on the gas side.

• The difference in liquid levels measures the pressure difference between the gas and the atmosphere.

• Example: Used in laboratories to measure the pressure of gases produced in chemical reactions.

Common Pressure Units

Pressure can be measured in several units. The following table summarizes common units and their relationships:

Unit	Abbreviation	Average Air Pressure at Sea Level
Pascal	Pa	101,325 Pa
Pounds per square inch	psi	14.7 psi
Torr (1 mmHg)	torr	760 torr (exact)
Inches of mercury	in Hg	29.92 in Hg
Atmosphere	atm	1 atm

Converting Between Pressure Units

Pressure units can be converted using known relationships. For example:

• $1 \text{ atm} = 14.7 \text{ psi}$

• $1 \text{ atm} = 760 \text{ mmHg}$

• $1 \text{ atm} = 101,325 \text{ Pa}$

Example: To convert 132 psi to mmHg:

$132 \text{ psi} \times \frac{1 \text{ atm}}{14.7 \text{ psi}} \times \frac{760 \text{ mmHg}}{1 \text{ atm}} = 6.82 \times 10^2 \text{ mmHg}$

The Simple Gas Laws

There are four basic properties of a gas: pressure (P), volume (V), temperature (T), and amount in moles (n). The simple gas laws describe the relationships between pairs of these properties.

• When one property changes, it affects the others.

• These laws are foundational for understanding gas behavior.

Boyle's Law: Pressure and Volume

Boyle's Law states that the volume of a gas is inversely proportional to its pressure at constant temperature and amount.

• $V \propto \frac{1}{P}$ (at constant T and n)

• $V_1 \times P_1 = V_2 \times P_2$

• Molecular Interpretation: Decreasing the volume increases the frequency of collisions with the container walls, raising the pressure.

• Example: Compressing a syringe decreases the volume and increases the pressure inside.

Charles's Law: Volume and Temperature

Charles's Law states that the volume of a fixed amount of gas at constant pressure increases linearly with increasing temperature (in Kelvin).

• $V \propto T$ (at constant P and n)

• $\frac{V_1}{T_1} = \frac{V_2}{T_2}$

• Molecular Interpretation: As temperature increases, gas particles move faster, causing more frequent and forceful collisions, so the gas expands to maintain constant pressure.

• Example: A balloon expands when heated because the gas inside occupies more volume.

Avogadro's Law: Volume and Amount (Moles)

Avogadro's Law states that the volume of a gas is directly proportional to the number of moles of gas at constant temperature and pressure.

• $V \propto n$ (at constant T and P)

• $\frac{V_1}{n_1} = \frac{V_2}{n_2}$

• Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules, regardless of the type of gas.

• Example: Doubling the amount of gas in a container (at constant T and P) doubles the volume.