Chapter 5.1 : Gases – Pressure, Measurement, and Units

Gases and the Gas Phase

The Nature of the Gas Phase

The gas phase is one of the fundamental states of matter, characterized by particles that move freely and are far apart compared to solids and liquids. Gases have neither a definite shape nor a definite volume, and they expand to fill their containers.

• Solid: Particles are closely packed in a fixed arrangement.

• Liquid: Particles are close but can move past each other.

• Gas: Particles are far apart and move independently.

Phase transitions: Heating or reducing pressure can convert a solid or liquid to a gas, while cooling or increasing pressure can condense a gas to a liquid or solid.

Density, Mass, and Volume of Gases

Calculating Gas Properties

Gases have low densities compared to solids and liquids. The density of a gas depends on its mass, volume, temperature, and pressure.

• Density formula: $d = \frac{m}{V}$, where m is mass and V is volume.

• Molar mass (M): $M = \frac{m}{n}$, where n is the number of moles.

• Temperature conversion: $T(K) = T(°C) + 273.2$

Example: If nitrogen is a gas at 0°C and 1 atm, with a density of 1.25 g/L, the volume of 1 mole is:

• $V = \frac{M}{d} = \frac{28.02\ g\ mol^{-1}}{1.25\ g\ L^{-1}} = 22.4\ L$

Additional info: 22.4 L is the molar volume of an ideal gas at standard temperature and pressure (STP).

Pressure

Definition and Formula

Pressure is a measure of how concentrated the force applied to an object is. It is defined as force per unit area:

• $P = \frac{F}{A}$

• F: Force (N, 1 Newton = 1 kg·m·s-2)

• A: Area (m2)

• P: Pressure (Pa, 1 Pascal = 1 kg·m-1·s-2)

Pressure: Force per Area

The area over which a force is applied is critical in determining pressure. For example, walking on a frozen pond distributes weight over a larger area, resulting in lower pressure, while skating concentrates force on a small area, increasing pressure.

• Example calculation:

• Walking: $P = \frac{100\ kg \times 9.80\ m\ s^{-2}}{0.0100\ m^2} = 98000\ Pa$

• Skating: $P = \frac{100\ kg \times 9.80\ m\ s^{-2}}{0.000900\ m^2} = 1,088,889\ Pa$

Gas Pressure

Origin of Gas Pressure

In the gas phase, molecules move freely and collide with the walls of their container. Each collision exerts a force on the surface, and the cumulative effect of many collisions results in measurable gas pressure.

• Pressure is proportional to the frequency and force of molecular collisions with surfaces.

• Even though each collision creates a small force, the large number of collisions leads to significant pressure.

Pressure as the Result of a Collision

Pressure can be analyzed as the result of collisions, using Newton's second law ($F = ma$) and the change in momentum during a collision.

• Example: A car of mass 1500 kg decelerates from 50 km/h to 0 in 2 seconds over an area of 0.25 m2:

• $F = m \frac{(V_f - V_i)}{\Delta t}$

• $P = \frac{F}{A}$

• Calculated pressure: $P = 41.7\ kPa$

Additional info: For gas molecules, the force per collision is tiny, but the number of collisions is enormous, resulting in observable pressure.

Units of Pressure

Common Pressure Units

Pressure can be measured in several units. The following table summarizes the most common units and their standard values:

Pressure Measured in	Unit	Standard Pressure
bar	bar	1 bar
pascal	Pa	100,000 Pa
kilopascal	kPa	100 kPa
torr (mmHg)	Torr or mmHg	750.06 Torr
atmosphere	atm	0.98692 atm
pounds per square inch	psi	14.504 psi

Converting Pressure Units

Pressure values can be converted between units using appropriate conversion factors. For example:

• $1\ atm = 101,325\ Pa = 760\ mmHg = 1.01325\ bar$

• To convert from bar to kPa: $1\ bar = 100\ kPa$

Extreme Pressures: The Mariana Trench Example

The Mariana Trench, the deepest point in the ocean, experiences extremely high pressures. At a depth of 11 km, the pressure is about 1086 bar, which is 1086 times the standard atmospheric pressure at sea level.

• $\frac{P_{\text{Mariana}}}{P_{\text{sea level}}} = \frac{1086\ bar}{1\ bar} = 1086$ times more

Measuring Gas Pressure

Barometers and Manometers

Atmospheric pressure is commonly measured using a barometer, often a glass tube filled with mercury. The height of the mercury column reflects the atmospheric pressure.

• Barometer: Measures atmospheric pressure using the height of a mercury column.

• Manometer: Measures the pressure of a gas in a container relative to atmospheric pressure.

Key relationships:

• If the mercury is higher on the gas side, $P_{\text{gas}} = P_{\text{atm}} - h$

• If the mercury is higher on the open side, $P_{\text{gas}} = P_{\text{atm}} + h$

Factors Influencing Gas Pressure

Several factors affect the pressure exerted by a gas:

• Volume: Increasing the volume decreases the frequency of collisions, lowering pressure.

• Amount of gas: More gas increases the number of collisions, raising pressure.

• Temperature: Higher temperature increases molecular speed and collision frequency, increasing pressure.

Key Concepts and Practice

• Understand the definition and origin of gas pressure.

• Be able to convert between different pressure units.

• Know how to measure gas pressure using barometers and manometers.

• Apply concepts to solve exercises involving density, mass, volume, and pressure of gases.

Additional info: For further practice, refer to textbook exercises such as "Chemistry: A Molecular Approach, Chapter 5" (e.g., problems 5.5, 5.21, 5.29, 5.53).