---

Structure 1.5.1—An ideal gas consists of moving particles with negligible volume and no intermolecular forces. All collisions between particles are considered elastic.

Ideal Gas Assumptions

An ideal gas is a hypothetical concept in the field of thermodynamics and gas behavior. It is based on a set of simplifying assumptions that help to model and analyze the behavior of real gases under different conditions. The description provided can be broken down into several key components:

1. Moving particles: An ideal gas consists of a large number of particles (atoms or molecules) in constant motion. These particles have kinetic energy as they move around, and their motion gives rise to the macroscopic properties of the gas, such as pressure and temperature.
2. Negligible volume: In an ideal gas, the volume occupied by the individual gas particles is considered to be negligible compared to the total volume of the gas. This assumption means that the size of the particles is so small that it doesn’t significantly affect the behavior of the gas, allowing for simpler mathematical models.
3. No intermolecular forces: An ideal gas assumes that there are no attractive or repulsive forces between the gas particles. This means that the particles don’t interact with each other, except during collisions. In reality, real gases do experience intermolecular forces, but these forces are often negligible under certain conditions (e.g., high temperatures or low pressures).
4. Elastic collisions: Collisions between the gas particles, as well as collisions with the walls of the container, are considered to be perfectly elastic. In an elastic collision, the total kinetic energy of the colliding particles is conserved. This means that no energy is lost to heat or other forms of energy during the collision.

These simplifying assumptions allow scientists and engineers to derive mathematical equations, such as the ideal gas law (PV=nRT), which can be used to predict and analyze the behavior of real gases under certain conditions. However, it is important to note that the ideal gas model has its limitations, and deviations from the ideal behavior may occur, especially at very high pressures or very low temperatures.

Intermolecular forces recap

Intermolecular forces are the forces that exist between molecules or particles in a substance. They play a crucial role in determining the physical and chemical properties of substances, such as boiling point, melting point, and viscosity. There are three primary types of intermolecular forces: London dispersion forces, permanent dipole-dipole interactions, and hydrogen bonding.

1. London dispersion forces (also known as van der Waals forces or induced dipole-induced dipole interactions): These are the weakest type of intermolecular forces and occur between all molecules, whether polar or nonpolar. London dispersion forces result from temporary fluctuations in electron distribution around a molecule, which create an instantaneous dipole.
2. Permanent dipole-dipole interactions: These forces occur between polar molecules, which have a permanent separation of positive and negative charges due to differences in electronegativity between the atoms within the molecule.
3. Hydrogen bonding: This is a special type of dipole-dipole interaction that occurs between molecules containing a hydrogen atom bonded to a highly electronegative atom (usually nitrogen, oxygen, or fluorine).

---

Structure 1.5.2—Real gases deviate from the ideal gas model, particularly at low temperature and high pressure.

Real gases deviate from the ideal gas model due to the assumptions made while developing the ideal gas concept. The ideal gas model assumes that the gas particles have negligible volume and that there are no intermolecular forces between them. These assumptions simplify the mathematical representation of gas behavior, but they do not always hold true, especially at low temperatures and high pressures.

1. Low temperatures: At low temperatures, the kinetic energy of the gas particles decreases. As a result, the particles move more slowly, and the effects of intermolecular forces become more pronounced. In the case of real gases, attractive forces between particles cause them to stick together or move closer, deviating from the ideal gas behavior.
2. High pressures: When the pressure is increased, gas particles are compressed and forced closer together. This means that the volume occupied by the particles themselves can no longer be considered negligible compared to the total volume of the gas.

One application of the understanding of real gas behavior and deviations from the ideal gas model is in the design and operation of liquefied natural gas (LNG) plants. LNG is natural gas that has been cooled and compressed to its liquid state. The liquefaction process involves cooling the natural gas to around -162°C at near-atmospheric pressure.

Understanding the deviations of real gases from the ideal gas model is crucial in the design and operation of an LNG plant for several reasons:

1. Accurate modeling of gas behavior: Engineers need to accurately predict the behavior of natural gas under various conditions. Alternative models like the van der Waals equation are used to account for deviations.
2. Optimizing the liquefaction process: Understanding real gas behavior helps engineers optimize heat exchange and compression processes.
3. Separation of impurities: Understanding the real gas behavior of impurities and their interactions under various conditions allows engineers to design efficient separation processes.

---

Structure 1.5.3—The molar volume of an ideal gas is a constant at a specific temperature and pressure.

Ideal Gas Equation

The molar volume of a gas is the volume occupied by one mole of the gas at a specific temperature and pressure. According to the ideal gas law, the relationship between the pressure (P), volume (V), temperature (T), and the amount of gas in moles (n) is given by the equation:

PV = nRT

• Pressure (P): Measured in pascals (Pa)
• Volume (V): Measured in cubic meters (m³)
• Amount of gas (n): Measured in moles (mol)
• Temperature (T): Measured in kelvin (K)
• Ideal gas constant (R): 8.314 JK⁻¹mol⁻¹ with SI units

Ensure that the units for each variable are consistent with the chosen value for the ideal gas constant (R).

To understand the concept of molar volume being constant for an ideal gas at a specific temperature and pressure, we can rearrange the ideal gas law equation to solve for molar volume (V_m):

V_m = V / n

So, the equation becomes:

PV_m = RT

Now, if we keep the temperature (T) and pressure (P) constant, the right side of the equation (RT) will also be constant. Therefore, the product of pressure and molar volume (PV_m) will remain constant. This means that under constant temperature and pressure conditions, the molar volume of an ideal gas will remain constant.

In other words, one mole of any ideal gas will occupy the same volume under the same temperature and pressure conditions, regardless of the gas’s chemical identity.

Worked example

Let’s consider an example where we have a gas with the following conditions:

• Pressure (P) = 100 kPa
• Volume (V) = 10 dm³
• Temperature (T) = 25°C
• Ideal gas constant (R) = 8.314 JK⁻¹mol⁻¹

We are asked to calculate the amount of gas (n) in moles.

First, we need to convert the units to their SI equivalents:

1. Convert pressure from kPa to Pa: 100 kPa * (1000 Pa / 1 kPa) = 100,000 Pa
2. Convert volume from dm³ to m³: 10 dm³ * (1 m³ / 1000 dm³) = 0.01 m³
3. Convert temperature from °C to K: 25°C + 273.15 = 298.15 K

Now that we have the SI units, we can use the ideal gas law equation, PV = nRT, to solve for n:

100,000 Pa x 0.01 m³ = n x 8.314 JK⁻¹mol⁻¹ x 298.15 K

n = (100,000 Pa x 0.01 m³) / (8.314 JK⁻¹mol⁻¹ x 298.15 K) n ≈ 0.402 mol

So, the amount of gas in this example is approximately 0.402 moles.

Questions

1. A gas sample has a pressure of 150 kPa, a volume of 5 dm³, and a temperature of 35°C. How many moles of gas are present?
2. What volume does 2 moles of an ideal gas occupy at a pressure of 200 kPa and a temperature of 50°C?
3. What is the pressure exerted by 0.5 moles of a gas with a volume of 3 dm³ at a temperature of 100°C?
4. A gas sample at a pressure of 100 kPa and a temperature of 27°C has a volume of 8 dm³. Calculate the number of moles of gas.
5. A 1.5 mol gas sample is kept at a pressure of 300 kPa and a temperature of 75°C. What volume does the gas occupy?

Answers

---

Structure 1.5.4—The relationship between the pressure, volume, temperature and amount of an ideal gas is shown in the ideal gas equation PV = nRT and the combined gas law

The ideal gas equation, PV = nRT, and the combined gas law both describe the relationship between pressure (P), volume (V), temperature (T), and the amount of an ideal gas in moles (n). The main difference between the two is that the ideal gas equation includes the amount of gas (n) and the ideal gas constant (R), while the combined gas law does not.

1. Ideal Gas Equation (PV = nRT): The ideal gas equation represents the behavior of an ideal gas, a hypothetical gas that assumes negligible volume for individual gas particles and no intermolecular forces between them. This equation relates the pressure, volume, temperature, and the amount of gas in moles, where R is the ideal gas constant (8.314 J/(mol·K)).
2. Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂): The combined gas law is derived from Boyle’s law, Charles’s law, and Gay-Lussac’s law. This law relates the initial state to the final state of a given gas sample undergoing changes in pressure, volume, and temperature, assuming that the amount of gas remains constant.

The combined gas law is derived by combining three fundamental gas laws:

1. Boyle’s Law (P₁V₁ = P₂V₂ at constant n and T): The pressure of a given amount of gas is inversely proportional to its volume when the temperature is held constant.
2. Charles’s Law (V₁/T₁ = V₂/T₂ at constant n and P): The volume of a given amount of gas is directly proportional to its absolute temperature when the pressure is held constant.
3. Gay-Lussac’s Law (P₁/T₁ = P₂/T₂ at constant n and V): The pressure of a given amount of gas is directly proportional to its absolute temperature when the volume is held constant.

To derive the combined gas law, we start with Boyle’s law and multiply both sides by T₁ and T₂:

P₁V₁T₂ = P₂V₂T₁

Rearranging gives:

P₁V₁/T₁ = P₂V₂/T₂

Questions

1. A gas sample initially has a pressure of 100 kPa, a volume of 2 dm³, and a temperature of 25°C. If the pressure is increased to 200 kPa and the temperature to 50°C, what will be the new volume?
2. A gas occupies a volume of 5 dm³ at 20°C and 150 kPa. If the volume is increased to 10 dm³ and the temperature to 40°C, what will be the new pressure?
3. A gas has an initial pressure of 300 kPa, a volume of 8 dm³, and a temperature of 30°C. If the pressure is decreased to 150 kPa and the volume to 4 dm³, what will be the new temperature?
4. A gas sample has an initial volume of 3 dm³ at 100 kPa and 25°C. If the pressure is increased to 200 kPa and the volume to 6 dm³, what will be the final temperature?
5. A gas initially has a pressure of 120 kPa, a volume of 5 dm³, and a temperature of 50°C. If the pressure is decreased to 60 kPa and the temperature to 20°C, what will be the new volume?

Answers