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# Chapter 04: The Gaseous State

Chapter 4

## The Gaseous State

In an ideal world where gases behave ideally, there are four laws which predict the behavior of gases. Life would be much simpler if gases in the real world strictly follow the ideal gas laws(as shown below), but in reality we know that is not the case. As we explore the behaviour of an ideal gas, we will be learning how to answer questions involving real gases and why they do not behave ideally.

It is crucial to understand these laws as the combination of these laws would allow one to derive the ideal gas equation - which is the crux of the chapter.

Law and description Graphical representation

At constant temperature and pressure, volume of a gas is directly proportional to number of moles of the gas

Boyle's law

At constant temperature and moles, volume of gas is inversely proportional to the pressure

Charles' Law

At constant pressure and moles, the volume of gas is directly proportional to its absolute temperature (measured in Kelvin)

Gay-Lussac's Law

At constant volume and moles, the pressure of a gas is directly proportional to its absolute temperature (K)

It is crucial to understand these laws as the combination of these laws would allow one to derive the ideal gas equation - which is the crux of the chapter.

## Ideal gas law : pV=nRT

where R is the molar gas constant (8.31 J K⁻¹mol⁻¹)

IMPORTANT NOTE: When using the ideal gas equation, each quantity MUST be expressed in its SI UNITS.  Here's a table to summarise the SI units as well as some commonly used units of measurements and its conversions.

Oxides SI units Other commonly used units + conversions
Pressure (p) Pa 1 atm = 101325 Pa
1 Pa = 1 N m⁻²
1 Bar = 1x10⁵ Pa
Volume (V) 1 dm³ = 10⁻³ m³
1 cm³ = 10⁻⁶ m³
Temperature (T) K T(°C) + 273 = T(K)

## Below is a worked example to show you how to utilise the ideal gas equation.

Worked example 1

The volume occupied by 0.10g of a gas is found to be 83.1cm³ (measured at 1.0 x 10⁵ Pa and 27°C). Assuming that the gas behaves ideally, what is the relative molecular mass of this gas?

Solution:

Many students tend to only glance over the ideal gas law equation and neglect this portion of the chapter. However, in order to secure precious marks, do not make the same error. Other than applications of the ideal gas law, calculation questions set on the chapter of gases would expect students to be able to apply Dalton’s Law of partial pressure. There are 2 sets of equations students should take care to remember.

In a mixture of gases that DO NOT REACT WITH EACH OTHER, total pressure is the sum of partial pressures of the components

where pᵢ is the partial pressure of any component, i, in the mixture

Partial pressure can be determined by the mole ratio of the component gases.

where χA is the mole fraction of A

## Worked example 2

A mixture of 0.5 mol of helium, 2.0 mol neon and 2.5 mol of argon has a total pressure of 100kPa. What is the partial pressure of each gas in the mixture?

Solution:

## Worked example 3

Flask X contains 1 dm³ of helium at 2kPa pressure and Flask Y contains 2 dm³ of neon at 1kPa pressure. If the flasks are connected at constant temperature, what is the final pressure?

Solution:

Students should familiarise themselves with the basic assumptions applied to IDEAL gases and understand the differences between the characteristics of an ideal and a real gas. With the basis of these assumptions, students can then go on to tackle questions dealing with the conditions for a real gas to approach ideality. The table below provides a concise summary and comparison between a real and ideal gas.

Assumptions applied to IDEAL GAS

• 1. The molecular size (hence, volume) of gas particles is negligible compared to total volume occupied by gas
• 2. There are negligible forces of attraction between gas particles
• 3. When particles collide, collision is perfectly elastic

Characteristics of REAL GAS

• 1. The particles have a certain volume (volume of particles not completely negligible compared to total volume occupied by the gas)
• 2. There are forces of attraction between the particles, though weak
• 3. When particles collide, collision is not elastic

Many questions in examinations may ask students regarding the conditions in which a real gas may deviate from ideal gas behaviour. Conditions include high pressure and low temperature (tip: each reason should be memorised)

Students must also remember that under the same conditions, gases also deviate from ideality to DIFFERENT EXTENTS due to the differences in the strength of their intermolecular forces of attraction. Let's take a look at worked example 4 to best make sense of this.

## Worked example 4

Place the following gases in order of decreasing ideality, with the most ideal first. Explain the reason for the order.

CH₄          Cl₂          HCl

Solution:

1. CH₄ and Cl₂ are non-polar, and their molecules are held together by weak instantaneous-dipole induced dipole attractions.
2. As there are more electrons in Cl₂ as compared to CH₄, the electron cloud of Cl₂ is more polarisable compared to that of CH₄. Hence, the id-id attractions between Cl₂ molecules are stronger than those between CH₄ molecules.
3. On the other hand, HCl is polar, with stronger permanent dipole-dipole interactions between its molecules.
4. HCl has the strongest intermolecular forces of attraction, followed by Cl₂ and CH₄. Hence, HCl will deviate the most from ideality, followed by Cl₂ and CH₄.

Lastly, this table would sum up the typical graphical interpretations of deviations from ideal gas conditions (commonly tested in exams)

###### Deviation due to different types of IMF

NOTE: the biggest deviation is represented by the biggest dip below the ideal gas line and NOT above the line.