S1.5.1 The ideal gas model

Assumptions of the Ideal Gas Model and Its Applications

You're holding a balloon filled with helium. As you release it, the balloon ascends into the sky, expanding as it rises. Why does this happen?

To answer this, we turn to the ideal gas model, a simplified yet powerful framework that explains the behavior of gases under most conditions.

Assumptions of the Ideal Gas Model

• The ideal gas model is based on five key assumptions.
• These assumptions simplify the complex behavior of real gases, allowing us to predict their behavior using mathematical relationships.

1. Gas Particles Are in Constant, Random Motion

Gas particles are never at rest; they move in straight lines until they collide with another particle or the walls of their container.

• This constant, random motion explains why gases fill any container they occupy, regardless of its shape.

2. Collisions Between Gas Particles Are Perfectly Elastic

When gas particles collide with each other or with the walls of their container, no energy is lost as heat or sound. These are perfectly elastic collisions, meaning the total kinetic energy of the system remains constant.

• This explains why the pressure exerted by a gas on its container walls doesn’t decrease over time, as long as temperature and volume remain constant.

3. Gas Particles Have Negligible Volume Compared to the Space They Occupy

Although gas particles have mass and volume, their size is so small compared to the distance between them that we treat their volume as negligible.

• This assumption explains why gases are compressible and why their behavior can be described using simple equations.

4. No Intermolecular Forces Act Between Gas Particles

In an ideal gas, particles neither attract nor repel each other.

• This assumption allows gas particles to move independently of one another.
• As a result, an ideal gas cannot condense into a liquid, no matter how much the temperature is lowered.

5. The Kinetic Energy of Gas Particles Is Proportional to Temperature (in Kelvin)

The average kinetic energy of gas particles is directly proportional to the gas's absolute temperature.

• This means that as temperature increases, particles move faster, increasing the pressure they exert on their container walls (if volume is constant).
• This relationship is why temperature is always expressed in Kelvin when dealing with gases.

Applications of the Ideal Gas Model

The ideal gas model provides a foundation for understanding and predicting the behavior of gases under a wide range of conditions. Here are some key applications:

1. Explaining Gas Behavior Under Standard Conditions

• Under standard conditions (STP: 0°C and 100 kPa), most gases behave similarly, regardless of their chemical identity.
• The molar volume of an ideal gas at STP is 22.7 dm³ mol⁻¹, meaning one mole of any ideal gas occupies this volume.
• This uniformity simplifies calculations in chemistry, such as determining the amount of gas produced in a reaction.

2. Deriving the Ideal Gas Equation

The ideal gas model forms the basis of the ideal gas equation, which relates pressure ($p$), volume ($V$), temperature ($T$), and the amount of gas ($n$):

$$pV=nRT$$

Here, $R$ is the universal gas constant ($8.31{\text{J K}}^{-1}{\text{mol}}^{-1}$). This equation enables us to predict how gases respond to changes in conditions, such as pressure changes during weather balloon ascents.

3. Predicting Deviations from Ideal Behavior

• The ideal gas model also provides a benchmark for identifying when real gases deviate from ideal behavior.
• At low temperatures or high pressures, intermolecular forces and the finite volume of gas particles become significant.
• Under these conditions, real gases condense into liquids or exhibit non-ideal pressure-volume relationships.

4. Designing Experiments and Industrial Applications

The ideal gas model is widely used in experimental setups and industrial processes. For example:

• Weather Balloons: Scientists use the ideal gas equation to predict how a balloon will expand as it rises to altitudes with lower pressure.
• Chemical Reactions: Chemists calculate the volume of gases produced or consumed in reactions, such as combustion or electrolysis.

Reflection and Practice