**Understanding Ideal Gases through Kinetic Theory**

The kinetic theory of gases provides a robust theoretical framework for analysing and understanding the behaviour of gases. It is particularly useful in the study of ideal gases—a simplified, modelled system that allows us to navigate the complex, multifaceted nature of real gases.

**Fundamental Assumptions**

**Particle Nature:**Gases are made up of a myriad of tiny particles, either atoms or molecules, constantly in a chaotic, random motion. Each particle is considered to be point-like, with its own kinetic energy resulting from motion.**Negligible Volume:**In the kinetic theory, the volume occupied by the individual gas particles is considered negligible compared to the overall volume of the gas. This assumption simplifies the mathematical treatment of gases, although it is an approximation.**Elastic Collisions:**The collisions between gas particles, and between particles and the container walls, are deemed to be perfectly elastic, meaning no net kinetic energy is lost during these interactions. The conservation of energy and momentum principles play a pivotal role here.

Kinetic theory of gas

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**Mathematical Representation**

The kinetic theory offers a potent mathematical framework, aligning microscopic properties, i.e., the motion of individual particles, with macroscopic attributes like pressure, volume, and temperature.

**Kinetic Energy and Temperature:**The average kinetic energy of gas particles is directly related to the absolute temperature of the gas, cementing a bridge between microscopic motion and macroscopic thermal properties.**Pressure Derivation:**The pressure exerted by a gas can also be understood from the kinetic theory, linking it to the frequency and force of particle collisions with container walls.

**Ideal Gases as a Modelled System**

Ideal gases serve as a theoretical construct, a model that lends itself to the analytical scrutiny of gases under diverse conditions. Although a real gas never aligns perfectly with the ideal gas model, this conceptualisation offers remarkably close approximations under varied conditions.

**Approximation of Real Gases**

**Simplicity:**By ignoring the interactions among particles, except during collisions, the ideal gas model facilitates straightforward, albeit approximate, mathematical treatments.**Accuracy:**The model's predictions, though based on simplifications, often align closely with the observed behaviours of many real gases, affirming its utility and relevance.

**Conditions for the Ideal Gas Approximation**

The applicability of the ideal gas model is not universal; recognising its boundaries and the specific conditions under which it renders reliable approximations is crucial.

**Temperature Considerations**

**High Temperatures:**At elevated temperatures, the kinetic energy of particles is substantial, reducing the relative impact of intermolecular forces. The ideal gas laws tend to offer more accurate predictions under these conditions.**Kinetic Energy Dominance:**The dominant kinetic energy ensures that the particles are in rapid motion, and the effects of attractions or repulsions between particles are minimal.

**Pressure Considerations**

**Low Pressures:**The assumptions of the kinetic theory align more congruently with the behaviour of gases at lower pressures. Here, the volume of gas particles is indeed negligible compared to the container’s volume.**Particle Separation:**At low pressures, particles are widely separated, making intermolecular forces inconsequential, aligning with the postulates of the kinetic theory.

**Density Considerations**

**Low Density:**Gases with low density have fewer particles per unit volume. This scenario minimises particle interactions, making the ideal gas model a reliable approximation.**Mathematical Predictions:**Under low-density conditions, the mathematical predictions of the ideal gas law dovetail with experimental observations, affirming the model’s utility.

Effect of an increase in temperature, decrease in volume and increase in the amount of gas at constant temperature

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**Distinguishing between Ideal and Real Gases**

The nuanced distinctions between ideal and real gases root in the oversimplifications of the kinetic theory and the tangible, complex behaviours exhibited by real gases.

**Intermolecular Forces**

**Presence in Real Gases:**Real gases are influenced significantly by intermolecular forces, especially noticeable at high pressures and low temperatures. These forces can skew behaviours away from the predictions of the ideal gas law.**Absence in Ideal Gases:**Ideal gases, in theory, lack intermolecular forces. This absence simplifies theoretical and mathematical treatments but also distances the model from the intricate realities of real gases.

Ideal gas vs Real gas

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**Particle Volume**

**Finite in Real Gases:**Real gas particles occupy a definite volume. This volume becomes significant under certain conditions, influencing properties like compressibility and expansion, which deviate from ideal gas predictions.**Negligible in Ideal Gases:**Ideal gases are treated as point particles with negligible volume. This simplification underpins many of the model’s mathematical conveniences but also its limitations.

**Behavioural Deviations**

**Compressibility and Expansion:**Real gases exhibit nuanced behaviours during compression and expansion, influenced by intermolecular forces and particle volume—factors not accounted for in the ideal gas model.**Phase Changes:**Real gases can transition into liquids or solids at specific temperatures and pressures, a phenomenon not encompassed within the ideal gas framework.

In conclusion, while the ideal gas model is a potent tool for analysing gas behaviour, appreciating the distinctions and the intricate dynamics that set real gases apart is vital. Balancing theoretical insights with empirical observations enriches the understanding and application of gas laws in real-world scenarios.

## FAQ

No, the ideal gas laws cannot be universally applied to all real gases under every condition. These laws are based on the assumptions of the kinetic theory, which includes the neglect of intermolecular forces and the volume occupied by gas particles. In reality, these factors become significant at high pressures and low temperatures. At high pressures, the volume of the gas particles is no longer negligible, and at low temperatures, the intermolecular forces (especially attractive forces) become significant, leading to deviations from the behaviours predicted by the ideal gas laws, such as condensation or an unexpected change in volume or pressure.

At extremely low temperatures, real gases exhibit behaviours significantly deviating from the predictions based on the ideal gas model. The kinetic energy of the gas particles decreases as the temperature drops, leading to a reduced particle speed. Consequently, the attractive intermolecular forces become more prominent, dominating the behaviour of the gas. This dominance can lead to a marked decrease in pressure and volume, and in many cases, the gas can liquify, undergoing a phase change. These behaviours starkly contrast the predictions of the ideal gas laws, which do not account for intermolecular forces or phase changes.

Yes, various equations of state have been developed to account for the deviations of real gases from ideal behaviour. The Van der Waals equation is a notable example, incorporating correction factors for the volume occupied by gas molecules and the intermolecular forces. These corrections make the equation more accurate for real gases under a broader range of conditions, especially at high pressures and low temperatures. It modifies the ideal gas law by including terms that account for the volume occupied by gas molecules and the attractive forces between them, thereby providing a more realistic description of gas behaviour under various conditions.

The ideal gas model ignores the effects of intermolecular forces and the volume of gas particles to simplify the mathematical and theoretical analysis of gas behaviour. By making these assumptions, the model allows for direct relationships between pressure, volume, and temperature to be established, as seen in the ideal gas law *PV*=*nRT*. While this simplification enables easy calculations and predictions, it also means that the model becomes less accurate under conditions where intermolecular forces and particle volume significantly impact gas behaviour, such as at very high pressures or low temperatures.

In the context of the kinetic theory and ideal gases, the speed of gas particles is directly related to the temperature of the gas. The theory posits that gas particles are in constant, random motion and their kinetic energy, which is associated with their speed, is proportional to the temperature of the gas. The higher the temperature, the greater the average speed of the particles. For ideal gases, this relationship is used to derive various gas laws and principles, such as the ideal gas law. However, it's essential to remember that in real gases, factors like intermolecular forces and the finite size of particles can influence the relationship between particle speed and temperature.

## Practice Questions

The kinetic theory of gases provides a foundation for the concept of ideal gases by assuming that gases consist of numerous small particles in constant, random motion, with negligible volume and experiencing elastic collisions. The theory correlates the macroscopic properties of gases, like pressure and temperature, to the microscopic behaviours of gas particles. Ideal gas laws are particularly reliable at high temperatures and low pressures. High temperatures ensure that kinetic energy dominates over intermolecular forces, reducing their effect. At low pressures, the volume of individual gas particles becomes insignificant compared to the overall gas volume, validating the assumptions of the kinetic theory.

Real gases deviate from ideal behaviour primarily due to the effects of intermolecular forces and the finite volume of gas particles, factors that the ideal gas laws overlook. For instance, at high pressures, real gases are often more compressible than predicted by the ideal gas laws. This deviation occurs because the attractive intermolecular forces facilitate the compression of the gas. Additionally, at low temperatures, real gases can liquify, an occurrence not accounted for in the ideal gas model. This liquification stems from the dominance of attractive intermolecular forces over the kinetic energy of particles, leading to condensation.