An introduction to the Ideal Gas Behaviour
Ideal gas behaviour is a theory that expects the gases to behave in a certain way and assumes that the gases have negligible or no space at all and they have no intermolecular force of attraction. Deviation of gases from their ideal gas behaviour occurs when the molecules of a gas are cooled down to a point where they no longer possess sufficient kinetic energy to overcome attractive intermolecular forces.
Ideal and Real Gases
Ideal gases are those gases that obey the ideal equation of PV = nRT under all amounts of pressure and temperature. But there is no such gas that behaves the same in every pressure and temperature. Hence, this concept is theoretical. Real gases are those who obey the gas law if the pressure is low or the temperature is high. All gases are real gases.
Difference Between Ideal Gas and Real Gas
The differences between ideal gas and real gas are given below.
Pressure, Volume, and Temperature Relationship in Gases - Why do the Real Gases Deviate?
The graphs below represent different gases and show how they behave under high and low pressure.
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The figure shows how gases behave differently from their ideal behaviour, particularly in high pressure. At low pressure, as shown in figure(b), the real gases behave more like that of the expected ideal behaviour. For gases such as CO2 and C2H4, they deviate more than other real gases because these gases tend to liquefy at lower pressures.
Now, the graph below shows the behaviour of real gas N2 under different temperatures.
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The figure shows that the real gas nitrogen behaves more according to the ideal gas behaviour when the temperature is high. Why do gases deviate so much under high pressure and low temperature? At both the conditions, the basic assumptions that the law of the ideal gas holdsare: the volume of the molecules of the gas are negligible and intermolecular interaction is negligible – these two become invalid.
Under low pressure, the gas molecules are farther apart from each other, and the volume of molecules is the same as the volume of the container. As the pressure increases, the molecular space contracts, and their volume becomes significant as compared to the container. If more pressure is exerted, then the gas liquefies under very high pressure such as CO2.
All the molecules attract each other by a combination of forces. At high temperatures, these have enough energy, and they overcome their attractive force and predominate by the effects of the molecular volume. On the other hand, with the decrease in the temperature, the energy of the molecules also decreases. Eventually, there comes the point where it becomes impossible for the molecules to overcome the force of attraction, and it results in the liquefaction of gas and turns into a liquid state. That is why the ideal gas behaviour is a theoretical concept and does not apply in real situations.
Van der Waals Equation
In 1873, J.D. Van der Waals did some modifications with the ideal law of gas equation to explain the behaviour of real gases, in which he took into account:
The volume of the gas molecules.
The forces of attraction between the gas molecules.
He put forward the following equation:
\[(P+\frac{a}{v^2})(v-b)=RT\]
For n moles of the gas,
\[(P+\frac{an^2}{v^2})(v-nb)=nRT\]
The constants ‘a’ and ‘b’ represent the scale of intermolecular attraction and the excluded volume, respectively. The higher the value of 'a', the greater is the molecular attraction and the gas will easily compress. The term 'b' represents the excluded volume that is occupied by gas particles. These constants are different for different gases.
Conclusion
Hence, the article explained the important concept of gases of deviation from ideal gas behaviour. The Van der Waals equation is important for understanding the variation of temperature and pressure on gases. The article will develop a strong understanding of the behaviour of ideal gases.
FAQs on Deviation From Ideal Gas Behaviour
1. What is meant by the deviation of a gas from ideal behaviour?
Deviation from ideal behaviour refers to the fact that real gases do not follow the ideal gas law (PV = nRT) under all conditions of temperature and pressure. The ideal gas law is based on two key assumptions: that gas molecules have no volume and that there are no intermolecular forces of attraction between them. In reality, gas molecules do occupy space and attract each other, causing their behaviour to differ, or deviate, from the theoretical predictions for an ideal gas.
2. What are the two main causes for a real gas to deviate from ideal behaviour?
The deviation of real gases from ideal behaviour is caused by the failure of two assumptions made by the kinetic theory of gases:
- Significant Molecular Volume: The ideal gas law assumes gas particles are point masses with negligible volume. At high pressure, molecules are pushed closer together, and their actual volume becomes a significant fraction of the container's volume, causing the gas to be less compressible than predicted.
- Intermolecular Forces of Attraction: The ideal gas law assumes no attractive forces between gas molecules. At low temperatures, molecules move slower and the attractive forces become significant, pulling molecules together and reducing the pressure they exert on the container walls compared to an ideal gas.
3. Under what specific conditions do real gases deviate most from ideal behaviour?
Real gases show the most significant deviation from ideal behaviour under conditions of high pressure and low temperature. Here’s why:
- At high pressure, the gas molecules are forced very close to each other. This makes the volume of the molecules themselves no longer negligible compared to the total volume of the container.
- At low temperature, the kinetic energy of the molecules decreases. This makes them unable to overcome the intermolecular forces of attraction, which then become significant and cause the gas to behave non-ideally, potentially leading to liquefaction.
4. How does the van der Waals equation account for the deviation from ideal gas behaviour?
The van der Waals equation is a modification of the ideal gas law that accounts for the behaviour of real gases by introducing two correction factors, 'a' and 'b'. The equation is: (P + an²/V²)(V - nb) = nRT.
- The term 'nb' corrects for the volume occupied by the gas molecules themselves (the excluded volume), leading to a smaller effective volume for the gas to move in.
- The term 'an²/V²' corrects for the intermolecular forces of attraction, which reduce the pressure exerted by the gas on the container walls. The constant 'a' is a measure of the strength of these forces.
5. What is the compressibility factor (Z) and how does it show deviation from ideal behaviour?
The compressibility factor (Z) is a term used to quantify the deviation of a real gas from ideal gas behaviour. It is defined as Z = PV/nRT. For a truly ideal gas, the value of Z is always 1. For a real gas:
- If Z > 1, it indicates a positive deviation. This typically occurs at very high pressures, where the volume of the molecules is the dominant factor, making the gas less compressible than an ideal gas.
- If Z < 1, it indicates a negative deviation. This happens at intermediate pressures, where intermolecular attractive forces dominate, pulling molecules together and making the gas more compressible than an ideal gas.
6. Why do gases like ammonia (NH₃) and carbon dioxide (CO₂) show greater deviation than hydrogen (H₂) and helium (He)?
Ammonia and carbon dioxide show greater deviation because they have stronger intermolecular forces of attraction compared to hydrogen and helium. NH₃ molecules are polar and exhibit hydrogen bonding, while CO₂ has significant London dispersion forces due to its larger electron cloud. These strong attractive forces make them easier to liquefy and cause significant deviations from ideal behaviour. In contrast, H₂ and He are small, nonpolar molecules with very weak intermolecular forces, so their behaviour is much closer to ideal over a wider range of conditions.
7. Why is understanding the deviation from ideal behaviour important in real-world applications?
Understanding this deviation is crucial for many industrial and scientific processes where gases are used under non-ideal conditions. For example:
- Industrial Chemistry: In the synthesis of ammonia (Haber's process), gases are under extremely high pressure, and calculations must account for real gas behaviour to predict yields and manage equipment.
- Transportation and Storage: When transporting gases like natural gas (methane) or LPG, they are compressed into a liquid state. The ideal gas law cannot predict the conditions needed for this liquefaction; the van der Waals equation or more complex models are required.
- Cryogenics: The liquefaction of gases like nitrogen and oxygen for cooling applications depends entirely on the effects of intermolecular forces at very low temperatures.
8. Can a real gas ever behave exactly like an ideal gas?
No, a real gas can never behave exactly like an ideal gas. This is because real gas molecules will always have a finite volume and will always exert some intermolecular forces, no matter how small. However, a real gas can approach ideal behaviour under conditions of very low pressure and very high temperature. Under these conditions, the molecules are far apart and moving very fast, which minimises the effects of both molecular volume and intermolecular forces, making the ideal gas law a very good approximation.
