How Does the Ideal Gas Equation Explain Gas Behavior?
In thermodynamics, we can say that the Ideal gas law is said to be a well-defined approximation of the behaviour that is of many gases under diverse conditions. The equation of Ideal Gas is the combination which is of empirical laws like Charle’s law and the Boyle’s law then the Gay-Lussac’s law and the law of Avogadro’s.
It can be defined as
The law of ideal gas which is the equation of state of a hypothetical ideal gas.
What is the Ideal Gas Equation?
An ideal gas is generally defined as one in which all collisions are between the atoms or we can say that the molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can visualize easily that it is a collection of perfectly hard spheres which collide but which otherwise we can say that they do not interact with each other. In such a gas, the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.
An ideal gas can be easily characterized by three state variables: that is the absolute pressure denoted by P volume denoted by V and absolute temperature denoted by T.
Ideal gas law: PV = nRT = NkT
n = is the number of moles
R = is the universal gas constant = 8.3145 J/mol K
N = is the number of molecules
k = is the Boltzmann constant = 1.38066 x 10-23 J/K = 8.617385 x 10-5 eV/K
= is the R/NA
NA = is the Avogadro's number = 6.0221 x 1023 /mol
But we can say that there is also a statistical element in the determination of the average kinetic energy of those molecules. The temperature which is said to be taken to be proportional to this average kinetic energy invokes the idea of kinetic temperature. One mole which is an ideal gas that too at STP occupies 22.4 litres.
The law of ideal gas is said to be the equation of state of a hypothetical ideal gas that is an illustration. In an ideal gas, there is no molecule-molecule interaction and we can say that only elastic collisions are allowed. It is said to be a good approximation which is the behaviour of many gases which are under many conditions although we can say that it has several limitations. In 1834 it was first stated by Émile Clapeyron as a combination of Boyle’s and Charles’ law.
What is an Ideal Gas?
An ideal gas that is said to be a theoretical gas that does not exist in reality but is assumed to exist for the purpose of simplifying calculations. We can also say that It also generates a reference point in relation to which the behaviour of other gases generally can be studied.
We can say that these collisions are assumed to be perfectly elastic which means that no energy of either of these particles is wasted.
In reality, however, when the gas which is actual gas particles collide with each other some of their energy that is wasted in changing directions and overcoming friction. However, we can say that at STP that is defined earlier, conditions most natural gases that act just like an ideal gas are subjected to reasonable restrictions.
Ideal Gas Law
In mathematical terms this law is represented as the following:
P ∝∝ 1/V or that PV = K
Where P = Pressure of the gas, V = Volume of the gas and K = constant. It means that both of the volume and pressure of a given mass that is of gas are inversely proportional to each other at a constant temperature. Furthermore, we can say that it also expresses that the product of pressure and volume that is for any gas is a constant and thus it can be used to study the comparison that is of the gas which is under different conditions as:
P’V’ = P”V”
where both the products are for the same as gas but under different volume and pressures.
The law of Charles’ states that ‘ When the pressure is of a sample of air is held constant and then we can say that the volume of the gas is directly proportional to its temperature‘, that is written as:
V ∝∝T
where V = Volume of a gas sample, T= Absolute temperature. Quite simply we can put as gases expand on heating and contract which is on cooling.
The law of Avogadro that states that ‘Equal volumes that are of all gases which are at conditions which are of same pressure and temperature have the same number of molecules’. It is written as follows:
V ∝∝ n or V/n =K
where V = volume of gas, n = Number of moles (1 mole=6.022 x 1023 molecules).
FAQs on Ideal Gas Equation: Concepts, Law, and Applications
1. What is the Ideal Gas Equation as per the CBSE Class 11 syllabus?
The Ideal Gas Equation is a fundamental formula in thermodynamics that describes the state of a hypothetical ideal gas. For Class 11 students, it is expressed as PV = nRT. This equation combines Boyle's Law, Charles's Law, and Avogadro's Law. In the equation:
- P stands for the pressure of the gas.
- V is the volume of the gas.
- n represents the number of moles of the gas.
- R is the universal gas constant.
- T is the absolute temperature of the gas in Kelvin.
2. What are the key assumptions made for an ideal gas?
The Ideal Gas Law is based on a set of assumptions about the behaviour of gas particles. These are the core properties that define an ideal gas:
- The gas particles themselves have a negligible volume compared to the volume of the container.
- There are no intermolecular forces of attraction or repulsion between the gas particles.
- All collisions between gas particles and with the walls of the container are perfectly elastic, meaning no kinetic energy is lost.
- The particles are in constant, random motion.
3. What is the value and importance of the universal gas constant (R)?
The universal gas constant, denoted by R, is a fundamental constant in physics and chemistry. Its value is approximately 8.314 J/(mol·K). The importance of R is that it acts as a crucial proportionality constant that links the energy scale in physics to the temperature scale when dealing with a specific amount of substance (a mole). It essentially bridges the macroscopic properties of a gas (pressure, volume) with its temperature and molar quantity.
4. How is the Ideal Gas Equation derived from the individual gas laws?
The Ideal Gas Equation is a synthesis of three empirical gas laws:
- Boyle's Law: At a constant temperature, pressure is inversely proportional to volume (P ∝ 1/V).
- Charles's Law: At constant pressure, volume is directly proportional to absolute temperature (V ∝ T).
- Avogadro's Law: At constant temperature and pressure, volume is directly proportional to the number of moles (V ∝ n).
5. Can you give a real-world example of the Ideal Gas Law in action?
A great real-world example is the inflation of a car's airbag. During a collision, a chemical reaction rapidly produces a large quantity of nitrogen gas (increasing n, the number of moles) in a very small, fixed volume. According to the Ideal Gas Equation, this sudden increase in the amount of gas causes a massive and almost instantaneous increase in pressure (P), which inflates the airbag to cushion the passenger.
6. Why is the concept of an 'ideal gas' so important in physics if no real gas is perfectly ideal?
The concept of an ideal gas is crucial because it provides a simplified model that makes the complex behaviour of real gases much easier to study and predict. While no real gas is truly ideal, this model works as an excellent approximation under specific conditions, primarily high temperature and low pressure. It establishes a fundamental baseline for understanding gas properties, from which more complex models like the van der Waals equation are developed to account for real-world deviations.
7. Under what conditions of temperature and pressure do real gases behave most like an ideal gas?
Real gases behave most like an ideal gas under conditions of high temperature and low pressure. The reasons are:
- At high temperatures, the kinetic energy of the gas particles is high enough to overcome the weak intermolecular forces of attraction between them.
- At low pressures, the gas particles are far apart from each other, making their individual volume truly negligible compared to the total volume of the container.
8. What is the difference between the Ideal Gas Equation forms PV = nRT and PV = NkT?
Both equations describe the same law but from different perspectives.
- PV = nRT is the macroscopic version, used when working with moles (n) of a gas. It uses the universal gas constant (R).
- PV = NkT is the microscopic version, used when working with the actual number of individual molecules (N). It uses the Boltzmann constant (k).
