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** Introduction**:

The ideal gas is stated as one in which all the collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. One can imagine it as a collection of perfectly hard spheres that collide however which otherwise don't interact with one other. In such a gas, the entire internal energy is in the form of kinetic energy and any change in internal energy is accompanied via a change in the temperature.

** Basic properties of ideal gases**:

A single-component collection of the ideal gas molecules is characterized through the given properties:

1) An ideal gas is thought to be a 'point mass'. A point mass is a particle so small, its mass is very close to zero. This signifies an ideal gas particle consists of virtually no volume.

2) Collisions between the ideal Gases are 'elastic'. This signifies that no repulsive or attractive forces are comprised throughout collisions. As well, the kinetic energy of the gas molecules remains constant as theses inter particle forces is deficient.

The ideal gas can be characterized via three state variables - absolute pressure (P), volume (V), and absolute temperature (T). The relationship among them might be expressed from kinetic theory and is termed as the Ideal gas law:

PV = nRT = NkT

Here,

n = number of moles

R = universal gas constant = 8.3145 J/mol K

N = number of molecules

k = Boltzmann constant = 1.38066 x 10^{-23} J/K = 8.617385 x 10^{-5} eV/K

k = R/N_{A}

N_{A} = Avogadro's number = 6.023 x 10^{23} /mol

The ideal gas law can be observed as occurring from the kinetic pressure of gas molecules colliding by the walls of a container in accordance by the Newton's laws. However there is as well a statistical element in the determination of the average kinetic energy of such molecules.

The temperature is considered to be proportional to this average kinetic energy; this raises the idea of kinetic temperature. One mole of an ideal gas at STP inhabits 22.4 liters.

** Kinetic Theory assumptions regarding ideal gases**:

There is no such thing as the ideal gas, obviously, however many gases act approximately as if they were ideal at ordinary working temperatures and pressures.

The assumptions are as follows:

A) Gases are formed of molecules which are in constant arbitrary motion in straight lines.

B) The molecules act as the rigid spheres.

C) Pressure is due to the collisions among the molecules and the walls of the container.

D) All the collisions, both between the molecules themselves, and between the molecules and the walls of the container, are perfectly elastic. (That signifies that there is no loss of kinetic energy throughout the collision.)

E) The temperature of gas is proportional to the average kinetic energy of the molecules.

And then the two absolutely key suppositions, as these are the two most significant manners in which real gases dissimilar from the ideal gases are as follows:

a) There are no (or totally negligible) intermolecular forces among the gas molecules.

b) The volume occupied via the molecules themselves is entirely negligible relative to the volume of the container.

** Other P, V, T, n Relationships (Empirical Gas Laws)**:

The ideal gas law might as well be employed to examine the behavior of a gas whenever pressure, volume, moles of gas and/or temperature is changed. Such additional laws are frequently named after the scientist(s) who investigated such properties.

The relationship between pressure and volume as holding moles and temperature constant is termed as Boyle's Law. Let us derive this law. Allocate subscripts to pressure and volume to point out two different pressures and volumes:

P_{1}V_{1} = nRT

P_{2}V_{2} = nRT

As both pressures and volumes are equivalent to nRT, they are equivalent to one other:

P_{1}V_{1} = P_{2}V_{2} = nRT (that is, ** Boyle's Law**)

The relationship between volume and temperature as holding moles and pressure constant is termed as ** Charles' Law**. Let us derive this law from the ideal gas law. Allocate subscripts to volume and temperature, and hold moles and pressure constant:

PV_{1} = nRT_{1}

PV_{2} = nRT_{2}

Take the constants to one side of the equation and the variables to the other side of the equation. Divide both sides of each and every equation by pressure, 'P', and by the temperature term, 'T_{1}' in the first equation and 'T_{2}' in the second equation. This is termed as Charles' Law:

V_{1}/T_{1} = V_{2}/T_{2} = nR/P

Now let us look at the situation, where pressure and temperature are varied and the moles and volume are held constant. This empirical gas law is known as the ** Guy-Lussac Law**.

P_{1}V = nRT_{1}

P_{2}V = nRT_{2}

Divide each and every equation via their respective temperature term and each and every equation through the volume, 'V':

P_{1}/T_{1} = P_{2}/T_{2} = nR/V

The subsequent empirical gas law we will discuss is termed as the ** Avogadro's Law**. This law mainly deals by the relationship between the volume and moles of a gas at constant pressure and temperature. Let us derive this law from the ideal gas law. Providing the moles and volume subscripts, as their conditions will vary:

PV_{1} = n_{1}RT

PV_{2} = n_{2}RT

Divide the equations by pressure, P, and divide each equation by their particular mole term:

V_{1}/n_{1} = V_{2}/n_{2}

** The Combined Gas Law**:

What goes on if none of the variables for a gas are constant (that is, pressure, volume, temperature and moles of the gas were vary)? The outcome would be the Combined Gas Law. Let us derive this law. Give pressure, volume, moles and temperature subscripts, as they are all varying:

P_{1}V_{1} = n_{1}RT_{1}

P_{2}V_{2} = n_{2}RT_{2}

Divide each and every equation by their corresponding mole and temperature term:

P_{1}V_{1}/n_{1}T_{1} = P_{2}V_{2}/n_{2}T_{2}

This equation is very helpful as it includes any empirical gas law relationship you might require to come up with. If temperature and moles are held constant, then the above equation simplifies down to the Boyle's Law. If moles and pressure are held constant, then the equation simplifies down to the Charles' Law and so on. If only moles are held constant, then replace the known pressure, volume and temperatures to the above equation and simplify for the unknown quantity.

** Other Equations derived from the Ideal Gas Law**:

By the ideal gas law, PV = nRT, one can derive other helpful expressions - ones that associate the molar mass and density of Gases to pressures and temperatures. This is frequently done merely by replacing a different known expression for one of the variables in the ideal gas law. For illustration: you know that the moles of a gas, 'n', can as well be deduced as the mass of the gas in grams over the molar mass of that gas:

n = g/MM

Here,

MM = molar mass

g = grams of gas

n = moles of gas

Replace this to the ideal gas law, and one gets the equation:

PV = gRT/MM

Multiplying both the sides by the molar mass, MM, gets:

(MM)PV = gRT

This equation is helpful for finding the molar mass of a gas from experimental data, here the pressure, mass, volume and temperature of the gas is evaluated.

Now, let us divide both the sides of the above expression via the volume, 'V':

(MM)P = gRT/V

As we are familiar that g/V is density, D, let us replace density in for g/V in the above equation:

(MM)P = DRT

This equation is helpful for associating the pressure, density and temperature of gas, in the similar manner as the other empirical gas laws we have met.

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