[Physics Class Notes] on Kinetic Theory Of Gases Pdf for Exam

Kinetic theory of gases supposes that a gaseous compound is stored in a close container. This causes the atoms in the gas to strike the walls of its container, which, in turn, leads to the formation of kinetic energy.

The primary objective of the kinetic theory of gases physics is to relate the temperature, volume and pressure of a gas to its speed, position and momentum. Nevertheless, here is a bit more about this theory for better comprehension.

Defining Kinetic Theory of Gases

Inside a closed container, gas molecules shoot off in random directions with speed and energy. If you can determine the position or speed of these molecules, you can also derive its pressure or temperature. 

To be more precise, this theory and formula help determine macroscopic properties of a gas, if you already know the velocity value or internal molecular energy of the compound in question.

However, before learning about the kinetic theory of gases formula, one should understand a few aspects, which are crucial to such a calculation.

What is Avagadro’s Number?

Avagadro’s number helps in establishing the amount of gas present in a specific space. This number is also known as a mole. 

1 mole = 6.0221415 x 1023

Interesting Note: Close to 1032 atmospheric molecules hit a human being’s body every day with speeds of up to 1700 km/hr. 

Therefore, one mole holds around 6.023 x 1023 atoms or molecules. The number of molecules or atoms in one mole remains constant for all gaseous compounds, irrespective of its components. 

Quick Exercise – 1

Q. Gas A has 18.06 x 1023 atoms in a closed container. Determine how many moles of Gas A are present in the container.

Solution:

Consider number of atoms of Gas A (N) = 18.06 x 1023

Number of atoms in one mole of Gas A (Na) = 6.02 x 1023

Thus, number of moles of Gas A (n) = N/Na

n = 18.06 x 1023/6.02 x 1023

Thus, n = 3 moles      

What is Molar Mass?

The mass of one mole is known as molar mass. Molar mass is essential to determine the number of moles in a gas sample if the mass of the sample is known. Consider Ms as the mass of a gas sample in grams and M as the molar mass. 

Therefore, n = Ms/M….eq.1

We can also derive molar mass (M) if the mass of one molecule (m) of the sample is known. In such a case,

M = m x Na (Avagadro’s number)….eq.2

Equating eq.1 and eq.2, we can derive the formula

n = Ms/(m x Na)     

Ideal Gas Law

Researchers say that one mole of different gases placed in containers of similar volume, under the same temperature, will produce the same pressure. This is known as the Ideal Gas Law, which is crucial for the derivation of kinetic theory of gas equation.

Thus, from this law, we can claim that pV = nRT

Here n represents the number of moles in a sample, and V is the container volume. T is the temperature at which this sample of gas is kept, and p is absolute pressure. R is the gas constant, which is the same for all gases.

R = 8.31 J/mol K

Another important figure to remember is Boltzmann’s Constant (k) = R/Na = 1.38 x 10-23 J/K    

Average Kinetic Energy Formula

To derive this formula, you must equate pV = nRT with pV = 1/3Nmv2

nRT = 1/3Nmv2

Multiply and divide by 2

nRT = 2/3N (1/2mv2)

1/2mv2 = 3nRT/2N

Now, since Na (Avagadro’s number) = N (total number of gas molecules)/n (number of moles)

1/2mv2 = 3nRT/2 (N/n)

1/2mv2 = 3RT/2N

We know R/N is equal to k or Boltzmann’s constant

Thus, we can say Kinetic energy = 3kT/2

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