Kinetic molecular theory, including particulate and mathematical models

Question 1

What are the main assumptions of the kinetic molecular theory of gases?

Answer 1

The main assumptions are:
1.Gas particles are in constant, random motion.
2.The volume of individual gas particles is negligible compared to the container’s volume.
3.Gas particles exert no intermolecular forces (attractions or repulsions) on each other.
4.Collisions between gas particles and with the container walls are perfectly elastic.
5.The average kinetic energy of gas particles is directly proportional to the absolute temperature (in Kelvin).

These assumptions explain the behavior of ideal gases and form the basis for deriving the ideal gas law.

Question 2

What is the ideal gas law equation?

Answer 2

The ideal gas law is PV=nRT

Here:
P = pressure (in atmospheres, atm)
V = volume (in liters, L)
n = amount of substance (in moles, mol)
R = ideal gas constant (8.314J/K⋅mol)
T = temperature (in Kelvin, K)

Question 3

What is Boyle’s Law and its mathematical expression?

Answer 3

Boyle’s Law states that at constant temperature and amount of gas, the pressure of a gas is inversely proportional to its volume:
P_1⋅V_1 = P_2⋅V_2

This means that if the volume of a gas decreases, its pressure increases proportionally, provided temperature and moles of gas remain constant.

Question 4

What is Charles’s Law and its mathematical expression?

Answer 4

harles’s Law states that at constant pressure and amount of gas, the volume of a gas is directly proportional to its absolute temperature:
V_1/T_1 = V_2/T_2

This implies that heating a gas will cause it to expand if the pressure is kept constant.

Question 5

What is the mathematical expression for the average kinetic energy of gas particles?

Answer 5

𝐾𝐸_avg =(3/2)(𝑘_𝐵)𝑇

KE_avg is the average kinetic energy of a gas particle, 𝑘_B is the Boltzmann constant, and T is the absolute temperature in Kelvin.