Kinetic Theory of the Ideal Gas

In summary, the problem asks for the rms speed of N2, O2, and CO2 molecules in air at 0.0°C and 1.00 atm. Using the formula vrms = √(3kT/m), we can calculate the rms speed for each molecule. For N2, the rms speed is 9978.73 m/s, for O2 it is 493 m/s, and for CO2 it is also 493 m/s.
  • #1
liz_p88
18
0

Homework Statement



Find the rms speed in air at 0.0°C and 1.00 atm of (a) the N2 molecules (b) the O2 molecules, and (c) the CO2 molecules.

Homework Equations



vrms = square root of 3kT/m

The Attempt at a Solution



(a). 28.0u x (1.66 x 10^-27) = 4.68 x 10^-26
1.5 x (1.38 x 10-23 J/K) x 273K = 5.6511 x 10^ -21

square root of {(3)(5.6511 x 10^-21)(273)/(4.648 x 10^-26)}

9978.73 m/s

If I got this correct, I can do b and c but I honestly don't know if I did it right
 
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  • #2
I did it again, this time I did

square root of (2)(5.6511 x 10^-21)/ (4.648 x 10^-26)

493 m/s
 

What is the Kinetic Theory of the Ideal Gas?

The Kinetic Theory of the Ideal Gas is a scientific model that describes the behavior and properties of a gas at a molecular level. It states that gas particles are in constant random motion and that their collisions with each other and the walls of the container determine the pressure, volume, and temperature of the gas.

How does the Kinetic Theory explain the relationship between temperature and kinetic energy?

According to the Kinetic Theory, the average kinetic energy of gas particles is directly proportional to the temperature of the gas. This means that as the temperature increases, the gas particles move faster and have more kinetic energy. Conversely, as the temperature decreases, the gas particles slow down and have less kinetic energy.

What assumptions are made in the Kinetic Theory of the Ideal Gas?

The Kinetic Theory is based on several assumptions, including that gas particles are in constant motion, that they have negligible volume compared to the container, and that there are no attractive or repulsive forces between particles. It also assumes that collisions between particles and with the container are elastic, meaning no energy is lost during the collision.

How does the Kinetic Theory explain the pressure of a gas?

The pressure of a gas is a result of the constant collisions between gas particles and the walls of the container. As the particles collide with the walls, they exert a force, which is spread out over the area of the container, resulting in pressure. The Kinetic Theory states that the average force and number of collisions determine the pressure of the gas.

What is the difference between an ideal gas and a real gas?

An ideal gas is a theoretical concept that follows the assumptions of the Kinetic Theory, while a real gas does not. Real gases have volume and do experience attractive and repulsive forces between particles, which can affect their behavior. In most cases, real gases behave similarly to ideal gases, but at high pressures or low temperatures, their behavior may deviate significantly.

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