At a given temperature O2 molecules will move (3/2)1/2 faster than O3 molecules on the average.

True or False? I'm not sure if it is true or false on this one, but I think its false.

If you mix a gas, eventually all the molecules have the same kinetic energy on the average, independent of their mass or the temperature at which they were introduced.

I think this is false, but I'm not completely sure.

In the kinetic theory of gases, pressure is due to the strength of the molecular bonds within each gas molecule.

I think this is true, but again, not sure.

(1/2) m (v^2)av = (3/2) kT

so m v^2 is the same for O2 and O3
m1 v1^2 = m2 v2^2
m2 = 2 and m1 = 3

3 v1^2 = 2 v2^2
so
v2^2/v1^2 = 3/2
v2/v1 = (3/2)^(1/2)
TRUE

If you mix a gas, eventually all the molecules have the same kinetic energy on the average, independent of their mass or the temperature at which they were introduced.

I think this is false, but I'm not completely sure.
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I think it true
(1/2) m (v^2)av = average kinetic energy the same for all the molecules at that temp = (3/2) kT

In the kinetic theory of gases, pressure is due to the strength of the molecular bonds within each gas molecule.

I think this is true, but again, not sure.
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False false false
Think of gas banging walls of the container.
It depends on how many and how fast they are moving
remember p = n R T/V

For the first question, it can be determined whether it is true or false by understanding the relationship between temperature and the average speed of gas molecules. The average kinetic energy of gas molecules is directly proportional to the temperature. The formula to calculate the average speed of gas molecules is given by v = (3kT/m)^(1/2), where v is the average speed, k is Boltzmann's constant, T is the temperature in Kelvin, and m is the mass of the gas molecule.

To compare the average speeds of O2 and O3 molecules at a given temperature, we need to consider their respective masses. The molecular mass of O2 is around 32 atomic mass units (amu), while the molecular mass of O3 is around 48 amu. Since the formula for average speed involves the square root of the inverse of the mass, the average speed of O2 molecules will be greater than the average speed of O3 molecules at the same temperature. Therefore, the statement is false. O2 molecules will not move (3/2)^(1/2) faster than O3 molecules on average.

For the second question, it is false that eventually, all the gas molecules will have the same kinetic energy on average, regardless of their mass or the temperature at which they were introduced. According to the kinetic theory of gases, temperature is a measure of the average kinetic energy of the molecules. However, the kinetic energy of individual gas molecules can vary based on their mass and velocity. In a gas mixture, gases with different masses will have different average kinetic energies, even at the same temperature. The kinetic energy is given by the equation KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass of the molecule, and v is the velocity.

Lastly, for the third question, it is false that pressure is due to the strength of molecular bonds within each gas molecule, according to the kinetic theory of gases. Pressure in a gas is a result of the collisions between gas molecules and the walls of the container. Gas molecules are constantly in motion and collide with each other and the walls of the container, exerting a force. The sum of these forces over a given area gives rise to pressure. The strength of molecular bonds within each gas molecule does not directly contribute to the pressure experienced by the gas.