If two molecules have the same temperature does it affect their average velocity depending on how heavy the molecules are or not?

For the same T, the kinetic energy is the same for the two molecules.

K. E. = 1/2 m*v2
So if K. E. is same and the masses are different, what must be true about the velocities of each.

That they are the same?

of course not.

Use K. E. = 1/2 m*v2
Now just put some numbers in. Say K. E. = 10 for both molecules.
Now put in something like 10 for mass for one and calculate v. Then put in 5 for the other and calculate v. Is v the same? No. Can you see that if 1/2 mv^2 = a constant, then if m goes UP, the v must go DOWN; or if m goes DOWN, then v must go UP. If one increases the other must decrease to keep the constant a constant. right?

Think about Boyle's law. It was
PV = k.
If pressure of a gas goes up the volume must go down. If presure goes down the volume goes up. You know that from the gas laws. This is the same kine of thing but instead of PV = k we have k=K.E. = 1/2 mv^2 and we know K. E. is the same from the kinetic moleuclar theory that tells us the K. E. is the same for all molecules at the same temperature.

Yes, the average velocity of molecules can be influenced by their mass, even when they are at the same temperature. To better understand this relationship, let's break it down.

In an ideal gas or a gas that closely obeys the ideal gas law, such as at low pressures and high temperatures, the average kinetic energy of the gas molecules is directly proportional to the temperature. Kinetic energy is determined by both the mass and velocity of the molecules.

The kinetic energy (KE) of a gas molecule can be expressed using the following equation:

KE = (1/2) * m * v^2

Where:
KE = kinetic energy
m = mass of the molecule
v = velocity of the molecule

From this equation, we can see that the kinetic energy depends on both the mass (m) and the square of the velocity (v^2). Therefore, if two molecules have the same temperature, their kinetic energies will be the same. This implies that their average kinetic energies are equal as well.

Given that the average kinetic energies are equal, we can write the equation for average kinetic energy (KE_avg) as:

KE_avg = (1/2) * m1 * v1^2 = (1/2) * m2 * v2^2

Since the temperatures are the same, we can write the equation in terms of velocity:

m1 * v1^2 = m2 * v2^2

Simplifying the equation, we get:

(m1 / m2) = (v2 / v1)^2

From this equation, we can conclude that the ratio of the masses (m1 / m2) is inversely proportional to the square of the ratio of velocities (v2 / v1)^2. Therefore, if the masses of the molecules differ, their velocities will also differ in order to maintain the same average kinetic energy at the same temperature.

To summarize, when two molecules have the same temperature, their average velocities will differ depending on their masses. Heavier molecules will have lower velocities compared to lighter molecules, while still maintaining the same average kinetic energy.