Your research director informs you that the molecules of a sample of gas at 397 k have a root‑mean‑square (rms) speed of 275 m/s and asks you to calculate the most probable speed and the average speed. also, while you're at it and before lunch, you should calculate the mass of a molecule.

Explanation:

Hello,

Since the rms speed is defined as:

Whereas is the molecular mass of the gas, we solve for it since it is involved in the mathematical definition of both the most probable (mp) speed and the average speed (a):

(remember that J=kg*m/s^2 that's why the result lies on kg/mol).

Now, the mp speed is computed via:

Finally, the average speed is computed via:

Best regards.

c. heat could easily travel through the molecules in the air and escape/enter the flask. removing the air slows down the heat transfer.  

first let us lay out the formula for potential

and kinetic energy:

pe = mgh

ke = (mv^2)/2

where: m=mass, v=velocity, g=gravitational

acceleration, h=height

calculating for mass using the known values of

pe:

340j = m (9.81 m/s^2) (50ft) (1m/3.28ft)

m = 2.27 kg

the law of conservation of energy states that

energy is neither created nor destroyed. therefore, the change in kinetic

energy from 50 ft to 35 ft would be equal to the change in potential energy

from 50 ft to 35 ft. however it would be opposite in signs since one is losing

while other is gaining.

ke(35ft) – ke(50ft) = - [ pe(35ft) – pe(50ft]

ke(50ft) = 0 since the brick is initially at rest

ke(35ft) = 340j - 2.27kg (9.81 m/s^2) (35ft)

(1m/3.28 ft)

ke(35ft)

= 102.38 j