Avarage kinetic speed of particles in a gas

[pugtm]

Homework Statement

gas contains a mixture of He and Ne. The
gas is at a temperature of 419 K, with 0.76mol
of He and 2 mol of Ne.
What is the average kinetic energy per
molecule of He?
Avogadro’s number is
6.02 × 1023 mol−1, and Boltzmann’s constant
is 1.38 × 10−23 J/K.
Answer in units of J.

B)What is the average kinetic energy per
molecule of Ne?

C)What is the average total kinetic energy of
He?
Answer in units of J.

D)What is the average total kinetic energy of
Ne?
Answer in units of J.

Homework Equations

PV=NKT
kinetic energy =1/2mv^2
V=Sqrt(3kt/m)

The Attempt at a Solution

part A
so using that third equation i come out with
V=sqrt(3*1.38e-23*419Kelvin/2* 1.66x10^-27kg)
so 1/2 v^2 m is the energy,
but for part 3
how do i determine the total energy?
just multiply this by the moles of hydrogen or do i take the nitrogen also into account?

 

[anathema]

To determine the average kinetic energy per molecule of He, you can use the formula for kinetic energy: KE = 1/2 * m * v^2, where m is the mass of the molecule and v is the average velocity. Since the gas is a mixture of He and Ne, you will need to find the average velocity of each molecule separately and then take the average of the two velocities.

To find the average velocity of He, you can use the formula V = sqrt(3 * k * T / m), where k is Boltzmann's constant, T is the temperature in Kelvin, and m is the mass of the molecule. Plugging in the values given in the problem, you should get an average velocity of 1.81 x 10^3 m/s for He.

To find the average velocity of Ne, you can use the same formula but substitute in the mass of Ne instead. Plugging in the values given, you should get an average velocity of 1.35 x 10^3 m/s for Ne.

To find the average kinetic energy per molecule of He, you can plug the average velocity of He into the kinetic energy formula, along with the mass of He. This should give you an average kinetic energy of 1.04 x 10^-20 J per molecule of He.

To find the average kinetic energy per molecule of Ne, you can use the same process but with the average velocity of Ne and the mass of Ne. This should give you an average kinetic energy of 1.29 x 10^-20 J per molecule of Ne.

To determine the average total kinetic energy of He, you will need to multiply the average kinetic energy per molecule of He by the number of moles of He (0.76). This should give you an average total kinetic energy of 7.90 x 10^-21 J for He.

To determine the average total kinetic energy of Ne, you will need to multiply the average kinetic energy per molecule of Ne by the number of moles of Ne (2). This should give you an average total kinetic energy of 2.58 x 10^-20 J for Ne.