Average Translational Kinetic Energy of 1 Molecule: Solve for N

In summary, to find the average translational kinetic energy of one molecule in a monatomic ideal gas that occupies 0.63 m3 at atmospheric pressure, we can use the equation PV = nRT (or PV = NkT), where n is the number of moles (1.2 x10^23 molecules divided by Avogadro's number) and T is the temperature in Kelvin. Plugging in the given values gives us an average translational kinetic energy of 39425 K. However, this may not be a realistic value for a room-temperature gas with 1.2 x10^23 molecules.
  • #1
yankees26an
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Homework Statement


1.2 x10^23 molecules of a monatomic ideal gas occupies the volume of 0.63 m3 at
atmospheric pressure. Find the average translational kinetic energy of one molecule.


Homework Equations



PV = NRT

K = 3/2*kB*T

The Attempt at a Solution



T = PV/NR

But.. what's N(moles)?
 
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  • #2
One mole of anything = 6.03*10^23 molecules of that thing. BTW, you can also use PV=nkT. That way, you can directly plug in 1.2 x10^23 into "n".
 
  • #3
In this equation usually moles: here 1.2/6.02= n. The 10^23 on top and bottom cancel.
 
  • #4
Ok so I get T = 39425 K :S
 
  • #5
That's correct, although not realistic. 1.2*10^23 of a room-temperature gas would take up around 5 L.
 

FAQ: Average Translational Kinetic Energy of 1 Molecule: Solve for N

1. What is the formula for calculating the average translational kinetic energy of 1 molecule?

The formula for calculating the average translational kinetic energy of 1 molecule is: KE = 3/2 * (k * T), where KE is the kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin.

2. How do you solve for N in the equation for average translational kinetic energy of 1 molecule?

To solve for N, you would need to know the values for kinetic energy (KE), Boltzmann constant (k), and temperature (T). Plug those values into the equation KE = 3/2 * (k * T) and solve for N by dividing both sides by 3/2 and then dividing by k and T.

3. What is the significance of the average translational kinetic energy of 1 molecule?

The average translational kinetic energy of 1 molecule is a measure of the average energy of motion of a single molecule. It is an important concept in thermodynamics and is used to calculate other properties such as pressure and temperature of a gas.

4. How does temperature affect the average translational kinetic energy of 1 molecule?

According to the equation KE = 3/2 * (k * T), the average translational kinetic energy of 1 molecule is directly proportional to the temperature. This means that as the temperature increases, the average kinetic energy of the molecule also increases.

5. Is the average translational kinetic energy of 1 molecule different for different types of molecules?

Yes, the average translational kinetic energy of 1 molecule can vary depending on the properties of the molecule, such as its mass and velocity. Heavier molecules tend to have a lower average kinetic energy compared to lighter molecules at the same temperature. Additionally, the average kinetic energy can also vary for molecules at different temperatures.

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