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

• yankees26an
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.
yankees26an

## 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.

PV = NRT

K = 3/2*kB*T

## The Attempt at a Solution

T = PV/NR

But.. what's N(moles)?

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".

In this equation usually moles: here 1.2/6.02= n. The 10^23 on top and bottom cancel.

Ok so I get T = 39425 K :S

That's correct, although not realistic. 1.2*10^23 of a room-temperature gas would take up around 5 L.

## 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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