What is the total translational kinetic energy of the gas molecules

In summary, the problem is asking for the total translational kinetic energy of 0.450 mol of air at atmospheric pressure occupying a volume of 5.00 L. The equation P=2/3(N/V)<Ktr> is given, with N=0.450 mol and V=5.00 L, but the pressure is not specified. Atmospheric pressure can be converted to 1 atm = 760 mm Hg = 101.3 kPa. Using the formula PV = NkT, the formula for finding the translational kinetic energy can be derived.
  • #1
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Homework Statement


What is the total translational kinetic energy of the gas molecules of 0.450 mol of air at atmospheric pressure that occupies a volume of 5.00 L (0.00500 m3)?


Homework Equations


P=2/3(N/V)<Ktr>
N= 0.450 mol
V= 5.00L
Want to find Ktr


The Attempt at a Solution


The problem is I don't know the pressure to use this formula or how to figure out what it is from the given information, if that's possible.
 
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  • #2
Well, atmospheric pressure is 1 atm = 760 mm Hg = 101.3 kPa.

If you need more help, given that the translational kinetic energy of one molecule of gas is KE = 3kT/2, use the formula PV = NkT to derive the formula for the case that you're dealing with.
 
  • #3


To find the total translational kinetic energy of the gas molecules, we can use the equation:

Ktr = 3/2 * N * k * T

where N is the number of moles, k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the temperature in Kelvin.

In this problem, we are given the number of moles (0.450 mol) and the volume (5.00 L). However, we are not given the temperature or the pressure.

To find the temperature, we can use the ideal gas law:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant (8.31 J/mol*K), and T is the temperature in Kelvin.

Since we are given the volume and the number of moles, we can rearrange the equation to solve for the temperature:

T = (PV)/(nR)

Now, we need to find the pressure. We are given that the air is at atmospheric pressure, which is typically around 101325 Pa. We can convert this to units of J/m^3 by multiplying by the conversion factor 1 Pa = 1 J/m^3.

So, the pressure (P) = 101325 J/m^3.

Now, we can plug in all the values into the equation for Ktr:

Ktr = 3/2 * 0.450 mol * (1.38 x 10^-23 J/K) * ((101325 J/m^3 * 0.00500 m^3)/(0.450 mol * 8.31 J/mol*K))

Ktr = 0.000397 J

Therefore, the total translational kinetic energy of the gas molecules is 0.000397 J.
 

1. What is translational kinetic energy?

Translational kinetic energy is the energy that an object possesses due to its motion. It is defined as the product of its mass and the square of its velocity divided by 2, and is measured in Joules (J).

2. How is the total translational kinetic energy of gas molecules calculated?

The total translational kinetic energy of gas molecules is calculated by summing up the individual translational kinetic energies of each molecule in the gas. This can be done using the formula: K = (1/2)mv^2, where K is the kinetic energy, m is the mass of the molecule, and v is its velocity.

3. What factors affect the total translational kinetic energy of gas molecules?

The total translational kinetic energy of gas molecules is affected by the mass and velocity of the molecules. The higher the mass and velocity, the higher the kinetic energy. Additionally, changes in pressure, temperature, and volume can also affect the kinetic energy of gas molecules.

4. Why is the concept of translational kinetic energy important in understanding gas behavior?

Translational kinetic energy is important in understanding gas behavior because it helps explain how gas molecules move and interact with each other. It also plays a role in determining properties of gases, such as their temperature and pressure.

5. Can the total translational kinetic energy of gas molecules be changed?

Yes, the total translational kinetic energy of gas molecules can be changed by altering the conditions of the gas, such as changing its temperature or pressure. In addition, external forces, such as collisions with other molecules or objects, can also affect the kinetic energy of gas molecules.

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