Average kinetic energy of a gas

Helium can be treated like an ideal gas.Helium molecules have a root-mean-square (r.m.s) speed of 730 m s-1 at a temperature of 45 oC.Calculate the r.m.s speed of the molecules at a temperature of 80 oC.

Step 1:            Write down the equation for the average translational kinetic energy:

Step 2:            Find the relation between cr.m.s and temperature T

Since m and k are constant, <c2> is directly proportional to T

<c2> ∝ T

Therefore, the relation between cr.m.s and T is:

Step 3:            Write the equation in full

where a is the constant of proportionality

Step 4:            Calculate the constant of proportionality from values given by rearranging for a:

T = 45 oC + 273.15 = 318.15 K

Step 5:            Calculate cr.m.s  at 80 oC by substituting the value of a and new value of T

T = 80 oC + 273.15 = 353.15 K

Exam Tip

Keep in mind this particular equation for kinetic energy is only for one molecule in the gas. If you want to find the kinetic energy for all the molecules, remember to multiply by N, the total number of molecules.You can remember the equation through the rhyme ‘Average K.E is three-halves kT’.

Enter the temperature of an ideal gas into the calculator to determine the average kinetic energy of the particles in the gas.

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Average Kinetic Energy Formula

The following formula is used to calculate the average kinetic energy of a gas.

K = (3/2) * (R / N) * T

• Where K is the average kinetic energy (Joules)
• R is the gas constant (8.314 J/mol * K)
• N is Avogadro’s number (6.022 * 1023 atoms/mol)
• T is the temperature in Kelvin

To calculate the average kinetic energy of a gas, divide the gas constant by Avogadro’s number, multiply by the temperature, then again by (3/2).

Average Kinetic Energy Definition

Average kinetic energy is defined as the average energy contained within the movement of particles of a gas.

Average Kinetic Energy Example

How to calculate average kinetic energy?

1. First, determine the temperature of the gas.

   Determine the temperature of the gas and depending on the units, convert them to units of Kelvin.

2. Calculate the average kinetic energy.

   Plug in the value of the temperature in Kelvin into the formula to determine the average kinetic energy.

FAQ

What is the average kinetic energy of a gas?

The average kinetic energy of a gas can be calculated using the formula (3/2)*(R/N)*T for ideal gases only.

According to Kinetic Molecular Theory, the average kinetic energy of gas molecules is a function only of temperature.

The formula is

#KE = 3/2kT#

where#T#is the Kelvin temperature and#k#is Boltzmann's constant.

#KE = 3/2 × 1.381 × 10⁻²³ "J·K⁻¹" × 273"K"#= 5.66 × 10⁻²¹ J

For a mole of molecules, the average kinetic energy is

#(5.66 × 10⁻²¹"J")/(1"molecule") × (6.022 × 10²³"molecules")/(1"mol")#= 3.41 ×10³ J/mol = 3.41 kJ/mol

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• How does the absolute temperature of a substance relate to the average kinetic energy of its molecules?

  What is the kinetic energy of a gas?

  The molar kinetic energy of a gas is proportional to its temperature, and the proportionality constant is 32 times the gas constant R. The video below demonstrates the relationship between molar kinetic energy and temperature.

  What is the formula for average kinetic energy?

  Average Kinetic Energy per Molecule The average kinetic energy of a molecule is directly proportional to its absolute temperature: K – = 1 2 m v 2 – = 3 2 k B T . K – = 1 2 m v 2 – = 3 2 k B T . The equation K – = 3 2 k B T K – = 3 2 k B T is the average kinetic energy per molecule.

  Is the average kinetic energy of gases the same?

  The average kinetic energy is the same for all gases at a given temperature, regardless of the identity of the gas. Furthermore, this kinetic energy is proportional to the absolute temperature of the gas.