Chemistry, 21.07.2019 23:30 mai1261

"at what gas temperature t e would the average translational kinetic energy of a helium atom be equal to that of an oxygen molecule in a gas of temperature 300 k"

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Based on equipartition theorem, the average kinetic energy of molecules is mathematically expressed as,
<K.E.> = $\frac{3kT}{2}$
where, k = Boltzmann's Constant.
T = temperature in Kelvins.

Thus from above expression, it can be seen that average kinetic energy of molecules is independent of mass and, it is dependent only on temperature.

Hence, at temperature of 300 K the average kinetic energy associated with both helium and oxygen will be same.

Answer from: damonsalvatoreisbae

The average translational kinetic energy of helium s equal to that of oxygen at $\boxed{300\;{\text{K}}}$ .

Further Explanation:

One of the states of matter is gas. In gases, the atoms and molecules have space between them and can easily move over each other hence gases are compressible. Gases neither have fixed shape nor volume. It occupies the shape and volume of the container. The examples of matter that are gases are nitrogen and carbon dioxide.

The kinetic theory is based on the following postulates:

1. Gas molecules have a large collection of individual particles with empty space between them and the volume of each particle is very small as compared to the volume of the whole gas.

2. The gas particles are in straight-line motion or random motion until they are not collided with the wall of the container or with each other.

3. The collision between the gas particles and the wall of the containers are an elastic collision that means molecules exchange energy but they don’t lose any energy during the collision. So the total kinetic energy is constant.

The formula to calculate the average translational kinetic energy of helium is as follows:

${{\text{E}}_{{\text{He}}}} = \frac{3}{2}{\text{k}}{{\text{T}}_{{\text{He}}}}$ …… (1)

Here,

${{\text{E}}_{{\text{He}}}}$ is the average translational kinetic energy of helium gas.

k is the Boltzmann constant.

${{\text{T}}_{{\text{He}}}}$ is the absolute temperature of helium gas.

The formula to calculate the average translational kinetic energy of oxygen is as follows:

${{\text{E}}_{{{\text{O}}_{\text{2}}}}} = \frac{3}{2}{\text{k}}{{\text{T}}_{{{\text{O}}_{\text{2}}}}}$ …… (2)

Here,

${{\text{E}}_{{{\text{O}}_{\text{2}}}}}$ is average translational kinetic energy of oxygen gas.

k is the Boltzmann constant.

${{\text{T}}_{{{\text{O}}_{\text{2}}}}}$ is absolute temperature of oxygen gas.

Since both gases have same average translational energy. So left-hand side of equation (1) and (2) becomes equal, and therefore right-hand side of both equations can be compared as follows:

$\frac{3}{2}{\text{k}}{{\text{T}}_{{{\text{O}}_2}}} = \frac{3}{2}{\text{k}}{{\text{T}}_{{\text{He}}}}$ …… (3)

Rearrange equation (3) to calculate ${{\text{T}}_{{{\text{O}}_{\text{2}}}}}$

${{\text{T}}_{{{\text{O}}_2}}} = {{\text{T}}_{{\text{He}}}}$ …… (4)

The value of ${{\text{T}}_{{\text{He}}}}$ is 300 K. So according to equation (4), ${{\text{T}}_{{{\text{O}}_{\text{2}}}}}$ also becomes 300 K.

Learn more:

1. What is the kinetic energy of electrons?

2. Calculate the frequency of yellow light:

Answer details:

Grade: High School

Subject: Chemistry

Chapter: Ideal gas equation

Keywords: 300 K, helium, oxygen, average translational kinetic energy, k, Boltzmann constant, absolute temperature, gas, kinetic theory, 3/2 kT, same, equal.

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