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# The Speed of Nitrogen Molecules

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The Speed of Nitrogen Molecules
The kinetic theory of gases states that the kinetic energy of a gas is directly proportional to the temperature of the gas. A relationship between the microscopic properties of the gas molecules and the macroscopic properties of the gas can be derived using the following assumptions:
• The gas is composed of pointlike particles separated by comparatively large distances.
• The gas molecules are in continual random motion with collisions being perfectly elastic.
• The gas molecules exert no long-range forces on each other.
One of the most important microscopic properties of gas molecules is velocity. There are several different ways to describe statistically the average velocity of a molecule in a gas. The most obvious measure is the average velocity . However, since the molecules in a gas are moving in random directions, the average velocity is approximately zero. Another measure of velocity is , the average squared velocity. Since the square of velocity is always positive, this measure does not average to zero over the entire gas. A third measure is the root-mean-square (rms) speed, , equal to the square root of . The rms speed is a good approximation of the the typical speed of the molecules in a gas.
This histogram shows a theoretical distribution of speeds of molecules in a sample of nitrogen ( ) gas. In this problem, you'll use the histogram to compute properties of the gas.
A. What is the average speed of the molecules in the gas?

=

B. Because the kinetic energy of a single molecule is related to its velocity squared, the best measure of the kinetic energy of the entire gas is obtained by computing the mean squared velocity, , or its square root . The quantity is more common than because it has the dimensions of velocity instead of the less-familiar velocity-squared.
What is the rms speed of the molecules in the nitrogen gas?

=

C. What is the temperature of the sample of gas described in the histogram?

=

D. Not available
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