In this lesson, we will learn how to calculate the proportion of particles, in an ideal gas, that have a given speed using the Maxwell–Boltzmann distribution function.

Q1:

An incandescent light bulb is filled with neon gas. The gas that is in close proximity to the element of the bulb is at a temperature of 2 3 0 0 K. Determine the root-mean-square speed of neon atoms in close proximity to the element. Use a value of 20.2 g/mol for the molar mass of neon.

Q2:

In a sample of a monatomic gas, a number of molecules 𝑛 1 have speeds that are within a very small range around the root-mean-square speed of atoms in the gas, 𝑣 𝑟 𝑚 𝑠 . A number of molecules 𝑛 2 have speeds that are within the same very small range around a speed of 3 . 0 0 ⋅ 𝑣 𝑟 𝑚 𝑠 . Determine the ratio of 𝑛 1 to 𝑛 2 .

Q3:

A sample of nitrogen is at a temperature of 3 0 1 5 K. 𝑁 2 has a molar mass of 28.00 g/mol.

What is the most probable speed of the nitrogen molecules?

What is the average speed of the nitrogen molecules?

What is the root-mean-square speed of the nitrogen molecules?

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