If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at

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Question: If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?

Options:

Correct Answer: 0.5 mJ

Solution:

Kinetic energy per molecule = (1/2)mv^2. Using v = 400 m/s and m = M/N_A, we find KE = 0.5 mJ.

If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?

If the RMS speed of a gas is 400 m/s, what is the kinetic energy per molecule at 300 K?

Step 1: Understand that the kinetic energy (KE) of a molecule can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the molecule and v is the speed.
Step 2: Identify the given values. The RMS speed (v) is 400 m/s.
Step 3: Find the mass of one molecule (m). To do this, use the formula m = M/N_A, where M is the molar mass of the gas and N_A is Avogadro's number (approximately 6.022 x 10^23 mol^-1).
Step 4: Substitute the values into the kinetic energy formula. You will need to calculate (1/2) * m * (400 m/s)^2.
Step 5: Calculate the kinetic energy per molecule. After substituting the values and performing the calculations, you will find that KE is approximately 0.5 mJ.

Kinetic Energy of Gases – The kinetic energy per molecule of a gas can be calculated using the formula KE = (1/2)mv^2, where m is the mass of the molecule and v is the RMS speed.
RMS Speed – RMS (Root Mean Square) speed is a measure of the average speed of gas molecules and is used in calculating kinetic energy.
Molecular Mass and Avogadro's Number – The mass of a single molecule can be derived from the molar mass (M) of the gas divided by Avogadro's number (N_A).