At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is

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Question: At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is 0.02 kg/mol?

Options:

Correct Answer: 900 K

Solution:

Using v_rms = sqrt(3RT/M), we can rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T = (600^2 * 0.02) / (3 * 8.314) = 900 K.

At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is 0.02 kg/mol?

At what temperature will the RMS speed of a gas be 600 m/s if its molar mass is 0.02 kg/mol?

Step 1: Write down the formula for RMS speed: v_rms = sqrt(3RT/M).
Step 2: Rearrange the formula to solve for temperature (T): T = (v_rms^2 * M) / (3R).
Step 3: Identify the values needed: v_rms = 600 m/s, M = 0.02 kg/mol, and R = 8.314 J/(mol·K).
Step 4: Calculate v_rms^2: 600^2 = 360000.
Step 5: Multiply v_rms^2 by M: 360000 * 0.02 = 7200.
Step 6: Calculate 3R: 3 * 8.314 = 24.942.
Step 7: Divide the result from Step 5 by the result from Step 6: 7200 / 24.942 ≈ 288.5.
Step 8: The final temperature T is approximately 288.5 K.

RMS Speed of Gas – The root mean square (RMS) speed of a gas is a measure of the average speed of gas particles and is related to temperature and molar mass.
Ideal Gas Law – The relationship between temperature, pressure, volume, and the number of moles of a gas, which can be applied to derive the RMS speed formula.
Gas Constant (R) – The universal gas constant used in calculations involving ideal gases, typically valued at 8.314 J/(mol·K).