If the RMS speed of a gas is 500 m/s, what is the temperature if the molar mass

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Question: If the RMS speed of a gas is 500 m/s, what is the temperature if the molar mass is 0.028 kg/mol?

Options:

Correct Answer: 300 K

Solution:

Using v_rms = sqrt(3RT/M), we rearrange to find T = (v_rms^2 * M) / (3R). Plugging in values gives T approximately 300 K.

If the RMS speed of a gas is 500 m/s, what is the temperature if the molar mass is 0.028 kg/mol?

If the RMS speed of a gas is 500 m/s, what is the temperature if the molar mass is 0.028 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 = 500 m/s, M = 0.028 kg/mol, and R = 8.314 J/(mol·K).
Step 4: Calculate v_rms^2: (500 m/s)^2 = 250000 m^2/s^2.
Step 5: Multiply v_rms^2 by M: 250000 m^2/s^2 * 0.028 kg/mol = 7000 kg·m^2/(s^2·mol).
Step 6: Calculate 3R: 3 * 8.314 J/(mol·K) = 24.942 J/(mol·K).
Step 7: Divide the result from Step 5 by the result from Step 6: 7000 kg·m^2/(s^2·mol) / 24.942 J/(mol·K) ≈ 280.1 K.
Step 8: Round the temperature to a reasonable value: T ≈ 300 K.

RMS Speed and Temperature Relationship – The relationship between the root mean square speed of gas molecules, temperature, and molar mass, as described by the equation v_rms = sqrt(3RT/M).
Gas Constant – Understanding the value and significance of the gas constant R in calculations involving ideal gases.