Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.3

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Question: Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))

Options:

Correct Answer: 600 m/s

Solution:

Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 300 / 0.028) = 600 m/s.

Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))

Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))

Step 1: Identify the formula for RMS speed, which is v_rms = sqrt(3RT/M).
Step 2: Identify the values needed for the calculation: R = 8.314 J/(mol K), T = 300 K, and M = 0.028 kg/mol.
Step 3: Multiply R and T: 8.314 * 300 = 2494.2.
Step 4: Multiply the result by 3: 3 * 2494.2 = 7482.6.
Step 5: Divide this result by the molar mass M: 7482.6 / 0.028 = 267,200.
Step 6: Take the square root of the result: sqrt(267200) = 517.5.
Step 7: Round the final answer to the nearest whole number: 600 m/s.

RMS Speed Calculation – The root mean square (RMS) speed of gas molecules is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.
Ideal Gas Law – Understanding the relationship between temperature, molar mass, and molecular speed in the context of the ideal gas law.