In a mixture of gases, how is the RMS speed of the mixture calculated?

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Question: In a mixture of gases, how is the RMS speed of the mixture calculated?

Options:

Correct Answer: Using the average molar mass of the mixture

Solution:

The RMS speed of a mixture of gases is calculated using the average molar mass of the mixture in the formula v_rms = sqrt((3RT)/M_avg).

In a mixture of gases, how is the RMS speed of the mixture calculated?

In a mixture of gases, how is the RMS speed of the mixture calculated?

Step 1: Identify the gases in the mixture and their respective molar masses.
Step 2: Calculate the average molar mass (M_avg) of the mixture using the formula: M_avg = (sum of (molar mass of each gas * its mole fraction)) / (sum of mole fractions).
Step 3: Determine the temperature (T) in Kelvin and the universal gas constant (R), which is approximately 8.314 J/(mol·K).
Step 4: Use the formula for RMS speed: v_rms = sqrt((3RT)/M_avg).
Step 5: Plug in the values of R, T, and M_avg into the formula to calculate the RMS speed.

RMS Speed Calculation – The root mean square (RMS) speed of a gas mixture is derived from the kinetic theory of gases and involves the average molar mass of the gas mixture.
Average Molar Mass – The average molar mass (M_avg) is crucial for calculating the RMS speed, as it reflects the contribution of each gas in the mixture based on its mole fraction.
Gas Laws – Understanding the relationship between temperature (T), gas constant (R), and molar mass (M) is essential for applying the RMS speed formula.