Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.3
Practice Questions
Q1
Calculate the RMS speed of a gas with molar mass 0.028 kg/mol at 300 K. (R = 8.314 J/(mol K))
500 m/s
600 m/s
700 m/s
800 m/s
Questions & Step-by-Step Solutions
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.
