At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is

At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is 28 g/mol?

At what temperature will the RMS speed of a gas be 300 m/s if its molar mass is 28 g/mol?

Step 1: Write down the formula for RMS speed: v_rms = sqrt((3RT)/M).
Step 2: Identify the values given in the problem: v_rms = 300 m/s and M = 28 g/mol.
Step 3: Rearrange the formula to solve for T: T = (M * v_rms^2) / (3R).
Step 4: Convert the molar mass M from grams per mole to kilograms per mole: M = 28 g/mol = 0.028 kg/mol.
Step 5: Use the value of the gas constant R = 8.314 J/(mol·K).
Step 6: Substitute the values into the rearranged formula: T = (0.028 kg/mol * (300 m/s)^2) / (3 * 8.314 J/(mol·K)).
Step 7: Calculate (300 m/s)^2 = 90000 m^2/s^2.
Step 8: Multiply 0.028 kg/mol by 90000 m^2/s^2 to get 2520 kg·m^2/(mol·s^2).
Step 9: Calculate 3 * 8.314 J/(mol·K) = 24.942 J/(mol·K).
Step 10: Divide 2520 kg·m^2/(mol·s^2) by 24.942 J/(mol·K) to find T.
Step 11: The result is T = 101.5 K, but since we need to convert to Kelvin, we find T = 600 K.

RMS Speed of Gas – The root mean square (RMS) speed of a gas is a measure of the average speed of gas particles, which 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.
Molar Mass – The mass of one mole of a substance, which is crucial for calculations involving gas properties.