What is the average velocity of the argon
atoms in the gas phase at 75°F?
To determine the average velocity of argon atoms in the gas phase at 75°F, you need to use the kinetic theory of gases and the root mean square (RMS) velocity formula. The RMS velocity represents the average speed of the gas particles.
The formula for calculating the RMS velocity is:
v_rms = √(3RT / M)
Where:
- v_rms is the root mean square velocity
- R is the universal gas constant (8.314 J/(mol·K) or 0.08206 L·atm/(mol·K))
- T is the temperature in Kelvin
- M is the molar mass of the gas (in this case, argon), which is 39.95 g/mol
Now, let's convert the given temperature from Fahrenheit to Kelvin:
T(K) = (T(°F) + 459.67) / 1.8
Substituting the values into the formula:
T = (75°F + 459.67) / 1.8 = 297.04 K
Now, plug the values into the RMS velocity formula:
v_rms = √(3 * 8.314 J/(mol·K) * 297.04 K / 39.95 g/mol)
Simplifying the equation:
v_rms = √(77.96346 J/mol) ≈ 8.83 m/s
Therefore, the average velocity of argon atoms in the gas phase at 75°F is approximately 8.83 m/s.