Question: SF6 is a gas at room temperature, which is at 295 K. What is its root-mean-square speed at that temperature?

 SF6 is a gas at room temperature, which is at 295 K. What is its root-mean-square speed at that temperature?

 

Answer:

The root-mean-square speed of a gas particle can be calculated using the equation:

 

v_rms = (3kT/m)^(1/2)

 

where v_rms is the root-mean-square speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the mass of the gas particle.

 

For SF6, the molar mass is 146 g/mol, so the mass of one SF6 molecule is 146 g/mol / 6 = 24.33 g/mol.

 

Substituting the values into the equation, we get:

 

v_rms = (3 * 1.38 x 10^-23 J/K * 295 K / 24.33 x 10^-23 g)^(1/2) = 384 m/s

 

Therefore, the root-mean-square speed of SF6 at room temperature (295 K) is 384 m/s.

 

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