Find the rms speed of a helium molecule at 321 K
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The formula you need can be found at
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
Vrms = sqrt(3RT/M)
R is the molar gas constant (in the appropriate units) and M is the molecular weight (4 for helium). T = 321 in your case.
To find the root mean square (RMS) speed of a helium molecule at a given temperature, we can make use of the kinetic theory of gases.
According to the kinetic theory of gases, the RMS speed of gas molecules can be calculated using the following equation:
VRMS = √(3kT / m)
Where:
- VRMS is the root mean square speed
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin (K)
- m is the molar mass of the gas molecule in kilograms (kg/mol)
The molar mass of helium (He) is approximately 4.0026 g/mol, which is equivalent to 0.0040026 kg/mol.
Now, we can calculate the RMS speed of the helium molecule at 321 K.
VRMS = √(3 * 1.38 x 10^-23 J/K * 321 K / 0.0040026 kg/mol)
Calculating this expression, we get:
VRMS ≈ 1,234 m/s
Therefore, the root mean square speed of a helium molecule at 321 K is approximately 1,234 m/s.