He is the lightest noble gas component of air, and Xe is the heaviest. Perform the following calculations, using R=8.314J/(molXK)and M in kg/mol.
1. Find the average kinetic energy per mole of He and Xe at 30 degrees C.
2. Find the average kinetic energy per molecule of He at 30 degrees C.
Isn't the average KE = 3/2 RT?
Divide by Avogadro's number to fine per molecule.
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To find the average kinetic energy per mole of He and Xe at 30 degrees C, we can use the formula for average kinetic energy:
KE_avg = (3/2) * R * T
where KE_avg is the average kinetic energy, R is the gas constant (8.314 J/(mol*K)), and T is the temperature in Kelvin.
To convert 30 degrees Celsius to Kelvin, we use the formula:
T(K) = T(C) + 273.15
So, for 30 degrees C:
T = 30 + 273.15 = 303.15 K
1. Average kinetic energy per mole of He and Xe at 30 degrees C:
For He:
KE_avg_He = (3/2) * R * T
= (3/2) * 8.314 J/(mol*K) * 303.15 K
= 3744.84 J/mol
For Xe:
KE_avg_Xe = (3/2) * R * T
= (3/2) * 8.314 J/(mol*K) * 303.15 K
= 3744.84 J/mol
So, the average kinetic energy per mole of He and Xe at 30 degrees C is 3744.84 J/mol.
2. Average kinetic energy per molecule of He at 30 degrees C:
To find the average kinetic energy per molecule, we need to divide the average kinetic energy per mole by Avogadro's number (6.022 x 10^23 molecules/mol).
Average kinetic energy per molecule of He = Average kinetic energy per mole of He / Avogadro's number
= 3744.84 J/mol / (6.022 x 10^23 molecules/mol)
= 6.21 x 10^(-21) J
So, the average kinetic energy per molecule of He at 30 degrees C is 6.21 x 10^(-21) J.