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Kinetic energy and speed of Hydrogen and Oxygen molecules

Hydrogen and Oxygen molecules in a gas sample have the same temperature. This means that the hydrogen molecules, on the average have the same kinetic energy and speed as oxygen molecule?

Solution This solution is FREE courtesy of BrainMass!

^ denotes power
E denotes 10 raised to the power

Kinetic energy of a molecule = 3/2 kT
where
k= Boltzmann's constant=1.38x 10^-23 J/K= 1.38E-23 J/K
T=Temperature in Kelvin

Thus if temperature is the same it means that kinetic energy of the molecules are equal as there are no other factors apart from k and T

Kinetic energy of a molecule = 1/2 m v ^2
Equating the two
3/2 kT = 1/2 m v^2

or v^2 = 3 kT/m
or v = square root of ( 3 kT/m )

For illustration
Say the temperature = 27 degress C = 300 K

mass of Hydrogen molecule= 3.321E-27 Kg
mass of Oxygen molecule= 5.313E-26 Kg

Therefore
velocity of Hydrogen molecule =square root of ( 3 kT/m )= 1934 m/s =square root of (3*1.38E-23*300/3.321E-27)
velocity of Oxygen molecule =square root of ( 3 kT/m )= 483 m/s =square root of (3*1.38E-23*300/5.313E-26)

Thus at the same temperature the ie 300 K the velocity of Hydrogen is higher than that of Oxygen
This is because from the equation v = square root of ( 3 kT/m )
velocity is inversely proportional to the square root of mass

If Temperature T is constant
v (Hydrogen) / v ( oxygen )= square root of (mass of Oxygen molecule / mass of Hydrogen molecule)

In our illustration above
mass of Oxygen molecule / mass of Hydrogen molecule= 16

Thus v (Hydrogen) / v ( oxygen )= square root of (mass of Oxygen molecule / mass of Hydrogen molecule)=
= 4 =square root of 16

In our illustration above
( velocity of Hydrogen molecule / velocity of Oxygen molecule) = 4 =1934/483

Thus the illustration demonstrates the point that velocity is inversely proportional to the square root of mass