contestada

a. Calculate the ratio of the translational partition functions of D2 and H2 at the same temperature and volume.

b. Calculate the ratio of the translational partition functions of xenon and helium at the same temperature and volume.

Respuesta :

Answer:

a) The ratio of the translational partition of D2 and H2 is 2.82

b) The ratio of the translational partition of xenon and helium is 187.56

Explanation:

a) The translational partition for Dâ‚‚ is equal to:

[tex]q_{D2} =(\frac{2\pi m_{D2}kT }{h^{2} } )^{3/2} V[/tex]

Where

m = mass of molecule

k = Boltzmann constant

T = absolute temperature

V = volume of container

h = Planck constant

If rewrite the equation:

[tex]q_{D2} =(\frac{2\pi kTV^{2/3} }{h^{2} } )m_{D2}^{3/2}[/tex]

The same for the Hâ‚‚ molecule:

[tex]q_{H2} =(\frac{2\pi kTV^{2/3} }{h^{2} } )m_{H2}^{3/2}[/tex]

Taking the ratio Dâ‚‚ and Hâ‚‚:

[tex]\frac{q_{D2} }{q_{H2} } =\frac{(\frac{2\pi kTV^{2/3} }{h^{2} } )m_{D2}^{3/2} }{(\frac{2\pi kTV^{2/3} }{h^{2} } )m_{H2}^{3/2} } =\frac{m_{D2}^{3/2} }{m_{H2}^{3/2} }[/tex]

Where

mHâ‚‚ = 2.015894 amu

mDâ‚‚ = 4.028204 amu

[tex]\frac{q_{D2}}{q_{H2} } =\frac{4.028204^{3/2} }{2.01594^{3/2} } =2.82[/tex]

b) The same way to part a)

[tex]\frac{q_{Xe} }{q_{He} } =\frac{m_{Xe}^{3/2} }{m_{He}^{3/2} } =\frac{131.293^{3/2} }{4.0026^{3/2} } =187.56[/tex]

batolisis

A) The ratio of the translational partition of functions D2 and H2 is : 2.82

B) The ratio of the translational partition of functions of xenon and helium is : 187.56

The formula for calculating translational partition

  • Q[tex]_{trans}[/tex]  = [tex](\frac{2\pi mK_{b}T }{h^{2} } )^{3/2} * V[/tex] ---- ( 1 )

A) Determine the translational partition functions of D2 and H2

we rewrite equation ( 1 )

[tex]Q_{trans} = q_{t}. D_{2} / q_{t}. H_{2}[/tex]  = [ ( mass of D₂ ) / ( mass of H₂ ) ] [tex]^{3/2}[/tex]

           = [  4.028204 amu / 2.015894 amu ][tex]^{3/2}[/tex]

           = 2.82

B ) Determine the translational partition of functions of xenon and helium

Rewriting equation ( 1 )

[tex]Q_{trans} = q_{t}. Xenon_{2} / q_{t}. Helium_{2}[/tex]

          = [ mass of xenon / mass of helium ][tex]^{3/2}[/tex]

          = [ 131.293 amu / 4.0026 amu ][tex]^{3/2}[/tex]

          = 187.56

Hence we can conclude that  The ratio of the translational partition of functions D2 and H2 is : 2.82  and The ratio of the translational partition of functions of xenon and helium is : 187.56

Learn more about  partition; https://brainly.com/question/6375509

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