--%>
Assignment Help - homework help

Rotational energy and entropy due to rotational motion.

The entropy due to the rotational motion of the molecules of a gas can be calculated.


Linear molecules: as was pointed out, any rotating molecule has a set of allowed rotational energies. For a linear molecule the allowed rotational energies of a molecule of moment of inertia I are given approximated by

1920_rotational energy.png 

Furthermore, the number of states corresponding to a given value of J is given by 2J + 1. These features of the rotational energy patterns allow the rotational partition function to be deduced. This result can be used to obtain the rotational entropy contribution. The rotational contribution to the entropy, which must be added to the rotational contribution, is given by

2218_rotational energy1.png 

The partition function for rotation of a linear molecule obtained is

977_rotational energy2.png    

For a linear molecule, which has just 2 rotational degrees of freedom, the value of U - U0 for rotation was found, with this expression, to be RT. The rotational entropy of a diatomic or a linear polyatomic molecule can thus be written

2119_rotational energy3.png 

When numerical values are inserted for the constants, the rotational contributions of linear molecules to the entropy of ideal gases are given by

S°rot (J K-1 mol-1) = 877.37 + 8.3144 (In I + In T - In σ) [I in kg m2]

Example: calculate the 25°C rotational entropy of 1 mol of CO molecules. The moment of inertia of a CO molecule, measured by method given is 14.50 × 10-47 kg m2.

Solution: substitution in eq. and recognizing that σ = 1, gives

S°rot (J K-1 mol-1) = 877.37 + 8.3144[In (14.50 × 10-47) + In 298.15]

= 877.37 + 8.3144 (-105.55 + 5.70)

= 47.17 J K -1 mol-1

For comparison, the translational entropy of 1 mol of CO at 25°C and a pressure of 1 bar is calculated, to be 150.472 J K-1 mol-1.

The much greater translational entropy contribution (compared with the rotational entropy contribution) can be understood in terms of the much closer spacing of the translational energy levels and therefore the much larger number of translational states throughout which the molecules are distributed.

Nonlinear molecules: it is applicable to all diatomic molecules and all linear molecules. Generally shaped molecules, with 3 rather than 2 rotational degrees of freedom, require the use of 3/2 RTfor the rotational energy and the rotational partition function for nonlinear molecules given. For gases composed of such molecules

2366_rotational energy4.png 

With numerical values this becomes

S°rot (J K-1 mol-1) = 1320.83 + 4.157 In IAIBIC + 12.471 In T - 8.3143 In σ [IA, IB, IC in kg m2]

Limitations: these equations cannot be applied to molecules with very low moments of inertia or at very low temperatures. In both cases the spacing of the energy levels becomes appreciable compared with the thermal energy, and the integration that produced, for example, is not valid.

   Related Questions in Chemistry

  • Q : Law of multiple proportions and Law of

    Describe the difference between law of multiple proportions and law of definite proportions?

    		•
  • Q : Diffusion Molecular View When the

    When the diffusion process is treated as the movement of particles through a solvent the diffusion coefficient can be related to the effective size of diffusing particles and the viscosity of the medium.To see how the experimental coefficients can be treat

    		•
  • Q : Molarity of sodium hydroxide Can

    Can someone please help me in getting through this problem. Determine the molarity of a solution having 5g of sodium hydroxide in 250ml  solution is: (i) 0.5  (ii) 1.0  (iii) 2.0   (d) 0.1Answer: The right answer i

    		•
  • Q : Microwave Adsorption The absorption of

    The absorption of microwave radiation increases the rotational energy of molecules and gives information about the moment of inertia of the molecules.Now we can begin the study of the spectroscopy that explores the different ways in which the energy of the

    		•
  • Q : Basic concepts Determination of correct

    Determination of correct mol. Mass from Roult's law is applicable to :

    		•
  • Q : Advantages of doing your own chemistry

    What are the advantages of doing your own chemistry assignments? State your comment?

    		•
  • Q : Chemistry brief discription of relative

    brief discription of relative lowering of vapour pressure

    		•
  • Q : Describe physical adsorption and its

    When the forces of attraction existing between adsorbate and adsorbent are van der Waal's forces, the adsorption is called physical adsorption. This type of adsorption is also known as physisorption or van der Waal's adsorption. Since the forces existing between adsorbent and adsorbate are very w

    		•
  • Q : Group Cations Explain how dissolving

    Explain how dissolving the Group IV carbonate precipitate with 6M CH3COOH, followed by the addition of extra acetic acid, establishes a buffer with a pH of approximately

    		•
  • Q : Depression in the freezing point When

    When 0.01 mole of sugar is dissolved in 100g of a solvent, the depression in freezing point is 0.40o. When 0.03 mole of glucose is dissolved in 50g of the same solvent, depression in the freezing point will be:(a) 0.60o  (b) 0.80o

    		•