--%>
Assignment Help - homework help

Molecular Diameters

The excluded volume b, introduced by vander Wall's as an empirical correction term, can be related to the size gas molecules. To do so, we assume the excluded volume is the result of the pairwise coming together of molecules. This assumption is justified when b values are obtained from second viral coefficient data. Fitting values for the empirical constants are derived from van der Waal's equation. Some b values obtained in this way are given in table.


So that we need to deal with a single molecular size parameter, we treat molecules as spherical particles. The diameter of a molecule is d. the volume of a molecule is v

The volume in which a pair of molecules cannot move because of each other's presence is indicated by the lightly shaded region. The radius of this excluded volume sphere is equal to the molecule diameter d. the volume excluded to the pair of molecules is 4/3πd3. We thus obtain,

= 4[4/3π (d/2)]3

The expression in brackets is the volume of a molecule.vander Waal's b term is the excluded volume per mole of the molecules. Thus we have, with N representing Avogadro's number,

B= 4n [4/3π (d/2)3] = 4N (vol. of molecule)

Molecular size and Lennard Jones intermolecular Attraction term based on second virial coefficient data:

Gas Excluded volume B, L mol-1 Molecular diam. D, pm ELJ, J × 10-21
He 0.021 255 0.14
Ne 0.026 274 0.49
Ar 0.050 341 1.68
Kr 0.058 358 2.49
Xe 0.084 405 3.11
H2 0.031 291 0.52
N2 0.061 364 1.28
O2 0.058 358 1.59
CH4 0.069 380 1.96
C(CH3)4 0.510 739 3.22


Van der Waal's equation and the Boyle temperature:

Gas Tboyle, K Tboyle/TC
H2 110 3.5
He 23 4.5
CH4 510 2.7
NH3 860 2.1
N2 330 2.6
O2 410 2.7


Example: calculate the radius of the molecule from the value of 0.069 L mol-1 for the excluded volume b that is obtained from the second virial coefficient data.

Solution: the volume of 1 mol of methane molecules is obtained by dividing the b value of 0.069 L mol-1 = 69 × 10-6 m3 mol-1 value by 4. Then division by Avogadro's number gives the volume per molecule. We have:

Volume of methane molecule = 69 × 10-6 m3/4 × 6.022 × 1023 

= 2.86 × 10-29 m3

The volume is equal to 4/3∏r3 and on this basis we calculate:

r = 1.90 × 10-10 m and d = 3.80 × 10-10 m = 380 pm

   Related Questions in Chemistry

  • Q : Explain the mechanism of Enzyme

    A mechanism for enzyme-catalyzed reactions that leads to the typical rate equation for these reactions can be described.A variety of rate equations are required to portray the rates of enzymes catalyzed reagents and physical conditions that are encountered

    		•
  • Q : Molecular crystals Among the below

    Among the below shown which crystal will be soft and have low melting point: (a) Covalent  (b) Ionic  (c) Metallic  (d) MolecularAnswer: (d) Molecular crystals are soft and have low melting point.

    		•
  • Q : Question on seminormal solution Provide

    Provide solution of this question. The weight of sodium carbonate required to prepare 500 ml of a seminormal solution is: (a) 13.25 g (b) 26.5 g (c) 53 g (d) 6.125 g

    		•
  • Q : Molecular basis of third law. The

    The molecular, or statistical, basis of the third law can be seen by investigating S = k in W.The molecular deductions of the preceding sections have led to the same conclusions as that stated in the third law of thermodynamics, namely, that a value can be

    		•
  • Q : Explain the preparation of phenols. The

    The methods used for the preparation of phenols are given below:    From aryl sulphonic acids

    		•
  • Q : Particles of quartz Particles of quartz

    Particles of quartz are packed by:(i) Electrical attraction forces  (ii) Vander Waal's forces  (iii) Covalent bond forces  (iv) Strong electrostatic force of attraction Answer: (iii)

    		•
  • Q : Equimolar solutions Select the right

    Select the right answer of the question. Equimolar solutions in the same solvent have : (a)Same boiling point but different freezing point (b) Same freezing point but different boiling poin (c)Same boiling and same freezing points (d) Different boiling and differe

    		•
  • Q : What do you mean by the term dipole

    What do you mean by the term dipole moment? Briefly describe it.

    		•
  • Q : The three facts on the evaporation

    Describe briefly the three facts on the evaporation?

    		•
  • Q : Negative deviation Which one of the

    Which one of the following non-ideal solutions shows the negative deviation: (a) CH3COCH3 + CS2   (b) C6H6 + CH3COCH3   (c) CCl4 + CHCl3  

    		•