--%>
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 : Neutralisation of phosphorous acids

    Provide solution of this question. To neutralise completely 20 mL of 0.1 M aqueous solution of phosphorous acid (H3 PO3) the volume of 0.1 M aqueous KOH solution required is: (a) 40 mL (b) 20 mL (c) 10 mL (d) 60 mL

    		•
  • Q : Determining mole fraction of water in

    A mixture has 18 g water and 414 g ethanol. What is the mole fraction of water in mixture (suppose ideal behaviour of mixture): (i) 0.1  (ii) 0.4  (iii) 0.7  (iv) 0.9 Choose the right answer from abo

    		•
  • Q : Ions in solution The accuracy of your

    The accuracy of your written English will be taken into account in marking. 1.    (a)   Identify the spectator ions in the following equation                    &nb

    		•
  • Q : Vapour pressure of a liquid Help me to

    Help me to go through this problem. The vapour pressure of a liquid depends on: (a) Temperature but not on volume (b) Volume but not on temperature (c) Temperature and volume (d) Neither on temperature nor on volume

    		•
  • Q : Decision about dipole moment is present

    How can you decide if there is a dipole moment or not?

    		•
  • Q : Laws of Chemical Combination Laws of

    Laws of Chemical Combination- In order to understand the composition of the compounds, it is necessary to have a theory which accounts for both qualitative and quantitative observations during chem

    		•
  • Q : Eutectic Formation In some two

    In some two component, solid liquid systems, a eutectic mixture forms.Consider, now a two component system at some fixed pressure, where the temperature range treated is such as to include formation of one or more solid phases. A simple behavior is shown b

    		•
  • Q : Question based on lowest vapour pressure

    Give me answer of this question. Among the following substances the lowest vapour pressure is exerted by: (a) Water (b) Mercury (c) Kerosene (d) Rectified spirit

    		•
  • Q : Explain methods for industrial

    The important methods for the preparation of alcohol on large-scale are given below:    

    		•
  • Q : Vapour pressure of water Give me answer

    Give me answer of this question. 5cm3 of acetone is added to 100cm3 of water, the vapour pressure of water over the solution: (a) It will be equal to the vapour pressure of pure water (b) It will be less than the vapour pressure of pure water

    		•