--%>
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 : Thermodynamics I) Sulphur dioxide (SO2)

    I) Sulphur dioxide (SO2) with a volumetric flow rate 5000cm3/s at 1 bar and 1000C is mixed with a second SO2 stream flowing at 2500cm3/s at 2 bar and 200C. The process occurs at steady state. You may assume ideal gas behaviour. For SO2 take the heat capacity at constant pressure to be CP/R = 3.267

    		•
  • Q : Basic concepts Determination of correct

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

    		•
  • Q : Relative lowering of the vapour pressure

    Choose the right answer from following.The relative lowering of the vapour pressure is equal to the ratio between the number of: (a) Solute moleules and solvent molecules (b) Solute molecules and the total molecules in the solution (c) Solvent molecules and the tota

    		•
  • Q : Question based on normality Provide

    Provide solution of this question. A 5 molar solution of H2SO4 is diluted from 1 litre to 10 litres. What is the normality of the solution : (a) 0.25 N (b) 1 N (c) 2 N (d) 7 N

    		•
  • Q : Explain gels and its various categories.

    Certain sols have the property of setting to a semi-solid, jelly-like form by enclosing the entire amount of liquid within itself when they are present at high concentrations. This process is called gelation and colloidal systems with jelly-like appearance are known as gels. Some common examples

    		•
  • Q : How much phosphorus is in superphosphate

    Superphosphate has the formulate: CaH4 (PO4)2 H2O calculate the percentage of Phosphorus in this chemical. Show your calculations

    		•
  • Q : What are lattices and unit cells? The

    The repeating, atomic level structure of a crystal can be represented by a lattice and by the repeating unit of the lattice, the unit cell.It was apparent very early in the study of crystals that the shapes of crystals stem from an ordered array of smaller

    		•
  • Q : Acid value definition The acid value

    The acid value definition is the number milligrams of KOH needed to neutralize the acid present in one gram oil and fats however why not employ NaOH for the neutralization?

    		•
  • Q : Colligative property problem Which is

    Which is not a colligative property: (a) Refractive index (b) Lowering of vapour pressure (c) Depression of freezing point (d) Elevation of boiling point    

    		•
  • Q : Solubility of a gas The solubility of a

    The solubility of a gas in water depends on: (a) Nature of the gas (b) Temperature (c) Pressure of the gas (d) All of the above. Can someone help me in finding out the right answer.

    		•