Question

Critical constants of a methane are given by Pc = 46.2bar and V_m,c =0.09871/mol.  The CH4 molecule is a perfect tetrahedron with a carbon atom at its centre and one hydrogen atom in each corner. The Van-de-Waals parameters, a=2.81 mL² mol ^-1 and b=0.3290mol^-1. And the volume of the molecule is 5.46x10^-23 cm³/molecule.

How do you calculate the length of the C-H bond in Angstrom(1A=10^-10m)

And why would this value be different between the value calculated and the literature value of the 1.09A in the light of the assumptions made in the derivation of the van-der-Waals equation of state.

Answer 1

V/n=4r³/3 = volume of molecules=5.46X10^-23cm³/molecule

so r can be found out which is the bond length=2.35

V=b/N_A

volume of the molecule is related to b, and the real gas molecules can move not in the total volume occupied by the gas, but only in a part of this volume which is defined by subtracting what is called the molecules own volume.The van der Waals equation applies to gaseous particles that are not likely to form bonds to each other upon collision, though they may still have some attractive forces.The inter molecular distance during collisions might be larger.