Lecture 11 : Non-covalent interactions 2 : Structures of Liquids
11.7
Problems
11.1)
Calculate the second virial coefficient B2, for a system wherein the particles interact via a) a hard sphere potential and b) a square well potential. Evaluate the value of B2 when = 3.4
, / kB = 120 K and = 3.4
11.2)
At what value of r does the Lennard-Jones (LJ) potential have a minimum value of - ?
11.3)
Generate a set of about 50 random numbers from your calculator and estimate their average value and the standard deviation from the average.
11.4)
Give about three examples of intramolecular and intermolecular hydrogen bonding (other than the examples given in lecture.
11.5)
Estimate the effect of dipole moment () on the boiling points (Tb) by comparing u
vs Tb for the following sets of molecules
a)
CH3Cl, C2H5Cl, C3H7Cl
b)
o-, m- and p- dichlorobenzenes.
You need to get the data from a handbook of chemistry/physics.
11.6)
In one second, what is the (approximate) average distance through which a nitrogen or oxygen molecule moves in air and a water molecule moves in liquid water at room temperature?
11.7)
In this lecture, we have discussed the nature and the pair distribution functions. How is the height of the first peak affected by an increase in temperature?
11.8)
For two electrons separated by r = 4 , what is the value of the electrostatic energy? Compare this value with the LJ interaction energy between two Ar atoms at 4 , and also the gravitational energy of attraction between two Ar atoms separated by the same distance.
11.9)
Will the product of the quadrupole moment and the diameter (approximate diameter in case of non spherical molecules) of the molecule give the polarizability of the molecule? Justify your answer.
= 3.4
, 
/ kB = 120 K and 
= 3.4
) on the boiling points (Tb) by comparing u
