2. non-ideal behaviour deviations from ideal behaviour can be described by the virial expansion pv nrtb(t)/(v/n) c(t)/(v/n) + where the functions b(t), c(t), etc. are called virial coefficients. by convention b(t) is called the second virial coefficient, c(t) the third, etc. deviations from the ideal gas law are related to gas molecules colliding with each other, in addition to hitting the walls of the containment vessel. this is why it makes sense to expand in powers of 1/(v/n), the number of moles per unit volume the measured values for b(t) at different temperatures for nitrogen (n2) are given in the following table t(k) b(cm3/mol) 100 -160 200 -35 300 -4.2 00 9.0 500 16.9 600 21.3 (a) compute the second term in the virial expansion for nitrogen at atmospheric pressure. explain the change of sign as one goes up in temperature as a consequence of the nature of intermolecular forces and their dependence on the speed of the molecules (b) the ideal gas law is an example of an equation of state. another example is the van der waals equation where a and b are gas-dependent constants. calculate b and c in terms of a and b for a gas obeying the van der waals equation (hint: use the binomial expansion )1p p(p 12/2 for lpl< < 1 apply this approximation to the quantity1 (nb/v) (c) use the data from the table and the expression for b(t) to find values for a and b for nitrogen.