Chapter 15, Problem 15.31P

With ${\stackrel{\to }{V}}_2=V_2$ , Eq.(15.66) for the osmotic pressure may be represented as a power series in x₁:

$\frac{\Pi V_2}{x_{1}RT}=1+B{x}_1+C{x}_1^2+\mathrm{...}$

Reminiscent of Eqs. (3.33) and (3.34), this series is called an osmotic virial expansion.
Show that the second osmotic virial coefficient B is :

$B=\frac{1}{2}\left[1-{\left(\frac{d^{2}In{\gamma }_2}{d{x}_1^2}\right)}_{x_1=0}\right]$

What is B for an ideal solution? What is B if $G^E=A{x}_1{x}_2$ ?