Prove the validity of the intercept method (Fig. 9.7) of determining partial molar volumes...

Prove the validity of the intercept method (Fig. 9.7) of determining partial molar volumes in a two-component solution as follows. (All the equations of this problem are for fixed T and P.) (a) Let where n = nA + nB. Verify that V =  (b) Take of the equation in (a) to show that . (c) Use [Eq. (1.35)] and the result for (b) to show that . Also, explain why the nB subscript can be omitted from . Let y = mxB+ b be the equation of the tangent line to the z- versus-xB curve at the point with xB = x'B and z = z', and let  and  be the partial molar volumes at x'B. Recall that, for the straight line y = mxB + b, the slope is m and the intercept at xB = 0 is b. The slope m is given by the result for (c) as . Also, since the tangent line passes through the point we have z' = mx'B + b = . Thereforewhich is what we wanted to prove. (d) Verify that the tangent line's intercept at