The fugacity of component 1 in a binary liquid mixture consisting of components 1 and 2 at \(298 \mathrm{~K}\) and 20 bar is given by \(\bar{f}_{1}=50 x_{1}-80 x_{1}^{2}+40 x_{1}^{3}\), where \(\bar{f}_{1}\) is in bar. Determine

(a) Fugacity \(f_{1}\) of pure component 1 ;

(b) Fugacity coefficient \(\phi_{1}\);

(c) Henry's law constant \(K_{1}\);

(d) Activity coefficient \(\gamma_{1}\).