The equation below will be the foundation for discussion of our discussion on 3 December 2021. \Delta G^{o}+\bar{R} T \ln \prod\left(\frac{f_{i}}{f_{i}^{o}}\right)^{v}=0 Let's derive this equation. Our system is an open reactor. a. Because the system is open, we begin with the Fourth FPR for an open system: d(n \bar{g})=(n \bar{v}) d P-(n \bar{s}) d T+\sum_{i} \mu_{i} d n_{i} If a system has reached chemical reaction equilibrium, what would be the value of dP and dT? Please use expression below to eliminate dni. dn₁ = v¡de 1. Please divide each remaining term by dɛ. e. If a chemical reaction equilibrium has been reached what will be the value of \frac{d(n \bar{g})}{d \varepsilon} ? - Please show that a condition for chemical reaction equilibrium is \sum_{i} \mu_{i} v_{i}=0 g. Please write the defining equation for the fugacity of a Species i in a mixture, fi. h. Please write the defining equation for the fugacity of PURE Species i at STP. Recall that a superscripted "o" denotes the Standard State. Also, we must assume (at least for now) that Species i is not an Ideal Gas. i. Please subtract Eq. h from Eq. g to show that \mu_{i}-\bar{g}_{i}^{o}=\bar{R} T \ln \left(\frac{\hat{f}_{i}}{f_{i}^{o}}\right) . Solve Eq. i for Hi and substitute into Eq. f. Then complete the derivation where \Delta G^{o}=\sum_{i} \bar{g}_{i}^{o} v_{i} \bar{g}_{i}^{o}=\Delta \bar{g}_{\text {formation, } i}^{o} \text { since the Gibbs Energy equals zero for the elements. }