Chapter 14, Problem 14.38P

Reaction-equilibrium calculations may be useful for estimation of the compositions of hydrocarbon feedstocks. A particular feedstock, available as a low-pressure gas at 500 K. is identified as “aromatic C8.” It could in principle contain the $C_8{H}_{10}$ isomers: o-xylene (OX), m-xylene (MX), p-xylene (PX), and ethylbenzene (EB). Estimate how much of each species is present, assuming the gas mixture has come to equilibrium at 500 K and low pressure. The following is a set of independent reactions (why?):

OX → MX (I)

OX → PX (II)

OX → EB (III)

1. Write reaction-equilibrium equations for each equation of the set. State clearly any assumptions.
2. Solve the set of equations to obtain algebraic expressions for the equilibrium vapor-phase mole fractions of the four species in relation to the equilibrium constants, $K_I,K_{II},K_{III}$ .
3. Use the following data to determine numerical values for the equilibrium constants at 500 K. State clearly any assumptions.
(</) Determine numerical values for the mole fractions of the four species.

Species	$\Delta H_{f_{298}}^{°}/J\cdot mo{l}^{-1}$	$\Delta G_{f_{298}}^{°}/J\cdot mo{l}^{-1}$
OX(g)	19,000	122,200
MX(g)	17,250	118,900
PX(g)	17,960	121,200
EB(g)	29,920	130,890