A research team studies the gas‐phase equilibrium
2SO2(g)+O2(g)⇌2SO3(g)
inside a flow reactor designed to simulate industrial conditions. Unlike a closed system, product SO3 is removed continuously at a constant rate of 0.20kPa⋅s−1, while reactant gases are not added or removed after t=0s. The initial partial pressures are SO2=45kPa and O2=25kPa.
The intrinsic chemical rates (not counting removal) follow the rate laws
Forward rate: kf[SO2]2[O2] and Reverse rate: kr[SO3]2,
with kf=3.2×10−5kPa−2⋅s−1 and kr=6.0×10−4kPa−1⋅s−1 at the reaction temperature.
(a) Explain qualitatively why the forward and reverse rate curves in this open system approach one another but never become exactly equal.
(b) Derive an algebraic condition that must be satisfied at the time t∗ when the net formation rate of SO3 becomes zero (i.e., the amount of SO3 in the reactor stops increasing). Express your result in terms of the intrinsic forward rate, intrinsic reverse rate, and the constant removal rate.
(c) Let xkPa be the partial pressure of SO3 present at time t∗. Express the intrinsic forward and reverse rates at t∗ in terms of x, and use the condition from part (b) to set up—but do not solve—an equation whose solution gives x.
(d) Discuss two practical strategies an engineer could employ to adjust reactor conditions so that x is minimized, thereby maximizing continuous production of SO3, and explain how each strategy affects the relative magnitudes of the forward and reverse rates.