A stream containing H₂S and inert gases and a second stream of pure SO₂ are fed to a sulfur recovery reactor, where the reaction 2H₂S + SO₂ ? 3S + 2H₂0 takes place. The feed rates are adjusted so that the ratio of H2S to SO2 in the combined feed is always stoichiometric. In the normal operation of the reactor the flow rate and composition of the H₂S feed stream both fluctuate. In the past, each time either variable changed the required SO₂ feed rate had to be reset by adjusting a valve in the feed line. A control system has been installed to automate this process. The H₂S feed stream passes through an electronic flow meter that transmits a signal R1 directly proportional to the molar flow rate of the stream, h. When n₁ = 100 k mol/h, the transmitted signal R_t = 15 mV. The mole fraction of H₂S in this stream is measured with a thermal conductivity detector, which transmits a signal R_a. Analyzer calibration data are as follows: The controller takes as input the transmitted values of ft1 and R1 and calculates and transmits a voltage signal R to a flow control valve in the SO₂ line, which opens and closes to an extent dependent on the value of R_c. A plot of the SO₂ flow rate, h, versus R on rectangular coordinates is a straight line through the points (R_c = 10.0m V, n_c = 25.0k mol/h) and (R_c = 25.0m, V n_c = 60.0k mol/h).

(a) Why would it be important to feed the reactants in stoichiometric proportion? (what are several likely reasons for wanting to automate the SO₂ feed rate adjustment?

(b) If the first stream contains 85.0 mole% H2S and enters the unit at a rate of n_f = 3.00 x l0² k mol/h, what must the value of n_c (k mol S0₂/h) be?

(c) Fit a function to the H2S analyzer calibration data to derive an expression for x as a function of R_a. Check the fit by plotting both the function and the calibration data on the same graph.

(d) Derive a formula for R( from specified values of R_t and R_a, using the result of part (c) in the derivation. (This formula would be built into the controller.) Test the formula using the flow rate and composition data of part (a).

(e) The system has been installed and made operational, and at some point the concentration of H₂S in the feed stream suddenly changes. A sample of the blended gas is collected and analyzed a short time later and the mole ratio of H₂S to SO₂ is not the required 2:1. List as many possible reasons as you can think of for this apparent failure of the control system.

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R₂(mV) x(mol H₂S/mol) Material flow - Electronic signal H₂S, inerts HOT 0 25.4 42.8 58.0 71.9 85.1 0.00 0.20 0.40 0.60 0.60 Computer Flowmeter Analyzer Re 0.80 0.80 1.00 SO₂ + Control valve: BLENDER Feed to reactor