Kinetic data for the reaction between sulfuric acid and diethyl sulfate are given in Examples 6.1 and 6.4. Suppose that V = 25.4 L, q_Af = q_Bf, c_Af = 11.0 g-mol/L, c_Bf = 5.5 g-mol/L, and the required effluent concentration of sulfuric acid is c_A = 4.0 g-mol/L. Find the flow rates

(a) Assuming that that the reaction may be taken to be irreversible

(b) Taking the reverse reaction into account.

Examples 6.1

The data in Table 6.1 were obtained for the reaction of sulfuric acid with diethyl sulfate, H₂SO₄ + (C₂H₅)₂SO₄ → 2C₂H₅SO₄H, in aqueous solution at 22.9◦C. The initial concentrations of both reactants were the same, 5.5 g-mol/L. What is the rate expression?

Figure 6.3. Computation of the second-order rate constant for the reaction between sulfuric acid and diethyl sulfate in aqueous solution.

In our symbolic nomenclature, H₂SO₄ is denoted by A, (C₂H₅)₂SO₄ is denoted by B, and 2C₂H₅SO₄H is denoted by M. c_A0 = c_B0 = 5.5 g-mol/L.
μ = 2 and ψ = 0. We assume mass action kinetics, so the rate with equal initial concentrations will be of the form r = kc²A .* As required by Eq. 6.11a, the data are plotted in Figure 6.3 as 1/cA versus t. There is some experimental scatter, but the data are clearly represented by the straight line shown in the figure. The rate constant is then determined from the slope to be k = 6.05×10⁻⁴ L/(g-mol min).

Table 6.1

Concentration of H₂SO₄ versus time for the reaction of sulfuric acid with diethyl sulfate in aqueous solution at 22.9◦C. Data of Hellin and Jungers, Bull. Soc. Chim. France, No. 2, pp. 386–400 (1957).

Equation 6.11a

Examples 6.4

The cleavage of diacetone alcohol in the presence of hydroxide ion (e.g., aqueous NaOH) at 25◦C appears to be a simple first-order decomposition:

Data for the apparent first-order reaction-rate constant are shown in the first two columns of Table 6.4 for various concentrations of NaOH in the reaction mixture. Show that the reaction exhibits mass action kinetics with a true rate r = kc_Ac_B. The third column in the table shows the pseudo-first-order rate constant k′ divided by the concentration of NaOH. The result is a constant value to within 3 percent, indicating that the true reaction rate is r = kc_Ac_B, where k = 0.47 L/(g-mol min).

Transcribed Image Text:

liters CA g-mole I 0.30 0.25 0.20 O 50 100 t, min Slope = 6.05 x 10-4. 150 L g-mol/min 200