Compare τ for a CSTR and t for a BR, and interpret the comparison graphically. The comparison is for the same $f_A$ (in reaction 12.3-1),

$A+… \rightarrow v_CC+…$ (12.3-1)

constant-density, isothermal BR (at same T as in CSTR), and any form of rate law for $( -r_A)$ .

Question

Compare τ for a CSTR and t for a BR, and interpret the comparison graphically. The comparison is for the same [latex]f_A[/latex] (in reaction 12.3-1),

[latex]A+... \rightarrow v_CC+...[/latex] (12.3-1)

constant-density, isothermal BR (at same T as in CSTR), and any form of rate law for [latex] ( -r_A)[/latex] .

Accepted Answer

For a BR, t is given by equation 17.1-2, rewritten as

[latex] t_{BR} /c_{Ao} = \underset{I}{}_0^{f_A} df_A / ( -r_A) [/latex] (17.1-2)

For a CSTR, from the definition of [latex] au ( = V_{ST} /q_o)[/latex] , and equation 14.3-15 for constant density (with [latex] q =q_o [/latex] ),

[latex] V = (c_{Ao} - c_A) q /( -r_A) (constant density ) [/latex] (14.3-15)

[latex] au _{ST} /c_{Ao} = f_A / ( -r_A) [/latex] (17.1-5)

Dividing equation 17.1-2 by 17.1-5, we obtain

[latex] \frac {t_{BR}}{ au _{ST}} = \frac {\int _{0}^{f_A}{df_A /( -r_A)}} {f_A /( -r_A) } [/latex] (17.1-6)

which is the same result as in equation 17.1-4 for the volume ratio with a = 0.

[latex] \frac{V_{BR}}{V_{ST} } = \frac{(1 + a)\int_{0}^{f_A}{df_A /(-r_A)}}{f_A/( -r_A)} (constant ho T) [/latex] (17.1-4)

Figure 17.1, a plot of reciprocal rate, [latex] 1 / ( -r_A)[/latex] , versus [latex]f_A [/latex] illustrates the results expressed separately by equations 17.1-2 and 17.1-5 . [latex] au /c_{Ao} [/latex] for a CSTR is equivalent to the area A + B . For normal kinetics, in which the rate decreases with increasing [latex]f_A [/latex] , area A represents the integral in equation 17.1-2, that is, [latex]t /c_{Ao} [/latex] ; in such a case, [latex] au \gt t [/latex]. Conversely, for abnormal kinetics, as might be experienced for an autocatalytic reaction (Chapter 8), [latex]t \gt au [/latex], since area A + B + C represents [latex]t /c_{Ao} [/latex] .

Question 17.1: Compare τ for a CSTR and t for a BR, and interpret the compa...

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