A commonly used equation in calorimetry analysis to determine the temperature at the maximum rate is given

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A commonly used equation in calorimetry analysis to determine the temperature at the maximum rate is given by

\[ T_{\max }=\frac{E_{a}}{2 n R_{g}}\left[\sqrt{1+\frac{4 n R_{g} T_{F}}{E_{a}}}-1ight] \]

Derive this equation from Equation 8-21. Use this equation to calculate \(T_{\max }\) for the ethanol acetic anhydride system of Examples 8-3 and 8-4. Compare to the experimental value.

xm 1 2n B -(T + 2n)+T [T+4n(1 + B)] (8-21)

Example 8-3 Figure 8-3 shows temperature-time and pressure-time data for the reaction of methanol and acetic

Example 8-4 Using the data in Figure 8-3 and the results of Examples 8-2 and 8-3, estimate the reaction order

Figure 8-3

Temperature (C) Pressure (psi) 200 180 160- 140 120 100- 80 60 40 20 0 500 450 0 400 350 300 250 200 150- 100

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