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.

Figure 8-3

Transcribed Image Text:

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