Question 18.5: Determine the time at which [I] is at a maximum for kA=2kI=0...

Thermodynamics, Statistical Thermodynamics, & Kinetics

Determine the time at which $\left[ I \right]$ is at a maximum for $k_{A}=2k_{I}=0.1 s^{-1}$ .

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This is the first example illustrated in Figure 18.8 where $k_{A}=0.1 s^{-1}$ and $k_{I}=0.05 s^{-1}$ . Using these rate constants and Equation (18.57), $t_{\max}$ is determined as follows:

$t_{\max}=\frac{1}{k_{A}-k_{I}}\ln\left( \frac{k_{A}}{k_{I}} \right)$ (18.57)

t_{\max}=\frac{1}{k_{A}-k_{I}}\ln\left( \frac{k_{A}}{k_{I}} \right)=\frac{1}{0.1  s^{-1}-0.05  s^{-1}}\ln\left( \frac{0.1  s^{-1}}{0.05 s^{-1}} \right)=13.9  s

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