<s>[INST] ### Preparation and Reactors
The following reaction is used to calculate the kinetics of propane combustion:
\[C_{3}H_{8}+5O_{2}\to 3CO_{2}+4H_{2}O\]
The reaction rate is -r\({}_{A}\) = kC\({}_{A}^{2}\)C\({}_{O2}\), and k = 2 \(\cdot\) 10\({}^{9}\) exp(-100000/RT), where k has a unit of (kmol/m\({}^{3}\))\({}^{-2}\)\(\cdot\) min\({}^{-1}\), R is 8.314 J/(mol \(\cdot\) K), and T is in K. The initial concentration of C\({}_{3}\)H\({}_{8}\) is 0.5 mol/m\({}^{3}\), and that of O\({}_{2}\) is 1 mol/m\({}^{3}\). A continuous stirred-tank reactor (CSTR) is used, and its volume is 10 m\({}^{3}\).
Assuming that the reaction is isothermal and that there is no change in the liquid volume, solve the following problems:
a) What is the residence time if the conversion of C\({}_{3}\)H\({}_{8}\) is 99%?[/INST]