Questions $(5$ Points each number$)$

Resolve the problem: Find $T_{\text{o}\text{p}\text{t}\text{i}\text{m}\text{a}\text{l}}$ that maximizes the yield $\frac{C_P}{C_{Ao}}$

Example #$1]$ Suppose $k_f={10}^8\frac{e^{-5000}}{T}se{c}^{-1}$

and $k_r={10}^{16}{e}^{-10,\frac{000}{T}}se{c}^{-1}$ where the temp. $T$ is in $\%.$

Find the value of $T$ that maximuzes the

concentration of $P($yjeld$)$ for the reaction.

Regl: $,AP$ in a butch reactor with $C_{P_P}=0$

Solution:

and reaction time, $t=1$ second.

$\frac{C_P}{C_{A_0}}=\frac{k_f[1-e^{-(k_f+k_r)t}]}{k_f+k_r},\{\begin{array}{c}\text{:}[t=1sec]\\ k_f=\\ k_r=\end{array}$

Resolve the problem: Find $T_{\text{o}\text{p}\text{t}\text{i}\text{m}\text{a}\text{l}}$ that maximizes the yield $\frac{C_B}{C_{\text{A}\text{i}\text{n}}}$

Answers:

Example #$2]$ Suppose the reaction is$,$

$A{k}_{1}B{k}_{2}C$

with $k_1={10}^{15}$exp$[-12,\frac{000}{T}]h_{r^{-1}}$ and $k_2={10}^{16}$exp$[-15,\frac{000}{T}]h_{r^{-1}}$

Find the temperature $($Topt$)$ that maximizes $C_{}$ occurring

in a perfect mixer with $\frac{?}{\text{b}\text{a}\text{r}}(t)$ or $=1hr$

Req ${?}_{\text{T}\text{o}\text{p}\text{t}}^{\text{'}d\text{:}}=?$

Solution:

$\frac{C_B}{C_{An}}=\frac{k_1}{(1+k_1)(1+k_2)}$