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  Soluction:given Data:the elemntry gas phase Reaction:\begin{array}{l}3 A+2 B \stackrel{K}{\rightarrow} 3 C+50 \\\text { at } T=427^{\circ} \mathrm{C} \text { \& } P=28.7 \mathrm{~atm} .\end{array}Reaction is fint adir with respect ANow,(a) Expreds the Rate low; & each peeive ad a function of time,the Rata low Exprestion is ad fallows.-r_{A}=k_{1} C_{A}^{x} c_{B}^{y}where x in axe arder of Raction w.r. to A d B.Here x=y=1So,\left[r_{A}=K_{1} C A \cdot C_{B}\right]and Conantration of eash species ad a function of Convirdion.\begin{aligned}C_{A} & =C_{0}\left(1 x_{A}\right)\left(m_{0}\left(_{B}^{3}\right)\right. \\C_{B} & =\left(C_{A 0}-\frac{2}{3} C_{A_{0}} X_{A}\right)\left(m a\left(m^{3}\right)\right. \\C_{C} & =\left(C_{0}+\left(\frac{3}{3}\right) C_{A_{0}} X_{A}\right)\left(m a m_{4}\left(m^{3}\right)\right. \\C_{D} & =\left(C_{D}+\frac{5}{3} C_{A_{0}} X_{A}\right)\left(m_{0}\left(m^{3}\right)\right.\end{aligned}\Rightarrow Mow, pant:(b)\nabla_{0}=\left.1000 \mathrm{dm}^{3}\right|_{\text {ce }} \text { (volumstic flow Rate) }Rate Constantk_{1}=20 \mathrm{dm}^{3} \text { imelise. }fred is squimear in A &B.for x A=.90Ritermine the valume of ffR:\begin{array}{l}\text { Hare } \rightarrow \text { aqume } \operatorname{Sar}(A ß B \text { ) } \\C A_{0}=\frac{1}{2}\left(\frac{P}{R T}\right)=\frac{1}{2} \times\left(\frac{28.7 \times 101.325 \times 10^{3}}{700 \times 8.314)}\right. \\\left.C_{A_{0}}=249.83 \mathrm{mal} / \mathrm{m}^{3}\right]=0.249 \frac{\mathrm{mal}}{\mathrm{dm}^{3}} \\\end{array}ad we thow, ferformance eof. for ffR:\begin{array}{l}\left(\frac{v}{f_{A_{0}}}\right)=\frac{1}{k \times a_{A_{0}} \times c_{B_{0}}} \int_{0}^{x_{A}} \frac{d x_{A}}{\left(1-x_{A}\right) \frac{\left(3-2 x_{A}\right)}{3}} \\\frac{V \times K C C_{B} C_{0}}{\text { HAO }_{0}}=3 \int_{0}^{x_{A}} \frac{d x_{A}}{\left(1-x_{A}\right)\left(3-2 x_{A}\right)} \\\frac{V \times 20 \times C A_{0} C_{0}}{C_{0} \nu_{0}}=3 \int_{0}^{x_{A}} \frac{d x_{A}}{\left(1 x_{A}\right)\left(32 x_{A}\right)} \\\left(\frac{V \times 20 \times \cdot 249}{1000}\right)=3 \times \int_{0}^{x_{A}} \frac{d x_{A}}{\left(1-x_{A}\right)\left(3-2 x_{A}\right)} \\V \times .00166=\int_{0}^{x_{A}} \frac{d x_{A}}{(1-x A)(3-2 x A)} \\V x .00166=\int_{0}^{x_{A}}\left(\frac{1}{1-x_{A}}-\frac{2}{\left(3-2 x_{A}\right)}\right) d x_{A} \\\end{array}\begin{array}{c}V x \cdot 00166=\left(-\ln (1-x)+\frac{2}{2} \ln (3-2 x y)\right)_{0}^{+9} \\V \times \cdot 00166=-\ln (1-.9)+\ln (3-2 x+9) \\V x \cdot 00166=2.4849 \\V=1496.9277 \mathrm{dm}^{3}\end{array}\Rightarrow Molo, part(c) If V=50 \mathrm{dm}^{3}, How many taberequired to achieve the proceds.Heve, calceletel totel rolemeRequived for 90 \% Convarion.V_{\text {Tate }}=1496.927 \mathrm{dm}^{3}if one PfR volume =50 \mathrm{dm}^{3}\begin{aligned}\text { Mombereff PfR(Stube) usel } & =\left(\frac{1496.927}{50}\right) \\n & =29.938 \\n & \cong 30 \text { tubed Ans }\end{aligned} ...