(Solved): The gas-phase reaction between methanol \( (A) \) and acetic acid (B) to form methyl acetate \( (C ...

The gas-phase reaction between methanol \( (A) \) and acetic acid (B) to form methyl acetate \( (C) \) and water (D) \[ \mathrm{CH}_{3} \mathrm{OH}+\mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{OOCCH}_{3}+\mathrm{H}_{2} \mathrm{O} \] takes place in a batch reactor and proceeds to equilibrium. When the reactor mixture comes to equilibrium, the mole fractions of the four reactive species are related by a reaction equilibrium constant \[ \frac{y_{C} y_{D}}{y_{A} y_{B}}=K_{e q}=4.87 \] The feed to the reactor consists of \( n_{\mathrm{AO}}, n_{\mathrm{B} 0}, n_{\mathrm{C} 0}, n_{\mathrm{D} 0} \) and \( n_{10} \) gram moles of \( \mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} \) and an inert gas I respectively. a. If \( n_{\mathrm{A} 0}=1.200 n_{\mathrm{B} 0} \), and all other input quantities are \( 0.0 \), what is the equilibrium fractional conversion of \( \mathrm{A} \) ? b. It is desired to produce \( 60.0 \) moles of methyl acetate starting with \( 67.0 \) moles of methanol, an unknown amount of acetic acid, and no other components. If the reaction proceeds to equilibrium, how much acetic acid must be fed? Required acetic acid: mol What is the composition of the final product? \( Y_{\text {acetic acid: }} \) \( y_{\text {methylacetate: }} \) \( y_{\text {methanol: }} \) b. It is desired to produce \( 60.0 \) moles of methyl acetate starting with \( 67.0 \) moles of methanol, an unknown amount of acetic acid, and no other components. If the reaction proceeds to equilibrium, how much acetic acid must be fed? Required acetic acid: \( \mathrm{mol} \) What is the composition of the final product? \( y_{\text {acetic acid: }} \) \( y_{\text {methylacetate: }} \) \( y_{\text {methanol: }} \) : \( y_{\text {water: }} \) : c. Suppose it were important to reduce the concentration of methanol by making its conversion at equilibrium \( 99.0 \% \). Again, assuming the feed to the reactor contains only methanol and acetic acid and that it is desired to produce \( 60.0 \) moles of methyl acetate, determine the extent of reaction and moles of methanol and acetic acid that must be fed to the reactor. Extent: Required methanol: \( \mathrm{mol} \) Required acetic acid: \( \mathrm{mol} \)