Chapter 1, Problem 1.3P

The reaction

A + B → 2C

takes place in an unsteady CSTR. The feed is only A and B in equimolar proportions. Which of the following sets of equations gives the correct set of mole balances on A, B, and C? Species A and B are disappearing and species C is being formed. Circle the correct answer where ail the mole balances are correct.

(a) $\begin{array}{l}{F}_{\text{B0}}-F_{\text{A}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{A}}}{dt}}\\ F_{\text{B0}}-F_{\text{B}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{B}}}{dt}}\\ -F_{\text{C}}+2{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{C}}}{dt}}\end{array}$

(b) $\begin{array}{l}{F}_{\text{A0}}-F_{\text{A}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{A}}}{dt}}\\ F_{\text{A0}}-F_{\text{B}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{B}}}{dt}}\\ -F_{\text{C}}-2{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{C}}}{dt}}\end{array}$

(c) $\begin{array}{l}{F}_{\text{A0}}-F_{\text{A}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{A}}}{dt}}\\ F_{\text{A0}}-F_{\text{B}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{B}}}{dt}}\\ F_{\text{C}}+{\displaystyle {\int }_{}^V{\text{r}}_{\text{C}}dV=\frac{d{N}_{\text{C}}}{dt}}\end{array}$

(d) $\begin{array}{l}{F}_{\text{B0}}-F_{\text{A}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{A}}}{dt}}\\ F_{\text{B0}}-F_{\text{A0}}-{\displaystyle {\int }_{}^V{\text{r}}_{\text{A}}dV=\frac{d{N}_{\text{B}}}{dt}}\\ -F_{\text{C}}+{\displaystyle {\int }_{}^V{\text{r}}_{\text{C}}dV=\frac{d{N}_{\text{C}}}{dt}}\end{array}$

(e) None of the above.