Question

Question #cecb0

Answer 1

Write on species mole basis

Explanation:

Let us denote each components using the following letters
`A = (NH_4)_2SO_4`
`B = NH_4^+`
`C = SO_4^(2-)`
`D = NH_3(aq)`
`E = H^+`
`F = H_2O`
`G = HSO_4^-`
`H = OH^-`

Then we have
`A \underset{k_2}{\stackrel{k_1}{\rightleftharpoons}}2B+C`
`B \underset{k_4}{\stackrel{k_3}{\rightleftharpoons}} D+E`
`C+F \underset{k_6}{\stackrel{k_5}{\rightleftharpoons}}G+H`

If you are writing a component wise mass balance then start with components that take part in a single reaction

`(dC_A)/dt = k_2C_B^2C_C-k_1C_A`
`(dC_D)/dt = k_3C_B-k_4C_DC_E`
`(dC_E)/dt = k_3C_B-k_4C_DC_E`

Generally water molecule is present in excess. Hence we don't write a balance for that. And hence the third reaction is generally treated as pseudo first order reaction.

`(dC_G)/dt = k_5C_C-k_6C_GC_H`
`(dC_H)/dt = k_5C_C-k_6C_GC_H`

Now onto the other 2 components

`(dC_B)/dt = k_1C_A-k_2C_B^2C_C-k_3C_B+k_4C_DC_E`
`(dC_C)/dt = k_1C_A-k_2C_B^2C_C - k_5C_c+k_6C_GC_H`

Then for each component do a mass balance as
`v_0(C_i)_o - v(C_i) +V(r_i) = V(dC_i)/dt`

where `i \in {A,B,C,D,E,G,H}`

If you are writing an overall balance then we have the overall reaction as
`A+F \underset{k_2}{\stackrel{k_1}{\rightleftharpoons}} B+D+E+G+H`

Then we can write balances for A,B,D,E,G,H given we have `k_1` and `k_2`.