Question

25. Write a mass balance for a solution of$F{e}_2({\mathrm{SO}}_4{)}_3$if the species

are${\mathrm{Fe}}^{3+},\mathrm{Fe}{\left(\mathrm{OH}\right)}^{2+},\mathrm{Fe}{\left(\mathrm{OH}\right)}_2^{+},{\mathrm{FeSO}}_4^{+},{\mathrm{SO}}_4^{2-}$androle="math" localid="1663402048017" ${\mathrm{SO}}_4^{2-}$.

Short answer

The mass balance for the given solution is,$3\left(\left({\mathrm{Fe}}^{3+}\right)+\mathrm{Fe}{\left(\mathrm{OH}\right)}^{2+}\right)+\left(\left(\mathrm{Fe}{\left(\mathrm{OH}\right)}_2^{+}\right)+2{\left({\mathrm{Fe}}_2\mathrm{SO}\right)}_4^{+}\right)+2\left({\mathrm{Fe}}_2\left({\mathrm{SO}}_4^{+}\right)\right)+\left({\mathrm{SO}}_4^{2-}\right)+\left({\mathrm{HSO}}_4^{-}\right)$

Step-by-step solution

Definition of mass balance

The mass balance states that the quantity of all species in a solution containing a particular atom (or group of atoms) must equal to the amount of that atom (or group) delivered to the solution.

Balancing the mass for given solution

In this case we will write amass balancefor a solution of$F{e}_2(S{O}_4{)}_3$if the following species are${\mathrm{Fe}}^{3+},\mathrm{Fe}{\left(\mathrm{OH}\right)}^{2+},\mathrm{Fe}{\left(\mathrm{OH}\right)}_2^{+},{\mathrm{FeSO}}_4^{+},{\mathrm{SO}}_4^{2-}$and localid="1663402637145" ${\mathrm{SO}}_4^{2-}$.

localid="1663402740511" $$\begin{gathered} 3\left(\mathrm{totalFe}\right)=2(\mathrm{total}\mathrm{sulfur}) \\ 3\left(\left({\mathrm{Fe}}^{3+}\right)+\mathrm{Fe}{\left(\mathrm{OH}\right)}^{2+}\right)+\left(\left(\mathrm{Fe}{\left(\mathrm{OH}\right)}_2^{+}\right)+2{\left({\mathrm{Fe}}_2\mathrm{SO}\right)}_4^{+}\right)+2\left({\mathrm{Fe}}_2\left({\mathrm{SO}}_4^{+}\right)\right)+\left({\mathrm{SO}}_4^{2-}\right)+\left({\mathrm{HSO}}_4^{-}\right) \end{gathered}$$

Here we wrote 2 in front of $\left({\mathrm{Fe}}_2{\left(\mathrm{OH}\right)}_2^{4+}\right)$because $\left({\mathrm{Fe}}_2{\left(\mathrm{OH}\right)}_2^{4+}\right)$contains 2 Fe.

Therefore, the mass balance for the given solution is, localid="1663402921524" $3\left(\left({\mathrm{Fe}}^{3+}\right)+\mathrm{Fe}{\left(\mathrm{OH}\right)}^{2+}\right)+\left(\left(\mathrm{Fe}{\left(\mathrm{OH}\right)}_2^{+}\right)+2{\left({\mathrm{Fe}}_2\mathrm{SO}\right)}_4^{+}\right)+2\left({\mathrm{Fe}}_2\left({\mathrm{SO}}_4^{+}\right)\right)+\left({\mathrm{SO}}_4^{2-}\right)+\left({\mathrm{HSO}}_4^{-}\right)$