Question

Write the mass balance for a saturated solution of$\mathbf{Ba}{\mathbf{\left(}{\mathbf{HsO}}_{\mathbf{4}}\mathbf{\right)}}_{\mathbf{2}}$ if the species in solution are $\mathit{B}{\mathit{a}}^{\mathbf{2}\mathbf{+}}\mathbf{,}\mathit{b}\mathit{a}\mathit{S}{\mathit{O}}_{\mathbf{4}}\left(aq\right)\mathbf{,}\mathit{H}\mathit{S}{\mathit{O}}_{\mathbf{4}}^{\mathbf{-}}\mathbf{,}\mathit{S}{\mathit{O}}_{\mathbf{4}}^{\mathbf{2}\mathbf{-}}$and${\mathbf{BaOH}}^{\mathbf{+}}$.SO

Short answer

The mass balance equation for the${\mathrm{BaOH}}^{+}$ solution is

$2\left\{\left[{\mathrm{Ba}}^{2+}\right]+\left[{\mathrm{BaSO}}_{4\left(\mathrm{aq}\right)}\right]+\left[{\mathrm{BaOH}}^{+}\right]\right\}=\left[{\mathrm{SO}}_4^{2-}\right]+\left[{\mathrm{HSO}}_4^{-}\right]+\left[{\mathrm{BaSO}}_4\left(\mathrm{nq}\right)\right]$.

Step-by-step solution

Concept used.

Mass balance:

All species in a solution containing a certain atom (or group of atoms) must be equal to the amount of that atom (or group) given to the solution.

Step 2: Calculate the two mass balances.

Species in solution:${\mathrm{Ba}}^{2+},{\mathrm{baSO}}_4\left(\mathrm{aq}\right),{\mathrm{HSO}}_4^{-},{\mathrm{SO}}_4^{2-}$ and ${\mathrm{BaOH}}^{+}$.

By definition Of mass balancerole="math" localid="1663415504126" $\mathrm{Ba}{\left(HS{O}_4\right)}_2$ solution is

$2\times \mathrm{total}\mathrm{barium}=\mathrm{total}\mathrm{sulfate}$

The mass balance equation is

$2\left\{\left[{\mathrm{Ba}}^{2+}\right]+\left[{\mathrm{BaSO}}_{4\left(\mathrm{aq}\right)}\right]+\left[{\mathrm{BaOH}}^{+}\right]\right\}=\left[{\mathrm{SO}}_4^{2-}\right]+\left[{\mathrm{HSO}}_4^{-}\right]+\left[{\mathrm{BaSO}}_4\left(\mathrm{nq}\right)\right]$