Question

24. Consider the dissolution of the compound,which gives ${\mathrm{X}}_2{\mathrm{Y}}_2^{2+},{\mathrm{X}}_2{\mathrm{Y}}^{4+},{\mathrm{X}}_2{\mathrm{Y}}_3\left(\mathrm{aq}\right)$and$Y^{2-}$. Use the mass balance to find an

expression for$\left[Y^{2-}\right]$in terms of the other concentrations. Simplify

your answer as much as possible.

Short answer

The solution using mass balance is given by,$\left[{\mathrm{Y}}^{2-}\right]=\left(X_2{Y}_2^{2+}\right)+2\left({\mathrm{X}}_2{\mathrm{Y}}^{4+}\right)$.

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 the amount of that atom (or group) delivered to the solution.

Balancing the mass for given solution

Here we will consider the dissolution of the compound $X_2{\mathrm{Y}}_3$, which gives ${\mathrm{X}}_2{\mathrm{Y}}_2^{2+},{\mathrm{X}}_2{\mathrm{Y}}^{4+},{\mathrm{X}}_2{\mathrm{Y}}_3\left(aq\right)$and $Y^{2-}$and use the mass balance to find an expression for $\left[Y^{2-}\right]$.

Here the mass balance would be:

$Y_{total}=\frac{3}{2}{X}_{total}$

Next, we would determine the expression for$\left[Y^{2-}\right]$using the

above:

$$\begin{gathered} 2\left({\mathrm{X}}_2{\mathrm{Y}}_2^{2+}\right)+\left({\mathrm{X}}_2{\mathrm{Y}}^{4+}\right)+3\left({\mathrm{X}}_2{\mathrm{Y}}_3\right)+\left[Y^{2-}\right]=\frac{3}{2}\left(2\left({\mathrm{X}}_2{\mathrm{Y}}_2^{2+}\right)+2\left({\mathrm{X}}_2{\mathrm{Y}}^{4+}\right)+2\left({\mathrm{X}}_2{\mathrm{Y}}_3\right)\right) \\ \left[Y^{2-}\right]=\left({\mathrm{X}}_2{\mathrm{Y}}_2^{2+}\right)+2\left({\mathrm{X}}_2{\mathrm{Y}}^{4+}\right) \end{gathered}$$

Therefore, the solution using mass balance is given by, $\left[Y^{2-}\right]=\left({\mathrm{X}}_2{\mathrm{Y}}_2^{2+}\right)+2\left({\mathrm{X}}_2{\mathrm{Y}}^{4+}\right)$.