The solubility of calcium sulfate (CaSO4) is found to be 0.67 g/L. Calculate the value of Ksp for calcium sulfate.Strategy We are given the solubility of CaSO4 and asked to calculate its Ksp. The sequence of conversion steps, according to Figure 16.9(a), is

Question

The solubility of calcium sulfate ([latex]CaSO_{4}[/latex]) is found to be 0.67 g/L. Calculate the value of Ksp for calcium sulfate.

Strategy We are given the solubility of [latex]CaSO_{4}[/latex] and asked to calculate its Ksp. The sequence of conversion steps, according to Figure 16.9(a), is

[latex]\begin{matrix} Solubility of & &molar solubility&&[Ca^{2+} ] and &&K_{sp} of \& ightarrow && ightarrow && ightarrow \CaSO_{4} in g/L& &of CaSO_{4}&&[SO^{2-} _{4}]&&CaSO_{4} \end{matrix} [/latex]

Accepted Answer

Consider the dissociation of [latex]CaSO_{4}[/latex] in water. Let s be the molar solubility (in mol/L) of [latex]CaSO_{4}[/latex].

[latex]\begin{matrix} & CaSO_{4}(s) & & \xrightleftharpoons[ ]{} & Ca^{2+} (aq)&+&SO^{2-} _{4}(aq) \ Initial (M): & & &&0&&0 &&&&& \ Change (M): & -s & &&+s &&+s &&&& \ \hline Equilibrium (M):&&&&s&&s && \end{matrix}[/latex]

The solubility product for [latex]CaSO_{4}[/latex] is

[latex]K_{sp}=[Ca^{2+} ][SO^{2-}_{4} ]=s^{2} [/latex]

First, we calculate the number of moles of [latex]CaSO_{4}[/latex]dissolved in 1 L of solution:

[latex]\frac{0.67 \cancel{g CaSO_{4}}}{1 L soln} imes \frac{1 mol CaSO_{4}}{136.2 \cancel{g CaSO_{4}}}=4.9 imes 10^{-3} mol/L=s [/latex]

From the solubility equilibrium we see that for every mole of [latex]CaSO_{4}[/latex] that dissolves, 1 mole

of [latex]Ca^{2+}[/latex] and 1 mole of [latex]SO^{2-}_{4}[/latex] are produced. Thus, at equilibrium

[latex][Ca^{2+}]=4.9 imes 10^{-3} M and [SO^{2-}_{4}]=4.9 imes 10^{-3} M[/latex]

Now we can calculate [latex]K_{sp}[/latex]:

[latex]K_{sp}=[Ca^{2+} ][SO^{2-}_{4} ] [/latex]

[latex]=(4.9 imes 10^{-3} )(4.9 imes 10^{-3} )[/latex]

=[latex]2.4 imes 10^{-5} [/latex]

Question 16.8: The solubility of calcium sulfate (CaSO4) is found to be 0.6...

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