The solubility product constant ([tex]\( K_{sp} \)[/tex]) expression for a given ionic compound is calculated based on the concentrations of the ions produced when the compound dissociates in water.
For the reaction [tex]\( U_2CO_3(s) \leftrightarrow 2Cu^+(aq) + CO_3^{2-}(aq) \)[/tex], we need to set up the [tex]\( K_{sp} \)[/tex] expression.
1. Identify the ions and their coefficients:
- [tex]\( Cu^+ \)[/tex] has a coefficient of 2, indicating 2 moles of [tex]\( Cu^+ \)[/tex] ions are produced.
- [tex]\( CO_3^{2-} \)[/tex] has a coefficient of 1, indicating 1 mole of [tex]\( CO_3^{2-} \)[/tex] ions is produced.
2. Write the [tex]\( K_{sp} \)[/tex] expression:
The [tex]\( K_{sp} \)[/tex] is the product of the concentrations of the dissociated ions, each raised to the power of their stoichiometric coefficients in the balanced dissolution equation.
For the equation:
[tex]\[ U_2CO_3(s) \leftrightarrow 2Cu^+(aq) + CO_3^{2-}(aq) \][/tex]
The [tex]\( K_{sp} \)[/tex] expression is:
[tex]\[ K_{sp} = [Cu^+]^2[CO_3^{2-}] \][/tex]
This reflects the coefficients from the balanced equation where [tex]\( [Cu^+] \)[/tex] concentration is squared (since there are 2 mol of [tex]\( Cu^+ \)[/tex] ions for every mole of [tex]\( U_2CO_3 \)[/tex] that dissolves) and [tex]\( [CO_3^{2-}] \)[/tex] concentration is to the first power (since there is 1 mol of [tex]\( CO_3^{2-} \)[/tex] ions for every mole of [tex]\( U_2CO_3 \)[/tex] that dissolves).
Thus, the correct formula for [tex]\( K_{sp} \)[/tex] is:
[tex]\[ K_{\text{sp}} = [Cu^+]^2[CO_3^{2-}] \][/tex]
