The molar solubility (S) of M2 X is 5 ×10^-5 M. Find S of each ion. How do you set up the calcul

step 1 Question 62 is a KSP and molar solubility question with various parts. It always helps with thes

The molar solubility (S) of M2 X is 5 ×10^-5 M. Find S of...

The molar solubility $(S)$ of $\mathrm{M}_{2} \mathrm{X}$ is $5 \times 10^{-5}$ M. Find $S$ of each ion. How do you set up the calculation to find $K_{\mathrm{sp}} ?$ What assumption must you make about the dissociation of $\mathrm{M}_{2} \mathrm{X}$ into ions? Why is the calculated $K_{\mathrm{sp}}$ higher than the actual value?

Key Concepts

Ionic Interactions and Activity Effects

The calculated Ksp is often higher than the actual value because the computation generally uses raw concentrations and assumes ideal behavior. In reality, interactions between ions in solution (such as ion pairing or non-ideal activity effects due to ionic strength) reduce the effective concentration of free ions. These activity effects mean that the real equilibrium involves lower effective concentrations, making the thermodynamic Ksp smaller than the value predicted by the simple concentration-based calculation.

Assumption of Complete Dissociation

The calculation assumes that upon dissolving, the salt completely dissociates into its constituent ions in the solution, without any ion pairing or formation of complex species. This simplifies the calculations by treating the stoichiometric ratios as directly converting molar solubility into ion concentrations, even though in some cases the actual dissociation may be slightly incomplete.

Molar Solubility

Molar solubility is the number of moles of a solute that can dissolve per liter of solution to form a saturated solution. It serves as the basis for calculating the concentration of individual ions when a sparingly soluble salt dissolves, allowing one to relate the measured solubility to the stoichiometry of the dissolution process.

Dissolution Stoichiometry

Dissolution stoichiometry involves writing the balanced chemical equation for the dissolution of a sparingly soluble salt. This determines how many moles of each ion are produced per mole of salt that dissolves. For a salt of formula M2X, the stoichiometry indicates that two moles of the metal ion (M+) and one mole of the anion (X^(2-)) are generated for every mole dissolved.

Solubility Product Constant (Ksp)

The solubility product constant, Ksp, is an equilibrium constant defined for the dissolution of a sparingly soluble salt in water. It is calculated by multiplying the concentrations of the resultant ions in the saturated solution, each raised to the power of its coefficient in the balanced dissolution equation. Setting up the Ksp expression correctly involves substituting the ion concentrations expressed in terms of the molar solubility and the stoichiometric coefficients.

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