DAT General Chemistry: Predicting Precipitation

DAT High-Yield Concept

The ion product ( $Q_{sp}$ ) uses initial (non-equilibrium) molarities in the solubility expression to evaluate solution saturation relative to $K_{sp}$ .
If $Q_{sp} < K_{sp}$ , no precipitate forms; if $Q_{sp} > K_{sp}$ , a precipitate forms until equilibrium ( $Q_{sp} = K_{sp}$ ) is established.
When mixing two solutions, always account for volume dilution ( $M_1 V_1 = M_2 V_2$ ) before calculating initial ion concentrations.
Onset of precipitation represents the exact threshold condition where $Q_{sp} = K_{sp}$ .

Comparing the Ion Product ( $Q_{sp}$ ) with $K_{sp}$

Ion Product ( $Q_{sp}$ ): The mathematical product of the molar concentrations of dissolved constituent ions, each raised to the power of its stoichiometric coefficient, calculated at non-equilibrium conditions.

For a sparingly soluble salt dissolution equilibrium:

\ce{M_a X_b(s) <=> a M^{m+}(aq) + b X^{n-}(aq)}

The solubility product constant is $K_{sp} = [\ce{M^{m+}}]^a [\ce{X^{n-}}]^b$ at equilibrium. The ion product $Q_{sp}$ uses the same expression but uses initial or instantaneous molar concentrations: $Q_{sp} = [\ce{M^{m+}}]_0^a [\ce{X^{n-}}]_0^b$ .

Condition	Solution State	Equilibrium Shift Direction	Precipitate Observed?
$Q_{sp} < K_{sp}$	Unsaturated	Forward (Dissolution)	No
$Q_{sp} = K_{sp}$	Saturated	At Equilibrium	No (Onset threshold)
$Q_{sp} > K_{sp}$	Supersaturated	Reverse (Precipitation)	Yes

Mnemonic: Compare Q to K:
• Q < K: Quiet liquid (No solid forms, unsaturated).
• Q > K: Quantity exceeds capacity (Precipitate forms, reverse shift).

Predicting Precipitation

To determine if a precipitate forms upon mixing two electrolyte solutions, follow these steps:

Identify potential insoluble products using solubility rules.
Calculate diluted ion concentrations based on total combined volume.
Substitute diluted concentrations into the $Q_{sp}$ expression.
Compare $Q_{sp}$ to $K_{sp}$ .

Worked Example 1: Predicting Precipitation upon Mixing

Will a precipitate of $\ce{PbCl2}$ form when $\pu{100.0 mL}$ of $\pu{0.020 M}$ $\ce{Pb(NO3)2(aq)}$ is mixed with $\pu{100.0 mL}$ of $\pu{0.020 M}$ $\ce{NaCl(aq)}$ ? ( $K_{sp}$ for $\ce{PbCl2}$ is $\pu{1.7 x 10^{-5}}$ ).

Step 1: Write the dissolution equilibrium equation.

\ce{PbCl2(s) <=> Pb^{2+}(aq) + 2 Cl^-(aq)}

Step 2: Calculate diluted ion concentrations.

$V_{total} = \pu{100.0 mL} + \pu{100.0 mL} = \pu{200.0 mL}$

[\ce{Pb^{2+}}] = \pu{0.020 M} \times \frac{\pu{100.0 mL}}{\pu{200.0 mL}} = \pu{0.010 M}

[\ce{Cl^-}] = \pu{0.020 M} \times \frac{\pu{100.0 mL}}{\pu{200.0 mL}} = \pu{0.010 M}

Step 3: Calculate $Q_{sp}$ .

Q_{sp} = [\ce{Pb^{2+}}][\ce{Cl^-}]^2 = (\pu{0.010})(\pu{0.010})^2 = \pu{1.0 x 10^{-6}}

Step 4: Compare $Q_{sp}$ to $K_{sp}$ .

$\pu{1.0 x 10^{-6}} < \pu{1.7 x 10^{-5}}$ . Because $Q_{sp} < K_{sp}$ , no precipitate of $\ce{PbCl2}$ will form.

DAT Exam Trap: Forgetting to dilute initial concentrations when mixing solutions is the most common error. Using undiluted $\pu{0.020 M}$ yields an incorrect $Q_{sp} = \pu{8.0 x 10^{-6}}$ . Always calculate new molarities using $M_2 = \frac{M_1 V_1}{V_{total}}$ .

Onset of Precipitation

The onset of precipitation represents the threshold concentration of an added ion required to just begin forming a solid. At the exact point of onset, the system is saturated and $Q_{sp} = K_{sp}$ .

Worked Example 2: Determining Onset Concentration

A solution contains $\pu{0.010 M}$ $\ce{Ba^{2+}(aq)}$ . What minimum concentration of $\ce{SO4^{2-}(aq)}$ is required to initiate precipitation of $\ce{BaSO4(s)}$ ? ( $K_{sp}$ for $\ce{BaSO4}$ is $\pu{1.1 x 10^{-10}}$ ).

Step 1: Write the dissolution equilibrium equation.

\ce{BaSO4(s) <=> Ba^{2+}(aq) + SO4^{2-}(aq)}

Step 2: Set $Q_{sp} = K_{sp}$ at the onset threshold.

K_{sp} = [\ce{Ba^{2+}}][\ce{SO4^{2-}}]

Step 3: Solve for the required ion concentration.

[\ce{SO4^{2-}}] = \frac{K_{sp}}{[\ce{Ba^{2+}}]} = \frac{\pu{1.1 x 10^{-10}}}{\pu{0.010 M}} = \pu{1.1 x 10^{-8} M}

Precipitation of $\ce{BaSO4(s)}$ begins when $[\ce{SO4^{2-}}]$ exceeds $\pu{1.1 x 10^{-8} M}$ .

DAT Exam Trap: Failing to apply stoichiometric exponents during onset calculations. For a salt like $\ce{Ag2CrO4(s) <=> 2Ag^+(aq) + CrO4^{2-}(aq)}$ , the expression is $K_{sp} = [\ce{Ag^+}]^2 [\ce{CrO4^{2-}}]$ . Omitting the exponent on $[\ce{Ag^+}]$ produces a incorrect threshold value.

Note: When multiple cations are present in a single solution, adding a common anion allows the compound requiring the lower onset anion concentration to precipitate first (selective precipitation, covered in depth in its own lesson).

Critical Thinking Questions

If solid $\ce{NaCl}$ is added to a saturated solution of $\ce{AgCl(s)}$ , how does the shift in equilibrium affect $Q_{sp}$ instantaneously relative to $K_{sp}$ ?
Equal volumes of $\pu{0.0020 M}$ $\ce{Ca(NO3)2}$ and $\pu{0.0020 M}$ $\ce{NaF}$ are mixed. If $K_{sp}$ of $\ce{CaF2}$ is $\pu{4.0 x 10^{-11}}$ , demonstrate why precipitation occurs by calculating $Q_{sp}$ .
How does temperature alter the threshold concentration required for the onset of precipitation of an ionic salt with an endothermic dissolution process?

References

Sources returned by Google Search grounding during lesson verification.

15.2 Predicting Precipitation – General Chemistry 3e — chem.libretexts.org
18.1: Solubility Product Constant, Ksp - Chemistry LibreTexts — chem.libretexts.org

Predicting Precipitation

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