Predicting Precipitation: Mixing Pb(NO₃)₂ and Na₂SO₄ Solutions

Q1. Does a precipitate form when 0.10 L of $8.0 \times 10^{-3}$ M Pb(NO$_3$)$_2$ is added to 0.40 L of $5.0 \times 10^{-3}$ M Na$_2$SO$_4$?

Background

Topic: Solubility Product Constant (Ksp) and Precipitation Prediction

This question tests your ability to predict whether a precipitate will form when two solutions are mixed, based on the concentrations of ions and the solubility product constant (Ksp). You will need to calculate the ion product (Q) and compare it to the Ksp for PbSO4.

Key Terms and Formulas

• Ksp (Solubility Product Constant): The equilibrium constant for the dissolution of a sparingly soluble salt.

• Ion Product (Q): The product of the concentrations of the ions at any moment; used to predict precipitation.

• Precipitation Rule: If Q > Ksp, a precipitate forms. If Q < Ksp, no precipitate forms.

Key formula:

$Q = [\text{Pb}^{2+}][\text{SO}_4^{2-}]$

Step-by-Step Guidance

1. Calculate the total volume after mixing: $V_{\text{total}} = 0.10\,\text{L} + 0.40\,\text{L}$.

2. Determine the new concentrations of Pb$^{2+}$ and SO$_4^{2-}$ after mixing, using dilution:

   • $[\text{Pb}^{2+}] = \frac{(0.10\,\text{L}) \times (8.0 \times 10^{-3}\,\text{M})}{V_{\text{total}}}$

   • $[\text{SO}_4^{2-}] = \frac{(0.40\,\text{L}) \times (5.0 \times 10^{-3}\,\text{M})}{V_{\text{total}}}$

3. Calculate the ion product Q using the diluted concentrations:

   • $Q = [\text{Pb}^{2+}][\text{SO}_4^{2-}]$

4. Look up the Ksp value for PbSO4 (you may need to use a textbook or data table).

5. Compare Q to Ksp to determine if a precipitate will form (but do not perform the final comparison yet).

Try solving on your own before revealing the answer!