Using a simple frame or just bolding for the box
Key Points:
Precipitation separation relies on solubility differences.
Large solubility differences often exist between ions of different charges (oxidation states), e.g., Ln(II) vs Ln(III).
Ln(II) sulfates (like EuSO$_4$, YbSO$_4$) are often less soluble than Ln(III) sulfates.
Ln(III) ions adjacent in the series (like Gd$^{3+$, Dy$^{3+$) have very similar properties and are hard to separate by precipitation.
Stability of oxidation states is crucial: Eu$^{2+$ and Yb$^{2+$ are relatively stable; Gd$^{2+$ is not.