Question
How would you distinguish between
  1. $\mathrm{Be}(\mathrm{OH})_2$ and $\mathrm{Ba}(\mathrm{OH})_2$
  2. $\mathrm{BeSO}_4$ and $\mathrm{BaSO}_4$

Answer

  1. $\mathrm{Be}(\mathrm{OH})_2$, beryllium hydroxide is soluble in aqueous sodium hydroxide solution whereas $\mathrm{Ba}(\mathrm{OH})_2, ($barium hydroxide$)$ does not, because $\mathrm{Be}(\mathrm{OH})_2$ is amphoteric in nature.
$\text{Be(OH)}_2+2\text{NaOH}\xrightarrow{ \ \ \ \ \ \ \ \ }\text{Na}_2[\text{Be(OH)}_4]\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{Sodium beryllate}$
  1. $\mathrm{BeSO}_4$ is soluble in water whereas $\mathrm{BaSO}_4$ is insoluble in water.

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