Question

what cation would be present in a solution which forms a precipitate when added to sodium carbonate and sodium sulfate solutions but which gives no visible reaction with sodium chloride or sodium hydroxide solution

Answer 1

$\mathrm{Ba}^{2+}$ is one of the most congruent ion that forms a precipitate when added to sodium carbonate and sodium sulfate solutions but which gives no visible reaction with sodium chloride or sodium hydroxide solution.

The reactions for processes with precipitate forming:

$$\mathrm{Ba}^{2+}_{\mathrm{(aq)}} + \mathrm{Na_2SO_4}_{\mathrm{(aq)}} \rightarrow 2\mathrm{Na^+}_{\mathrm{(aq)}} + \mathrm{BaSO_4}_{\mathrm{(s)}} \downarrow \text{ (white precipitate)}$$ $$\mathrm{Ba}^{2+}_{\mathrm{(aq)}} + \mathrm{Na_2CO_3}_{\mathrm{(aq)}} \rightarrow 2\mathrm{Na^+}_{\mathrm{(aq)}} + \mathrm{BaCO_3}_{\mathrm{(s)}} \downarrow \text{ (white precipitate)}$$

The reaction for process with no visible reaction:

For $\mathrm{Ba}^{2+} + \mathrm{NaCl}$ there is no some reaction

$$\mathrm{Ba}^{2+}_{\mathrm{(aq)}} + 2\mathrm{NaOH}_{\mathrm{(aq)}} = 2\mathrm{Na^+}_{\mathrm{(aq)}} + \mathrm{Ba(OH)}_{2\mathrm{(aq)}}$$