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When I performed this experiment in my school, I could not observe any sort of remarkable change (I must have performed it incorrectly or something).

I wanted to know what should have been the correct observation when the white precipitate (BaSO4 I think?) is reacted with conc. $\ce{HCl}$.

Also, if possible could you please tell me why this happens? And if possible if you could provide an image/video of the final observation, I would be grateful.

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If I understand it correctly, you are not interested in the precipitation reaction itself,

$$\ce{Ba^2+(aq) + SO4^2-(aq) <=>> BaSO4(s) \tag{1}}$$

but in the eventual reaction

$$\ce{BaSO4(s) + H+(aq) ->[HCl conc] ??? \tag{2}} $$

Concentrated $\ce{HCl}$ indirectly increases solubility of $\ce{BaSO4(s)}$ by decreasing concentration(more exactly activity) of sulfates by equilibrium

$$\ce{SO4^2-(aq) + H+(aq) <=>> HSO4-(aq) \tag{3}}$$

what partially shifts the precipitation equilibrium (1) to the left in favor of dissolved barium and sulfate ions.

Depending on the ratio of the precipitate and acid, the (partial) dissolving of the precipitate $\ce{BaSO4(s)}$ in concentrated HCl

$$\ce{BaSO4(s) + H+(aq) <=>[HCl] Ba^2+(aq) + HSO4-(aq) \tag{4}} $$

may or may not be noticeable.

That means if you put just a little amount of the precipitate to a large excess of the acid, it may dissolve completely or at least significantly. If, OTOH, you put large amount of precipitate to relatively small volume of acid, you may not notice at all, if e.g. 1% of it has dissolved.

Heating and/or stirring speeds up eventual dissolution, but heating is not advised due releasing gaseous hydrogen chloride. Aside of dissolution itself, not other noticeable visual, acoustic nor smell (aside of $\ce{HCl}$) effects are expected.

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