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How will the action of dilute hydrochloric acid enable you to distinguish between the following:
Sodium carbonate and sodium sulphite.

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Hint : When dilute hydrochloric acid is added to sodium sulphite, it reacts with sodium sulphite and sulphur dioxide gas is evolved. After the reaction of hydrochloric acid with sodium sulphite, sodium chloride and sulphur dioxide gas are formed. The smell of sulphur dioxide gas is similar to that of a just-struck match. The reaction of dilute hydrochloric acid with sodium carbonate gives sodium chloride, carbon dioxide gas and water. Carbon dioxide is acidic in nature and is a colourless gas. If the carbon dioxide gas formed in this reaction is passed through lime water, it turns the lime water milky.

Complete Step By Step Answer:
When sodium carbonate reacts with dilute hydrochloric acid, sodium chloride is formed with the liberation of carbon dioxide gas. The reaction is given below:$N{a_2}C{O_3} + 2HCl \to 2NaCl + {H_2}O + C{O_2} \uparrow $
When sodium sulfite reacts with dilute hydrochloric acid, sodium chloride is formed with the liberation of sulphur dioxide gas. The reaction is given below:$N{a_2}S{O_3} + 2HCl \to 2NaCl + {H_2}O + S{O_2} \uparrow $

Note :
Dilute hydrochloric acid is used to extract basic substances from mixtures or in the removal of basic impurities. The dilute acid converts bases like ammonia or an organic amine into a water soluble chloride salt. When sodium carbonate and hydrochloric acid are mixed, two molecules of hydrochloric acid give their hydrogen atoms to the sodium carbonate. This produces carbonic acid. The sodium from sodium carbonate forms a salt with the chloride particles from the hydrochloric acid producing sodium chloride.