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Sulfuric acid, represented as \( \mathrm{H}_2\mathrm{SO}_4 \), is known for its ability to react with various substances, often liberating gases in the process. When a substance reacts with dilute sulfuric acid, it typically undergoes either a decomposition or a displacement reaction, releasing different gaseous products. In the case of carbonate ions, \( \mathrm{CO}_3^{2-} \), they react with sulfuric acid to produce carbon dioxide \( \mathrm{CO}_2 \), a colorless gas. This reaction is represented as:

• \( \mathrm{CO}_3^{2-} + \mathrm{H}_2\mathrm{SO}_4 \rightarrow \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O} + \mathrm{SO}_4^{2-} \)

Similarly, sulfite ions, \( \mathrm{SO}_3^{2-} \), react with dilute sulfuric acid to produce sulfur dioxide \( \mathrm{SO}_2 \), which is also colorless:

• \( \mathrm{SO}_3^{2-} + \mathrm{H}_2\mathrm{SO}_4 \rightarrow \mathrm{SO}_2 + \mathrm{H}_2\mathrm{O} + \mathrm{SO}_4^{2-} \)

In contrast, sulfide ions \( \mathrm{S}^{2-} \) will produce hydrogen sulfide \( \mathrm{H}_2\mathrm{S} \), a gas with a characteristic rotten egg smell. Understanding these reactions is essential for predicting the behavior of substances in chemical processes involving sulfuric acid.

Gas identification tests are crucial for determining the type of gas produced in a chemical reaction. One common test involves using baryta water \( \mathrm{Ba(OH)_2} \), which is used specifically to detect carbon dioxide. When carbon dioxide is bubbled through baryta water, it forms a white precipitate of barium carbonate:

• \( \mathrm{CO}_2 + \mathrm{Ba(OH)_2} \rightarrow \mathrm{BaCO}_3 + \mathrm{H}_2\mathrm{O} \)

This reaction results in turbidity, allowing us to confirm the presence of \( \mathrm{CO}_2 \).
Another test involves an acidified dichromate solution. This test identifies gases capable of reducing dichromate ions. Sulfur dioxide \( \mathrm{SO}_2 \) is one such gas that reduces dichromate \( \mathrm{Cr}_2\mathrm{O}_7^{2-} \) to chromium \( \mathrm{Cr}^{3+} \), turning the solution from orange to green:

• \( \mathrm{SO}_2 + \mathrm{Cr}_2\mathrm{O}_7^{2-} + 2\mathrm{H}^+ \rightarrow 2\mathrm{Cr}^{3+} + \mathrm{SO}_4^{2-} + \mathrm{H}_2\mathrm{O} \)

Such chemical tests are important tools for chemists to identify and confirm the nature of gases evolved in various reactions.

Analyzing a chemical reaction involves understanding the substances and their interactions. In the context of reactions with sulfuric acid and the resulting gases, analyzing the reaction means predicting which gas is produced based on the initial compounds.
For instance, given the options in the exercise, understanding the properties and behaviors of carbonate \( \mathrm{CO}_3^{2-} \), sulfide \( \mathrm{S}^{2-} \), sulfite \( \mathrm{SO}_3^{2-} \), and nitrite \( \mathrm{NO}_2^{-} \) ions is key.

• Carbonates react to release \( \mathrm{CO}_2 \).
• Sulfites release \( \mathrm{SO}_2 \).
• Sulfides form \( \mathrm{H}_2\mathrm{S} \).
• Nitrites generally do not yield a colorless gas with sulfuric acid.

By systematically considering the reactions of each ion with \( \mathrm{H}_2\mathrm{SO}_4 \), we can perform deductive reasoning to identify the substance and gas involved. Utilizing typical reaction conditions and subsequent tests, like those with baryta water or dichromate solutions, aids in confirming the analysis. This methodical approach helps chemists validate their predictions about reaction outcomes.