Question

Which acid ionizes to the greater extent in water, nitrous acid, \(\mathrm{HNO}_{2}\), or hydrofluoric acid, HF? Consult Table \(13.5\) for \(K_{\mathrm{a}}\) values.

Short answer

The acid with the higher Ka value, as found in Table 13.5, ionizes to the greater extent in water. As such, without the actual values, a definitive answer cannot be given. But please refer to the table to find out the correct answer.

Step-by-step solution

Look Up the Ka Values

Consult Table 13.5, or any table that provides the Ka values for various acids. Record the Ka for nitrous acid (\(HNO_{2}\)) and hydrofluoric acid (HF).

Compare the Ka Values

Compare the two Ka values. If the Ka of \(HNO_{2}\) is larger than that of HF, then nitrous acid ionizes to a greater extent in water. If HF's Ka is larger, then hydrofluoric acid ionizes to a greater extent in water.

Conclusion

Having compared the Ka values, conclude which acid ionizes to the greater extent.

Key concepts

Ka values

The \(K_a\) value, also known as the acid dissociation constant, is a measure of the strength of an acid in solution. It quantifies the extent to which an acid dissociates into its ions in water. Stronger acids will dissociate more completely, resulting in higher \(K_a\) values compared to weaker acids.
Lower \(K_a\) values indicate that the acid is not very strong and only partially ionizes in water. When comparing two acids, you can determine which one ionizes more based on their \(K_a\) values: the larger the \(K_a\), the greater the ionization of the acid.

• A higher \(K_a\) value means a stronger acid which dissociates more in water.
• A lower \(K_a\) value indicates a weaker acid, with less dissociation.
• Comparing \(K_a\) values helps to establish which acid ionizes more extensively.

Nitrous Acid

Nitrous acid \( (\mathrm{HNO}_{2}) \) is a weak acid commonly used in making diazo compounds and as an oxidizing agent.
In water, nitrous acid partially disassociates into hydrogen ions \( (\mathrm{H}^+) \) and nitrite ions \( (\mathrm{NO}_{2}^{-}) \).
Its \(K_a\) value is typically found in tables and provides insight into its ionization level when compared with other acids.
Recognizing \(HNO_2\) as a weak acid explains reactions like its use as a mild acid in atmospheric sciences, indicating its moderate capacity to release \(\mathrm{H}^+\) ions into an aqueous solution.

• Nitrous acid is relatively weak, so it doesn’t fully ionize in water.
• Used in specific chemical reactions due to its properties as a mild oxidizing agent.
• The partial ionization makes it useful for controlled reactions where equilibrium is important.

Hydrofluoric Acid

Hydrofluoric acid \( (\mathrm{HF}) \) is a unique and potent acid, distinctive for its ability to etch glass due to the reaction with silicon compounds.
Unlike strong acids, HF does not fully ionize in aqueous solution, making it a weak acid.
It will dissociate into hydrogen ions \( (\mathrm{H}^+) \) and fluoride ions \( (\mathrm{F}^-) \) to some extent, but the extent is less compared to stronger acids, hence, its relatively low \(K_a\).

• HF is a weak acid despite its strong corrosive effects.
• Its safety hazards due to the ability to damage tissues and materials make handling it with care essential.
• It is intriguing due to its discrepancies in strength versus the typical effects it causes.

Evaluating HF's \(K_a\) helps underline its specific behaviors in acid-base chemistry, providing a measure for how much it ionizes in solution.