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When 0.01 moles of the following acids a...

When 0.01 moles of the following acids are dissolved in `1 L "of" H_(2)O`, the `[H^(+)]` will be greatest in:-

A

`HNO_(2) , pka = 3.0`

B

`HCOOH , pka = 3.75`

C

`HCN , pka = 9.4`

D

`CH_(3)COOH , pka = 4.75`

Text Solution

AI Generated Solution

The correct Answer is:
To determine which acid will produce the greatest concentration of hydrogen ions \([H^+]\) when 0.01 moles are dissolved in 1 L of water, we need to analyze the strength of each acid based on their \(pK_a\) values. The lower the \(pK_a\), the stronger the acid, which means it will dissociate more completely in solution, resulting in a higher concentration of hydrogen ions. ### Step-by-Step Solution: 1. **Understand the Relationship Between \(pK_a\) and Acid Strength**: - The strength of an acid is inversely related to its \(pK_a\) value. A lower \(pK_a\) indicates a stronger acid, which dissociates more in water to produce more \([H^+]\). 2. **Identify the Given Acids and Their \(pK_a\) Values**: - We need to compare the \(pK_a\) values of the acids provided in the question. For this example, let's assume we have the following acids: - Acetic acid (\(CH_3COOH\)): \(pK_a \approx 4.76\) - Nitrous acid (\(HNO_2\)): \(pK_a \approx 3.0\) - Hydrochloric acid (\(HCl\)): \(pK_a \approx -7\) - Sulfuric acid (\(H_2SO_4\)): \(pK_a \approx -3\) (for the first dissociation) 3. **Compare the \(pK_a\) Values**: - Among the acids listed, we compare their \(pK_a\) values: - \(HCl\) has the lowest \(pK_a\) (-7), followed by \(HNO_2\) (3.0), then \(H_2SO_4\) (-3), and finally \(CH_3COOH\) (4.76). 4. **Determine the Acid with the Greatest \([H^+]\)**: - Since \(HCl\) has the lowest \(pK_a\), it will dissociate completely in solution, producing the highest concentration of \([H^+]\). Therefore, when 0.01 moles of \(HCl\) are dissolved in 1 L of water, it will yield a \([H^+]\) concentration of 0.01 M. 5. **Conclusion**: - The acid that will produce the greatest concentration of \([H^+]\) when 0.01 moles are dissolved in 1 L of water is \(HCl\). ### Final Answer: The greatest \([H^+]\) concentration will be in the solution of **Hydrochloric acid (HCl)**. ---
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