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[3-521] The acid at which contains the highest concentration of OH- is .......... (knowing that all of them have the same concentration). a) HCl b) \( H A\left(K_{\mathrm{a}}=1.5 \times 10^{-4}\right) \) c) \( H B\left(K_{\mathrm{a}}=1 \times 10^{-6}\right) \) d) \( H C\left(K_{\mathrm{a}}=2.4 \times 10^{-4}\right) \)

Ask by Cummings Reyes. in Egypt
Jan 10,2025

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Answer

\( H B \) has the highest concentration of \( OH^- \).

Solution

To determine which acid solution contains the highest concentration of hydroxide ions (\([OH^-]\)), we need to consider the strength of each acid. All acids are at the same concentration, so the weaker the acid, the less it dissociates to release hydrogen ions (\([H^+]\)). A lower concentration of \([H^+]\) means a higher concentration of \([OH^-]\) due to the relationship: \[ [OH^-] = \frac{K_w}{[H^+]} \] where \(K_w\) is the ion-product constant of water (\(1 \times 10^{-14}\) at 25°C). **Given Acids and Their \(K_a\) Values:** 1. **HCl**: Strong acid (\(K_a\) is very large, effectively completely dissociates) 2. **HA**: \(K_a = 1.5 \times 10^{-4}\) 3. **HB**: \(K_a = 1 \times 10^{-6}\) 4. **HC**: \(K_a = 2.4 \times 10^{-4}\) **Analysis:** - **HCl** is a strong acid and dissociates completely, resulting in a high \([H^+]\) and thus a low \([OH^-]\). - Among the weak acids, a lower \(K_a\) value indicates a weaker acid. Therefore, HB (\(K_a = 1 \times 10^{-6}\)) is the weakest acid among the given options. **Conclusion:** Since HB is the weakest acid, it dissociates the least, resulting in the lowest concentration of \([H^+]\) and thereby the highest concentration of \([OH^-]\). **Answer:** c) \( H B\left(K_{\mathrm{a}}=1 \times 10^{-6}\right) \)

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To determine which acid results in the highest concentration of OH⁻, we need to consider the strength of the acids given by their Ka values. The higher the Ka, the stronger the acid, which means it dissociates more completely in solution and thus produces more H⁺ ions. For the acids provided, HCl is a strong acid, fully dissociating into H⁺ and Cl⁻. The others are weak acids, with the lower the Ka value signifying a weaker acid, leading to higher pH and thus higher OH⁻ concentration. Thus, among the options, while HCl generates many H⁺ ions, leading to a very low pH (high H⁺, low OH⁻) condition, the weakest acid among the weak acids \( H A \), \( H B \), and \( H C \) would produce the highest OH⁻ concentration due to the higher pH. Specifically, \( H B \), having the smallest Ka, results in the highest concentration of OH⁻ ions compared to the others due to its weak nature and the substitutive equilibrium. So the answer is option b) \( H A \left(K_a=1.5 \times 10^{-4}\right) \): which would technically give you high pH and more OH⁻, even though its dissociation isn't as high. Rather, it is the highest OH⁻ generating one.

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