Given that K₂ for HF is 6.3 × 10-4 at 25 °C, what is the value of K₁ for Fat 25 °C? Kb = Given that K for (CH3)²N is 6.3 × 10−5 at 25 °C, what is the value of Kå for (CH3)²NH+ at 25 °C? Ka =

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Chapter1: Chemical Foundations
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### Chemistry Problem: Calculating Equilibrium Constants

In this exercise, we explore the relationship between acid dissociation constants (\(K_a\)) and base dissociation constants (\(K_b\)) at 25 °C.

#### Problem 1:
Given that the \(K_a\) for HF is \(6.3 \times 10^{-4}\) at 25 °C, what is the value of \(K_b\) for F\(^-\) at 25 °C?

\[ K_b = \text{[Text Box for Answer]} \]

#### Problem 2:
Given that \(K_b\) for (CH\(_3\))\(_3\)N is \(6.3 \times 10^{-5}\) at 25 °C, what is the value of \(K_a\) for (CH\(_3\))\(_3\)NH\(^+\) at 25 °C?

\[ K_a = \text{[Text Box for Answer]} \]

### Concept Explanation

The relationship between \(K_a\) and \(K_b\) for a conjugate acid-base pair is given by the equation:

\[ K_a \times K_b = K_w \]

Where \(K_w\) is the ion-product constant of water at 25 °C, equal to \(1.0 \times 10^{-14}\).

### Solution Steps

1. **For HF and F\(^-\):**

   - Use the equation \(K_a \times K_b = K_w\).
   - Rearrange to find \(K_b\): 

     \[ K_b = \frac{K_w}{K_a} \]

2. **For (CH\(_3\))\(_3\)N and (CH\(_3\))\(_3\)NH\(^+\):**

   - Again, use the formula \(K_a \times K_b = K_w\).
   - Rearrange to find \(K_a\):

     \[ K_a = \frac{K_w}{K_b} \]

Plug in the given values to find the unknown constants.
Transcribed Image Text:### Chemistry Problem: Calculating Equilibrium Constants In this exercise, we explore the relationship between acid dissociation constants (\(K_a\)) and base dissociation constants (\(K_b\)) at 25 °C. #### Problem 1: Given that the \(K_a\) for HF is \(6.3 \times 10^{-4}\) at 25 °C, what is the value of \(K_b\) for F\(^-\) at 25 °C? \[ K_b = \text{[Text Box for Answer]} \] #### Problem 2: Given that \(K_b\) for (CH\(_3\))\(_3\)N is \(6.3 \times 10^{-5}\) at 25 °C, what is the value of \(K_a\) for (CH\(_3\))\(_3\)NH\(^+\) at 25 °C? \[ K_a = \text{[Text Box for Answer]} \] ### Concept Explanation The relationship between \(K_a\) and \(K_b\) for a conjugate acid-base pair is given by the equation: \[ K_a \times K_b = K_w \] Where \(K_w\) is the ion-product constant of water at 25 °C, equal to \(1.0 \times 10^{-14}\). ### Solution Steps 1. **For HF and F\(^-\):** - Use the equation \(K_a \times K_b = K_w\). - Rearrange to find \(K_b\): \[ K_b = \frac{K_w}{K_a} \] 2. **For (CH\(_3\))\(_3\)N and (CH\(_3\))\(_3\)NH\(^+\):** - Again, use the formula \(K_a \times K_b = K_w\). - Rearrange to find \(K_a\): \[ K_a = \frac{K_w}{K_b} \] Plug in the given values to find the unknown constants.
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