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To solve these problems, we need to use the relationship between the acid dissociation constant (\( K_a \)) and the base dissociation constant (\( K_b \)) for conjugate acid-base pairs. This relationship is given by:

\[
K_a \times K_b = K_w
\]

where \( K_w \) is the ionization constant of water at 25°C, which is \( 1.0 \times 10^{-14} \).

### Problem 1: \( K_b \) for \( \text{BrO}^- \)

Given:
- \( K_a \) for \( \text{HBrO} \) = \( 2.8 \times 10^{-9} \)

We can find \( K_b \) for \( \text{BrO}^- \) by rearranging the equation:

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

Substituting the given values:

\[
K_b = \frac{1.0 \times 10^{-14}}{2.8 \times 10^{-9}} = 3.57 \times 10^{-6}
\]

So, \( K_b \) for \( \text{BrO}^- \) is \( 3.57 \times 10^{-6} \).

---

### Problem 2: \( K_a \) for \( \text{NH}_4^+ \)

Given:
- \( K_b \) for \( \text{NH}_3 \) = \( 1.8 \times 10^{-5} \)

Similarly, we can find \( K_a \) for \( \text{NH}_4^+ \) using:

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

Substituting the given values:

\[
K_a = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.56 \times 10^{-10}
\]

Thus, \( K_a \) for \( \text{NH}_4^+ \) is \( 5.56 \times 10^{-10} \).

---

Would you like a deeper explanation of any part of these calculations?

### Related Questions
1. What is the significance of \( K_a \) and \( K_b \) in acid-base chemistry?
2. How does temperature affect the value of \( K_w \)?
3. Can \( K_a \) or \( K_b \) alone determine if a solution is acidic or basic?
4. What are conjugate acid-base pairs, and how are they determined?
5. Why is \( K_w \) always constant at a specific temperature?

**Tip:** Always check units and significant figures when dealing with equilibrium constants in calculations.

Given that Ka for HBrO is 2.8 × 10^-9 at 25 °C, what is the value of Kb for BrO- at 25 °C? Given that Kb for NH3 is 1.8 × 10^-5 at 25 °C, what is the value of Ka for NH4+ at 25 °C?

Learn how to calculate the Kb for BrO- and Ka for NH4+ at 25°C using the conjugate acid-base relationship. This problem uses Ka * Kb = Kw, with provided values for Ka of HBrO and Kb of NH3, ideal for undergraduate chemistry students.

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