The ionization constant of `overset(o+)(NH_(4))` ion in water is `5.6 xx 10^(-10)` at `25^(@)C`. The rate constant the reaction of `overset(o+)NH_(4)` and `overset(ɵ)(OH)` ion to form `NH_(3)` and `H_(2)O` at `25^(@)C` is `3.4 xx 10^(10)L mol^(-1) s^(-1)`. Calculate the rate constant for proton transfer from water to `NH_(3)`.

Explanation

To solve the problem, we need to find the rate constant for the proton transfer from water to NH3. We will use the given ionization constant of the NH4+ ion and the rate constant for the reaction of NH4+ and OH- ions.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Ionization constant of NH4+ (K_a) = \(5.6 \times 10^{-10}\)
- Rate constant for the reaction of NH4+ and OH- (K_b) = \(3.4 \times 10^{10} \, \text{L mol}^{-1} \text{s}^{-1}\)
- Ion product of water (K_w) = \(1.0 \times 10^{-14}\) at 25°C.
...