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Q.

The ionisation constant of ${NH}_{4}^{+}$ in water is 5 .6 x 10^-10 at 25°C. The rate constant for the reaction of ${NH}_{4}^{+}$ and OH^- to form NH₃ and H₂O at 25°C is 3 .4 x10¹⁰ L mol^-1s^-1.
The rate constant for proton transfer from water to NH₃is:

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a

6 .07 x 10^-10 s^-1

b

6 .07 x 10⁵ s^-1

c

6 .07 x 10^-5 s^-1

d

6 .07 x 10¹⁰s^-1

answer is A.

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Detailed Solution

$\begin{array}{l} {NH}_{3} + H_{2} O ⇌ {NH}_{4}^{+} + {OH}^{-}; K_{b} = 3 .4 \times 10^{10} \\ {NH}_{4}^{+} + H_{2} O ⇌ {NH}_{4} OH + H^{+}; K_{a} = 5 .6 \times 10^{- 10} \\ K_{base {NH}_{3}} = \frac{K_{f}}{K_{b}} = \frac{K_{w}}{K_{acid {NH}_{4}^{+}}} (∵ K_{acid} \times K_{base} = K_{w}) \\ or \frac{K_{f}}{3 .4 \times 10^{10}} = \frac{10^{- 14}}{5 .6 \times 10^{- 10}} \\ or K_{f} = 6 .07 \times 10^{5} s^{- 1} \end{array}$

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The ionisation constant of NH4+ in water is 5 .6 x 10-10 at 25°C. The rate constant for the reaction of NH4+ and OH- to form NH3 and H2O at 25°C is 3 .4 x1010 L mol-1s-1. The rate constant for proton transfer from water to NH3 is: