1. Tardigrade
  2. Question
  3. Chemistry
  4. The ionisation constant of NH4+ in water is 5.6× 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× 1010Lmol- 1s- 1 . The rate constant for proton transfer from water to NH3 is

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Q. The ionisation constant of $NH_{4}^{+}$ in water is $5.6\times 10^{- 10}$ at $25^\circ C$ . The rate constant for the reaction of $NH_{4}^{+}$ and $OH^{-}$ to form $NH_{3}$ and $H_{2}O$ at $25^\circ C$ is $3.4\times 10^{10}Lmol^{- 1}s^{- 1}$ . The rate constant for proton transfer from water to $NH_{3}$ is

NTA AbhyasNTA Abhyas 2022

Solution:

$NH_{4}^{+}\rightleftharpoons NH_{3}+H^{+};k_{1}=5.6\times 10^{10}$ …(i)
$H_{2}O\rightleftharpoons H^{+}+OH;k_{2}=1\times 10^{14}$ …(ii)
$K=\frac{k_{1}}{k_{2}}=\frac{5.6 \times 1 0^{- 10}}{1 \times 1 0^{- 14}}$
$=5.6\times 10^{4}$
By subtracting equation (ii) from equation (i) we get
$NH_{4}^{+}+OH\rightleftharpoons NH_{3}+H_{2}O$
From equation
$k_{f}=3.4\times 10^{10}/mil^{- 1}S^{- 1}$
$NH_{3}+H_{2}O\rightleftharpoons NH_{4}^{+}+OH^{-}$
$k_{r}=?$
$K=\frac{k_{f}}{k_{r}}$
So $k_{r}=\frac{k_{f}}{K}=\frac{3.4 \times 1 0^{10}}{5.6 \times 1 0^{4}}$
$=6.07\times 10^{5}$