Question

Liquid $N{H}_3$ ionises to a slight extent. At a certain temp. its self ionization constant $K_{SIC\left(N{H}_3\right)}={10}^{-30}$ The number of $N{H}_4{}^{+}$ ions are present per $100c{m}^3$ of pure liquid are:

• A. ${10}^{-15}$
• B. $6.022\times {10}^8$
• C. $6.022\times {10}^7$
• D. $6.022\times {10}^6$

Answer 1

Answer: (C)

$6.022\times {10}^7$

Liquid ${NH}_3$ ionizes to a slight extent

$2{NH}_3\left(l\right)\rightleftharpoons {NH}_4^{+}+{NH}_2^{-}$

$n-2x$ $x$ $x$

$\therefore$ Self ionisation constant, $K_{SIC}=\left[{NH}_4^{+}\right]\left[{NH}_2^{-}\right]={10}^{-30}$

$\therefore$ $x.x={10}^{-3}\Rightarrow x^2={10}^{-30}\Rightarrow x={10}^{-15}$ mol/lit

$\therefore$ $\left[{NH}_4^{+}\right]={10}^{-15}$ mol/lit

No. of ${NH}_4^{+}$ ions in $100$ ${cm}^3$

$=\frac{100{cm}^3}{1000{cm}^3/lit}\times {10}^{-15}$ mol/lit $\times 6.022\times {10}^{23}$

$=6.022\times {10}^7$

$\therefore$ Correct answer is C.