Chemical and Ionic Equilibrium 1 Question 43
45. (a) The degree of dissociation is 0.4 at $400 \mathrm{~K}$ and $1.0 \mathrm{~atm}$ for the gaseous reaction $\mathrm{PCl}{5} \rightleftharpoons \mathrm{PCl}{3}+\mathrm{Cl}_{2}$. Assuming ideal behaviour of all the gases, calculate the density of equilibrium mixture at $400 \mathrm{~K}$ and $1.0 \mathrm{~atm}$ (relative atomic mass of $\mathrm{P}=31.0$ and $\mathrm{Cl}=35.5)$.
(b) Given, $\left[\mathrm{Ag}\left(\mathrm{NH}{3}\right){2}^{+}\right] \rightleftharpoons \mathrm{Ag}^{+}+2 \mathrm{NH}_{3}$,
$$ \begin{aligned} K_{c} & =6.2 \times 10^{-8} \text { and } K_{\text {sp }} \text { of } \mathrm{AgCl} \ & =1.8 \times 10^{-10} \text { at } 298 \mathrm{~K} . \end{aligned} $$
If ammonia is added to a water solution containing excess of $\mathrm{AgCl}(s)$ only. Calculate the concentration of the complex in $1.0 \mathrm{M}$ aqueous ammonia.
$(1998,3 M+5 M)$
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Solution:
- (a)
Average molar mass $=\frac{208.5}{1.4}=148.9$
$$ \rho(\text { density })=\frac{p M}{R T}=\frac{1 \times 148.9}{0.082 \times 400}=4.54 \mathrm{~g} / \mathrm{L} $$
(b) $\left.\underset{-x}{\mathrm{AgCl}(s)+2 \mathrm{NH}{3}(a q)}=\underset{1-2 x}{\left[\mathrm{Ag}\left(\mathrm{NH}{3}\right)_{2}^{+}\right.}\right]+\underset{x}{\mathrm{Cl}^{-}}$
$$ K=\frac{K_{\mathrm{sp}}}{K_{c}}=2.9 \times 10^{-3}=\left(\frac{x}{1-2 x}\right)^{2} $$
$x=0.049 \mathrm{M}$
