Chemical and Ionic Equilibrium - Result Question 45
####45. (a) The degree of dissociation is 0.4 at $400 K$ and $1.0 atm$ for the gaseous reaction $PCl _5 \rightleftharpoons PCl _3+Cl _2$. Assuming ideal behaviour of all the gases, calculate the density of equilibrium mixture at $400 K$ and $1.0 atm$ (relative atomic mass of $P=31.0$ and $Cl=35.5)$.
(b) Given, $\left[Ag\left(NH _3\right) _2^{+}\right] \rightleftharpoons Ag^{+}+2 NH _3$,
$$ \begin{aligned} K _c & =6.2 \times 10^{-8} \text { and } K _{\text {sp }} \text { of } AgCl \ & =1.8 \times 10^{-10} \text { at } 298 K . \end{aligned} $$
If ammonia is added to a water solution containing excess of $AgCl(s)$ only. Calculate the concentration of the complex in $1.0 M$ aqueous ammonia.
$(1998,3 M+5 M)$
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Solution:
- (a)
Average molar mass $=\frac{208.5}{1.4}=148.9$
$$ \rho(\text { density })=\frac{p M}{R T}=\frac{1 \times 148.9}{0.082 \times 400}=4.54 g / L $$
(b) $\left.\underset{-x}{AgCl(s)+2 NH _3(a q)}=\underset{1-2 x}{\left[Ag\left(NH _3\right) _2^{+}\right.}\right]+\underset{x}{Cl^{-}}$
$$ K=\frac{K _{sp}}{K _c}=2.9 \times 10^{-3}=\left(\frac{x}{1-2 x}\right)^{2} $$
$x=0.049 M$
