Question

For the reaction $F_2\rightleftharpoons 2F$, Calculate the degree of dissociation of fluorine at $4$ atm and $1000k$, when $K_p=1.4\times {10}^{-2}$ atm.

Answer 1

$n_6=1-\alpha +2\alpha =1+\alpha$
$K_p=\frac{(P_F{)}^2}{\left(P_{F_2}\right)}=\frac{{\left(\frac{2\alpha }{1+\alpha }P\right)}^2}{\left(\frac{1-\alpha }{1+\alpha }P\right)}$
$K_p=\frac{4{\alpha }^2}{1-{\alpha }^2}P$
$1.4\times {10}^{-2}=\frac{4{\alpha }^2}{1-{\alpha }^2}4$
$=0.0875\times {10}^{-2}=\frac{{\alpha }^2}{1-{\alpha }^2}$
$=1+0.0875\times {10}^{-2}=\frac{{\alpha }^2+1-{\alpha }^2}{1-{\alpha }^2}$
$=1-{\alpha }^2=\frac{1}{1.000875}$
$\alpha =0.0295$