Question

Tritium, $T$ (an isotope of $H$) combines with fluorine to form weak acid $TF$, which ionizes to give $T^{+}$. Tritium is radioactive and is a $\beta -$ emitter. A freshly prepared aqueous solution of $TF$ has $pT$ (equivalent of $pH$) of $1.5$ and freezes at $-{0.372}^{\circ }C$. If $600mL$ of freshly prepared solution were allotted to stand for $24.8$years.
If ionization constant of $TF$ is $K_a=7.3\times {10}^{-x}$, value of $x$ is :

(Given $K_f$ for water$=1.86kgmol{K}^{-1},t_{1/2}$ for tritium$=12.4years$).

Answer 1

$P_T=1.5\Rightarrow \left[T^{+}\right]=0.0316=C\alpha .......\left(i\right)$

$0.372=1.86\times C(1+\alpha )$

$C+C\alpha =0.2.........\left(ii\right)$

From equation (i) & (ii)

$C=0.1684,\alpha =0.1876$

$K_a=\frac{C{\alpha }^2}{1-\alpha }=\frac{0.1684(0.1876{)}^2}{(1-0.1876)}=7.3\times {10}^{-3}$

So, $x=3$