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 (equialent of pH) of `1.5` and freezes at `-0.372^(@)C`. If 600mL of freeshly prepared solution were allowed to stad for `24.8` years, calculate (i) ionization constant of TF (ii) Number of `beta-`particles emitted.
(Given `K_(f)` for water `= 1.86 kg mol K^(-1) t_(1//2)` for tritium `= 12.4` years).

Answer

(i) `K_(a) = 7.3 xx 10^(-3)` (ii) `3.7 xx 10^(22)`

Explanation

`P^(T) = 1.5 rArr [T^(+)] = 0.0316 = C alpha` ...(i)
`0.372 = 1.86 xx C (1-alpha)`
`C + C alpha = 0.2` ...(ii)
from equation (i) & (ii)
`C = 0.1684, alpha = 0.1876`
`k_(a) = (C alpha^(2))/(1-alpha) = (0.1684(0.1876)^(2))/((1-0.1876)) = 7.3 xx 10^(-3)`
In `600 mL` solution `[TF] = C -Calpha = 0.1368 "mole"//L`
so moles `= 0.1368 xx 0.6 = 0.08208`
mole left after `24.8` years `= (0.08208)/(4) = 0.02052`
moles disinitegrated
`= 0.08208 - 0.02052 = 0.06156`
mole of `beta-`particle emitted `= 0.06156`
No.of `beta`-particle emitted `= 0.06156 xx 6.023 xx 10^(23)`
`= 3.7 xx 10^(22)`