Question

The age of water or wine may be determined by measuring its radioactive tritium(3H) content. Tritium, present in a steady state in nature, is formed primarily by cosmicirradiation of water vapor in the upper atmosphere, and it decays spontaneously by a firstorder process with a half-life of 12.5 years. The formation reaction does not occursignificantly inside a glass bottle at the surface of the earth.Calculate the age of a suspected vintage wine that is 20 % as radioactive as a freshlybottled specimen.

Answer 1

Answer: 29.0 years

Explanation:

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

$t_{\frac{1}{2}}=\frac{0.693}{k}$

$k=\frac{0.693}{12.5years}=0.0554years^{-1}$

b) for decomposition of 80 % of reactant

$t=\frac{2.303}{0.0554}\log\frac{100}{100-80}$

$t=\frac{2.303}{0.0554}\log\frac{100}{20}$

$t=29.0 years$

The age of a suspected vintage wine that is 20 % as radioactive as a freshlybottled specimen is 29.0 years