Fine brandies (several hundred dollars per bottle) are considered to be at their

Question

Fine brandies (several hundred dollars per bottle) are considered to be at their peak when they are between 50 and 100 years old. In order to authenticate a vendor's claim as to the age of a bottle of brandy, a small sample of the brandy can be sent off for tritium analysis. Tritium is a natural isotope of hydrogen and it has the isotopic symbol H and it is naturally present at extremely low concentrations in the brandy. For tritium, t_1/2 = 12.3 years. If the tritium activity of a brandy sample is observed to be 13.88 % the tritium activity of fresh brandy (meaning only 13.88 % of the original tritium remains - think about how this 13.88% fils into the integrated rate law...), is the brandy in question worth the money? Show calculations.

Explanation / Answer

Half life of tritium = 12.3 years

Rate constant for a first order reaction =0.693/half life= 0.693/12.3=0.056341 /yr

for a first order reaction C= CO*e(-kt)

where C= Concentration at any time t, 0.1388Co

and k= rate constant =0.056341/yr

0.1388Co=Co*e(-0.056341*t)

t= 35.05 years

since brandies are considered to be at their peak between 50 to 100 years and the present case it is only 35 years, the brandy is not worth its money.

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