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  4. A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ/mol) for this process is closest to (Given, R = 8.3 J mol- 1K- 1,ln((2/3))=0.4,e- 3=4.0 )

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Q. A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ/mol) for this process is closest to
(Given, R = 8.3 J $mol^{- 1}K^{- 1},ln\left(\frac{2}{3}\right)=0.4,e^{- 3}=4.0$ )

NTA AbhyasNTA Abhyas 2022

Solution:

$ln\frac{k_{2}}{k_{1}}=\frac{E a}{R}\left[\frac{1}{T_{1}} - \frac{1}{T_{2}}\right]$
$ln\frac{60}{40}=\frac{E a}{8.3}\left[\frac{1}{300} - \frac{1}{400}\right]$
$Ea=3.98 \, kJ/mole$