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 )

Question

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 ) (A) 39.8 (B) 19.9 (C) 3.98 (D) 7.96

Tardigrade Admin · Accepted Answer

ln(k2/k1)=(E a/R)[(1/T1) - (1/T2)] ln(60/40)=(E a/8.3)[(1/300) - (1/400)] Ea=3.98 kJ/mole

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 $m o l^{- 1} K^{- 1}, l n (\frac{2}{3}) = 0.4, e^{- 3} = 4.0$ )

39.8

19.9

3.98

7.96

$l n \frac{k _{2}}{k _{1}} = \frac{E a}{R} [\frac{1}{T _{1}} - \frac{1}{T _{2}}]$
$l n \frac{60}{40} = \frac{E a}{8.3} [\frac{1}{300} - \frac{1}{400}]$
$E a = 3.98 k J / m o l e$

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−1K−1,ln(32​)=0.4,e−3=4.0 )