A sample of milk splits after 60 min. at 300K and after 40 min at 400K when the population of lactobacillus acidophilus in it doubles . The activation energy (in kJ/mol) for this process is closest to

(Given, $R = 8.3 {J mol}^{- 1} K^{- 1}), ln (\frac{2}{3}) = 0.4, e^{- 3} = 4.0)$

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Solution

The generation time can be utilized to get an indication of the rate ratio. Let the amount generated be (x).
$Rate = \frac{Amount generated}{Time Taken}$
${Rate}_{300 K} = \frac{(x)}{60}$
${Rate}_{400 K} = \frac{(x)}{40}$
$\frac{{Rate}_{300 K}}{{Rate}_{400 K}} = \frac{40}{60}$
For the same concentration (which is applicable here), the rate ratio can also be equaled to the ratio of rate constants.
$ln [\frac{K_{at 400K}}{K_{at 300K}}] = \frac{E_{a}}{R} [\frac{1}{T_{1}} - \frac{1}{T_{2}}]$
$ln \frac{60}{40} = \frac{E_{a}}{8.3} [\frac{1}{300} - \frac{1}{400}]$
$E_{a} = 0.4 \times 8.3 \times 1200 = 3984 J/mol = 3.98 kJ/mol$

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A sample of milk splits after 60 min. at 300K and after 40 min at 400K 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(23)=0.4,e−3=4.0)

A sample of milk splits after 60 min. at 300K and after 40 min at 400K when the population of lactobacillus acidophilus in it doubles . The activation energy (in kJ/mol) for this process is closest to

(Given, $R = 8.3 {J mol}^{- 1} K^{- 1}), ln (\frac{2}{3}) = 0.4, e^{- 3} = 4.0)$