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  • 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 proces

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_______.

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

Option: 1

3.984


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

The formula of activation energy -

\mathrm{ln\frac{K_{2}}{K_{1}}\: =\: \frac{E_{a}}{R}\left [ \frac{1}{T_{1}}-\frac{1}{ T_{2}} \right ]}

\mathrm{ln\left ( \frac{60}{40} \:\right )\: =\: \frac{E_{a}}{8.3}\: x\: \frac{100}{400\, x\, 300}}

\mathrm{ln\left ( \frac{3}{2} \:\right )\:\times8.3 \times 1200 =E_{a} }

\mathrm{E_{a} = 0.4 \times8.3 \times 1200 }

\mathrm{E_{a} = 3984 \ J/mol }

\mathrm{E_{a} = 3.984 \ kJ/mol }
 

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