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QJEEM20Ch12b8: JEE Main 2020 Chemistry - Class 12 JEEM20Ch12b8 Solution: A sample of milk splits after 60 min. at 300 K and after 40…

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 activa tion energy (in kJ/ mol) for this process is closest to__________.

(Given, R = 8.3 J mol–1 K–1, ln⁡(32)=0.4, e–3 = 4.0)

Step-by-Step Verified Solution

Using Arrehenius equation

K = Ae−EaRT

ln⁡(k400k300)=EaR(1300−1400)

⇒ ln⁡(6040)=EaR(100300×400)

⇒ ln⁡(32)=Ea1200R

∴ Ea = 0.4 × 1200 × 8.3 = 3984 J/mol

Ea = 3.984 kJ/mol = 3.98 kJ/mol

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