Question

A given sample of milk turns sour at room temperature ($27^{\circ }C$) in $5$ hours. In a refrigerator at $-3^{\circ }C$, it can be stored $10$ times longer .The energy of activation for the souring of milk is

• A. $2.303\times 10RkJ\cdot mo{l}^{-1}$
• B. $2.303\times 5RkJ\cdot mo{l}^{-1}$
• C. $2.303\times 3RkJ\cdot mo{l}^{-1}$
• D. $2.303\times 2.7RkJ\cdot mo{l}^{-1}$

Answer 1

Answer: (D)

Energy of activation is given by

$\log \frac{k_2}{k_1}=\frac{E_a}{2.303R}\left[\frac{T_2-T_1}{T_1{T}_2}\right]$

Here, $\frac{k_2}{k_1}=\frac{1}{10}$

$T_1=27^{\circ }C=300K$

$T_2=-3^{\circ }C=270K$

$\therefore \log \frac{1}{10}=\frac{E_a}{2.303R}\left(\frac{270-300}{270\times 300}\right)$

$-1=-\frac{E_a}{2.303R}\frac{30}{270\times 300}$

$E_a=+2.303\times 2700\times RJmo{l}^{-1}$

$=+2.303\times 2.7\times RkJmo{l}^{-1}$