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. $2.303 \times 10 \, R \, kJ \cdot mol^{-1}$
• B. $2.303 \times 5\, R\, kJ \cdot mol^{-1}$
• C. $2.303 \times 3\, R\, kJ \cdot mol^{-1}$
• D. $2.303 \times 2.7 \,R \,kJ \cdot mol^{-1}$

Answer 1

Answer: (D)

Energy of activation is given by

$\log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right]$

Here, $\frac{k_{2}}{k_{1}}=\frac{1}{10}$

$T_{1}=27^{\circ} C=300\, K$

$T_{2}=-3^{\circ} C=270 \,K$

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

$-1=-\frac{E_{a}}{2.303 \,R} \frac{30}{270 \times 300}$

$E_{a}=+2.303 \times 2700 \times R \,J \,m o l^{-1}$

$=+2.303 \times 2.7 \times R\, kJ\,mol^{-1}$