Question

Raw milk sours in about $4 \,h$ at $27^{\circ} C$, but in about $48 \,h$ in a refrigerator at $17^{\circ} C$. What is the activation energy for souring of milk?

• A. $78.3 \,kJ\, mol ^{-1}$
• B. $46.21 \,kJ \,mol ^{-1}$
• C. $23.5\, kJ \,mol ^{-1}$
• D. $80.8 \,kJ \,mol ^{-1}$

Answer 1

Answer: (A)

$K \propto \frac{1}{t}$
$ \log \frac{k_{2}}{k_{1}} =\log \frac{t_{1}}{t_{2}}=\frac{E_{a}}{R}\left(\frac{T_{2}-T_{1}}{T_{1} \cdot T_{2}}\right) $
$ \log \frac{48}{4} =\frac{E_{a}}{8.314}\left(\frac{10}{300 \times 290}\right) $
$ E_{a} =78.0 \,kJ \,mol ^{-1} $