Question

At room temperature $\left({20}^{\circ }C\right)$ orange juice gets spoilt in about 64 hours. In a refrigerator at $3^{\circ }C$ juice can be stored three times as long before it gets spoilt. Estimate (a) the activation energy of the reaction that causes the spoiling of juice. (b) How long should it take for juice to get spoilt at ${40}^{\circ }C$?

• A. (a) $21.9kJmo{l}^{-1}$ (b) 10.47 hour
• B. (a) $43.46kJmo{l}^{-1}$ (b) 20.47 hour
• C. (a) $434.6kJmo{l}^{-1}$ (b) 10.47 hour
• D. None of these

Answer 1

Answer: (B)

(a) $43.46kJmo{l}^{-1}$ (b) 20.47 hour

(a) $E_a=\frac{2.303RT{T}^{\prime }}{T^{\prime }-T}log\frac{k^{\prime }}{k}$

$E_a=\frac{2.303\times 8.314\times 293\times 276}{276-293}log\frac{1}{3}$

$E_a=43457J/mol$

$E_a=43.46kJ/mol$

(b) $log\frac{k^{\prime }}{k}=\frac{E_a}{2.303R}\frac{T^{\prime }-T}{T{T}^{\prime }}$

$log\frac{k^{\prime }}{k}=\frac{43457}{2.303\times 8.314}\frac{[313-293]}{293\times 313}=0.4949$

$\frac{k^{\prime }}{k}=3.126$

Time required for juice to get spoil at $40{}^{o}C=\frac{64}{3.126}=20.47hr$