A given sample of milk turns sour at room tem | vedclass

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Question

(C) The rate constant $k$ is inversely proportional to the time $t$ taken for the reaction to occur $(k \propto 1/t)$.Given $t_1 = 5 \ h$ at $T_1 = 30

Vedclass · Accepted Answer

$2.303 	imes 2.7 R \ kJ \cdot mol^{-1}$

Vedclass · Answer

(C) The rate constant $k$ is inversely proportional to the time $t$ taken for the reaction to occur $(k \propto 1/t)$.Given $t_1 = 5 \ h$ at $T_1 = 300 \ K$ and $t_2 = 50 \ h$ at $T_2 = 270 \ K$.Thus,$k_1/k_2 = t_2/t_1 = 50/5 = 10$,which means $k_2/k_1 = 1/10$.Using the Arrhenius equation: $\log(k_2/k_1) = \frac{E_a}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} ight]$.Substituting the values: $\log(1/10) = \frac{E_a}{2.303 R} \left[ \frac{270 - 300}{270 	imes 300} ight]$.$-1 = \frac{E_a}{2.303 R} \left[ \frac{-30}{81000} ight]$.$-1 = \frac{E_a}{2.303 R} \left[ \frac{-1}{2700} ight]$.$E_a = 2.303 	imes 2700 	imes R \ J \cdot mol^{-1} = 2.303 	imes 2.7 	imes R \ kJ \cdot mol^{-1}$.

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

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