If the time taken milk to sour at $40^{o} C$ in min is $(12.5 + x)$ , find the value of $x$ ___________.

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Solution

By using the data for 20 $^{o} C$ and 3 $^{o} C$ , calculate the activation energy.

$E_{a} = 2.303 R \frac{T_{1} T_{2}}{T_{2} - T_{1}} l o g \frac{k_{2}}{k_{1}} = 2.33 \times 8.314 \times \frac{293 \times 276}{276 - 293} l o g \frac{1}{3} = 43457 J / m o l$

By using the data for 20 $^{o} C$ and 40 $^{o} C$ , calculate the ratio of the rate constants.

$l o g \frac{k_{2}}{k_{1}} = \frac{E_{a}}{2.303 R} (\frac{1}{T_{1}} - \frac{1}{T_{2}}) = \frac{43457}{2.303 \times 8.314} (\frac{1}{293} - \frac{1}{313}) = 0.49496$

Hence, $\frac{k_{2}}{k_{1}} = 3.125$
Hence, the time taken for the milk to sour at $40^{o} C$ is $\frac{64}{3.125} = 20.5 m i n$ .

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