Glass is typically metastable, and these metastable structures are prone to convert into a more thermodynamically stable structure. Suppose a crystalline glass which is already in BCC structure has tendency to get converted into end centered structure. The activation energy required to initiate the process is 11488 J per mol at 300 K. Calculate the ratio (nearest integer) of number of end centered cubic unit cells to BCC unit cell
after 0.23 hours, if the reaction follows first order kinetics.
[Assume pre-exponential factor for the above conversion is 1000 hr⁻¹, R = 8.314 J/mol K, lnP = 2.3 log₁₀P]

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answer is 9.

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Detailed Solution

$\begin{array}{l} K = A_{0} e^{- \frac{E_{a}}{R T}} \\ \ln K = \ln A_{0} - \frac{E_{a}}{RT} \\ \log K = \log 1000 - \frac{11488}{8.3114 \times 300 \times 2.30} \\ = 3 - 2 - = 1 \\ K = 10 {hr}^{- 1} \end{array}$
$\begin{array}{l} Kt = \ln (\frac{A_{0}}{A_{t}}) \\ 2.3 = 2.3 \log (\frac{(A_{0})}{(A_{t})}) \\ (\frac{A_{0}}{A_{t}}) = \frac{10}{1} = \frac{A}{A_{0} - x} \\ \frac{(E \cdot C)_{t}}{(B \cdot C \cdot C)_{t}} = 9 \end{array}$