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For a homogeneous gaseous reaction,
\( \mathrm{P} \)
\( \mathrm{A} \longrightarrow \mathrm{B}+\mathrm{C}+\mathrm{D} \), the initial pressure was \( \mathrm{P}_{0} \)
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while pressure after time \( \mathrm{t} \) was \( \mathrm{P} \). Derive an expression for rate constant \( \mathrm{K} \) in terms of \( \mathrm{P}_{0}, \mathrm{P} \) and \( t \). assume first order reaction.
(A) \( \frac{2.303}{\mathrm{t}} \log _{10}\left(\frac{\mathrm{P}_{\mathrm{o}}}{3 \mathrm{P}_{\mathrm{o}}-\mathrm{P}}\right) \)
(B) \( \frac{2.303}{t} \log \left(\frac{2 \mathrm{P}_{\mathrm{o}}}{3 \mathrm{P}_{\mathrm{o}}-\mathrm{P}}\right) \)
(C) \( \frac{2.303}{\mathrm{t}} \log _{10}\left(\frac{\mathrm{P}}{2 \mathrm{P}_{\mathrm{o}}-\mathrm{P}}\right) \)
(D) \( \frac{2.303}{\mathrm{t}} \log _{10}\left(\frac{2 \mathrm{P}}{\mathrm{P}_{\mathrm{o}}-\mathrm{P}}\right) \)
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