For a homogeneous gaseous reaction $A \to B + C + D$ , the initial pressure was $P_{0}$ while pressure after time ‘t’ was P if $(P > P_{0})$ . The expression for the rate constant k is

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$k = \frac{2.303}{t} \log (\frac{2 P_{0}}{3 P_{0} - P})$

$k = \frac{2.303}{t} \log (\frac{P_{0}}{P_{0} - P})$

$k = \frac{2.303}{t} \log (\frac{3 P_{0}}{2 P_{0} - P})$

$k = \frac{2.303}{t} \log (\frac{2 P_{0}}{4 P_{0} - P})$

answer is A.

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Detailed Solution

$A \to B + C + D$

$\begin{array}{l} P_{0} 0 0 0 \\ P_{0} - x x x x \end{array}$

$\begin{array}{l} P = P_{0} - x + x + x + x \\ = P_{0} + 2 x \\ 2 x = P - P_{0} \\ x = \frac{P - P_{0}}{2} \\ ∴ P_{0} - x = P_{0} - \frac{P + P_{0}^{2}}{2} \\ = \frac{3 P_{0} - P}{2} \\ ∴ k = \frac{2.303}{t} \log (\frac{2 P_{0}}{3 P_{0} - P}) \end{array}$