The half-life of decomposition of gaseous CH_ | vedclass

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(A) For a reaction of order $n$,the half-life $(t_{1/2})$ is related to the initial pressure $(P_0)$ as: $(t_{1/2}) \propto (P_0)^{1-n}$.Therefore,$\f

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$2$

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(A) For a reaction of order $n$,the half-life $(t_{1/2})$ is related to the initial pressure $(P_0)$ as: $(t_{1/2}) \propto (P_0)^{1-n}$.Therefore,$\frac{(t_{1/2})_1}{(t_{1/2})_2} = \left(\frac{P_1}{P_2}\right)^{1-n} = \left(\frac{P_2}{P_1}\right)^{n-1}$.Given: $(t_{1/2})_1 = 440 \ sec$,$P_1 = 364 \ mm \ Hg$; $(t_{1/2})_2 = 880 \ sec$,$P_2 = 182 \ mm \ Hg$.Substituting the values: $\frac{440}{880} = \left(\frac{182}{364}\right)^{n-1}$.$\frac{1}{2} = \left(\frac{1}{2}\right)^{n-1}$.Comparing the exponents: $n-1 = 1$,which gives $n = 2$.

The half-life of decomposition of gaseous $CH_3CHO$ at initial pressure of $364 \ mm$ and $182 \ mm$ of $Hg$ were $440 \ sec$ and $880 \ sec$ respectively. The order of the reaction is

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