The half-lives of two samples are 0.1 s and | vedclass

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(B) The relationship between half-life $(t_{1/2})$ and initial concentration $(a)$ for a reaction of order $n$ is given by: $t_{1/2} \propto a^{1-n}$

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$2$

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(B) The relationship between half-life $(t_{1/2})$ and initial concentration $(a)$ for a reaction of order $n$ is given by: $t_{1/2} \propto a^{1-n}$ Taking the ratio for two different concentrations: $\frac{(t_{1/2})_1}{(t_{1/2})_2} = \left(\frac{a_1}{a_2}\right)^{1-n}$ Substituting the given values: $\frac{0.1}{0.4} = \left(\frac{200}{50}\right)^{1-n}$ $\frac{1}{4} = (4)^{1-n}$ $(4)^{-1} = (4)^{1-n}$ Comparing the powers: $-1 = 1 - n \Rightarrow n = 2$. Thus,the reaction is of the second order.

The half-lives of two samples are $0.1 \ s$ and $0.4 \ s$. Their respective concentrations are $200$ and $50$. What is the order of the reaction?

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