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A first order reaction takes 40 min for 30% decomposition. Calculate t 1/2.

4.19   A first order reaction takes 40 min for 30% decomposition. Calculate t_{1/2}

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M manish

For the first-order reaction,

t =\frac{2.303}{k}\log \frac{[R]_{0}}{[R]}
k =\frac{2.303}{40}\log \frac{100}{100-30}               (30% already decomposed and remaining is 70%)

    =8.918\times 10^{-3} min^{-1}

therefore half life = 0.693/k
                            = 0.693/8.918\times 10^{-3}
                            = 77.7 (approx) 

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