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

Given:

Time t = 40 min

When 30% decomposition is undergone, 70% is the concentration.

We know, time taken

Where, k- rate constant

[R]_{°} -Initial concentration

[R]-Concentration at time ‘t’

⇒

⇒

⇒

⇒ 258.23 = (2.303/k)

We know, Half-life t_{1/2} = 0.693/k

Which can be written as, t_{1/2} = 0.3010 × (2.303/k)

⇒ t_{1/2} = 0.3010 × 258.23

⇒ t_{1/2} = 77.72 min

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