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vii. A first order reaction takes 40 minutes for 30% decomposition. Calculate its half life. (77.66 min)

Answer:-

Given:

[A]_{0} = 100%, [A]_{t} = 100 - 30 = 70%, t = 40 min

To find:

Half-life of reaction (t_{1/2})

Formula:

k = 2.303/t * log_{10}[A]_{0}/[A]_{t}

Calculation:

Substituting these values into the formula:

k = 2.303/40 min * log_{10} 100/70

= 2.303/40 min * log_{10} 1.429

= 2.303/40 min * 0.155

= 0.008924 min^{-1}

t_{1/2} = 0.693/k = 0.693/(0.008924 min^{-1}) = 77.66 min

The half-life of the reaction is 77.66 min.